Question 1

Match the polynomial function with its graph.
-$$f ( x ) = ( x - 5 ) ( x - 2 )$$

Accepted Answer

The answer of Match the polynomial function with its graph.
-\[f...

Question 2

Solve.
-The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.

Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the triangle. Let $x$ be the length of the shorter leg; then the longer leg is $x + 14$. Substituting these into the theorem gives $x^2 + (x + 14)^2 = 26^2$. Solving this equation yields $x = 10$, so the legs are 10 inches and 24 inches long.

Question 3

Solve.
-Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Accepted Answer

The answer of Solve.
-Find the length of the shorter leg...

Question 4

Solve.
-The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 48 square centimeters. Find the side of the
Square.

Accepted Answer

Let the side of the square and the length of the rectangle be x cm. The width of the rectangle is x + 4 cm. The area of the square is x^2, and the area of the rectangle is x(x + 4). The sum of the areas is x^2 + x(x + 4) = 48. Simplifying gives 2x^2 + 4x = 48. Dividing by 2 gives x^2 + 2x = 24. Solving the quadratic equation x^2 + 2x - 24 = 0, we find x = 4 cm.

Question 5

Fill in the blank with one of the words or phrases listed below.

-is the process of writing a polynomial as a product.

Accepted Answer

Factoring is the process of writing a polynomial as a product of its factors.

Question 6

Fill in the blank with one of the words or phrases listed below.

-A is a finite sum of terms in which all variables are raised to nonnegative integer powers and no variables appear in any denominator.

Accepted Answer

A polynomial is defined as a mathematical expression consisting of a finite sum of terms, each term including a variable raised to a nonnegative integer power and possibly multiplied by a coefficient. The definition provided matches that of a polynomial, which can consist of one term (monomial), two terms (binomial), or more.

Question 7

Match the polynomial function with its graph.
-$$f ( x ) = 2 x ^ { 2 } - 9 x + 10$$

Accepted Answer

The answer of Match the polynomial function with its graph.
-\[f...

Question 8

Fill in the blank with one of the words or phrases listed below.

-The is the sum of the exponents on the variables contained in the term.

Accepted Answer

The degree of a term is defined as the sum of the exponents on the variables contained in that term.

Question 9

Solve.
-A triangle is $2 \mathrm {~cm}$ wider than it is tall. The area is $12 \mathrm {~cm} ^ { 2 }$. Find the width (length of the base).

Accepted Answer

The answer of Solve.
-A triangle is $2 \mathrm {~cm}$ wider...

Question 10

Solve.
-The force in newtons needed to stretch a certain spring $x$ centimeters from its resting position is given by the polynomial function $f ( x ) = 6 x ^ { 2 }$, where 6 is the spring constant. If a force of 150 newtons is applied, how far will the spring be stretched?

Accepted Answer

To find the distance the spring is stretched, set $f(x) = 150$ and solve for $x$: $150 = 6x^2$. Dividing both sides by 6 gives $x^2 = 25$, and taking the square root gives $x = 5$ cm.

Question 11

Solve.
-Kara is making a box by cutting out 2 -in.-by-2-in. squares from a square piece of cardboard and folding the edges to make a 2-inch-high box. What size of cardboard does Kara need to make a 2-inch-high box with a volume of 8 cubic inches?

Accepted Answer

The volume of the box is 8 cubic inches, so the area of the base is 4 square inches. Since the base is a square, each side of the base is 2 inches. The cardboard must be at least 6 inches by 6 inches to make a 2-inch-high box with a volume of 8 cubic inches.

Question 12

Solve.
-The outside dimensions of a picture frame are $38 \mathrm {~cm}$ and $31 \mathrm {~cm}$. The area of the picture inside the frame is 690 square centimeters. Find the width of the frame.

Accepted Answer

The answer of Solve.
-The outside dimensions of a picture frame...

Question 13

Solve.
-A flagpole is supported by a wire fastened 27 feet from its base. The wire is 9 feet longer than the height it reaches on the flagpole. Find the length of the wire.

Accepted Answer

Let the height the wire reaches on the flagpole be h feet. Then, the length of the wire is h + 9 feet. Using the Pythagorean theorem for the right triangle formed, we have: (h + 9)^2 = h^2 + 27^2. Solving this equation gives h = 36 feet, so the length of the wire is 36 + 9 = 45 feet.

Question 14

Match the polynomial function with its graph.
-$$f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 )$$

Accepted Answer

The answer of Match the polynomial function with its graph.
-\[f...

Question 15

Solve.
-An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. After $t$ seconds, the height $h ( t )$ of the object is given by the function $h ( t ) = - 16 t ^ { 2 } + 48 t + 160$. Find how long it takes the object to hit the ground.

Accepted Answer

To find when the object hits the ground, set $h(t) = 0$ and solve for $t$: $-16t^2 + 48t + 160 = 0$. Factoring or using the quadratic formula gives $t = 5$ seconds as the time it takes for the object to hit the ground.

Question 16

Solve.
-A window washer accidentally drops a bucket from the top of a 64-foot building. After t seconds, the height h(t) is given by the function h(t) = -16t2 + 64. Find how long it takes the bucket to hit the ground.

Accepted Answer

The bucket hits the ground when h(t) = 0. Solving -16t^2 + 64 = 0 gives t^2 = 4, so t = 2 seconds.

Question 17

Solve.
-One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. Let $x$ be the length of the smaller leg. Then, the other leg is $x + 35$ inches, and the hypotenuse is $x + 40$ inches. Setting up the equation: $x^2 + (x + 35)^2 = (x + 40)^2$. Solving this equation gives $x = 25$ inches. Therefore, the sides are 25 inches, 60 inches (25 + 35), and 65 inches (25 + 40), which matches option A.

Question 18

Fill in the blank with one of the words or phrases listed below.

-A is a polynomial with one term.

Accepted Answer

A monomial is a polynomial with just one term.

Question 19

Match the polynomial function with its graph.
-$$f ( x ) = x ( x - 1 ) ( x + 1 )$$

Accepted Answer

The answer of Match the polynomial function with its graph.
-\[f...

Question 20

Solve.
-A certain rectangle's length is $3 \mathrm { ft }$ longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.

Accepted Answer

The dimensions of the rectangle can be found by setting up the equation $w(w + 3) = 180$, where $w$ is the width and $w + 3$ is the length. Solving this quadratic equation gives $w = 12$, so the length is $12 + 3 = 15$. Therefore, the dimensions are $12 \mathrm { ft }$ by $15 \mathrm { ft }$.

Quiz 5: Polynomials and Polynomial Functions

Match the polynomial function with its graph. - $f ( x ) = ( x - 5 ) ( x - 2 )$

Solve. -The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.

Solve. -Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Solve. -The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 48 square centimeters. Find the side of the Square.

Fill in the blank with one of the words or phrases listed below. -is the process of writing a polynomial as a product.

Fill in the blank with one of the words or phrases listed below. -A is a finite sum of terms in which all variables are raised to nonnegative integer powers and no variables appear in any denominator.

Match the polynomial function with its graph. - $f ( x ) = 2 x ^ { 2 } - 9 x + 10$

Fill in the blank with one of the words or phrases listed below. -The is the sum of the exponents on the variables contained in the term.

Solve. -The force in newtons needed to stretch a certain spring $x$ centimeters from its resting position is given by the polynomial function $f ( x ) = 6 x ^ { 2 }$ , where 6 is the spring constant. If a force of 150 newtons is applied, how far will the spring be stretched?

Solve. -Kara is making a box by cutting out 2 -in.-by-2-in. squares from a square piece of cardboard and folding the edges to make a 2-inch-high box. What size of cardboard does Kara need to make a 2-inch-high box with a volume of 8 cubic inches?

Solve. -A flagpole is supported by a wire fastened 27 feet from its base. The wire is 9 feet longer than the height it reaches on the flagpole. Find the length of the wire.

Match the polynomial function with its graph. - $f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 )$

Solve. -An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. After $t$ seconds, the height $h ( t )$ of the object is given by the function $h ( t ) = - 16 t ^ { 2 } + 48 t + 160$ . Find how long it takes the object to hit the ground.

Solve. -A window washer accidentally drops a bucket from the top of a 64-foot building. After t seconds, the height h(t) is given by the function h(t) = -16t2 + 64. Find how long it takes the bucket to hit the ground.

Solve. -One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with one term.

Match the polynomial function with its graph. - $f ( x ) = x ( x - 1 ) ( x + 1 )$

Solve. -A certain rectangle's length is $3 \mathrm { ft }$ longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.

Quiz 5: Polynomials and Polynomial Functions

Match the polynomial function with its graph. - f(x) =(x−5) (x−2) f ( x ) = ( x - 5 ) ( x - 2 ) f(x) =(x−5) (x−2)

Solve. -The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.

Solve. -Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Solve. -The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 48 square centimeters. Find the side of the Square.

Fill in the blank with one of the words or phrases listed below. -is the process of writing a polynomial as a product.

Fill in the blank with one of the words or phrases listed below. -A is a finite sum of terms in which all variables are raised to nonnegative integer powers and no variables appear in any denominator.

Match the polynomial function with its graph. - f(x) =2x2−9x+10f ( x ) = 2 x ^ { 2 } - 9 x + 10f(x) =2x2−9x+10

Fill in the blank with one of the words or phrases listed below. -The is the sum of the exponents on the variables contained in the term.

Solve. -A triangle is 2 cm2 \mathrm {~cm}2 cm wider than it is tall. The area is 12 cm212 \mathrm {~cm} ^ { 2 }12 cm2 . Find the width (length of the base) .

Solve. -The force in newtons needed to stretch a certain spring xxx centimeters from its resting position is given by the polynomial function f(x) =6x2f ( x ) = 6 x ^ { 2 }f(x) =6x2 , where 6 is the spring constant. If a force of 150 newtons is applied, how far will the spring be stretched?

Solve. -Kara is making a box by cutting out 2 -in.-by-2-in. squares from a square piece of cardboard and folding the edges to make a 2-inch-high box. What size of cardboard does Kara need to make a 2-inch-high box with a volume of 8 cubic inches?

Solve. -The outside dimensions of a picture frame are 38 cm38 \mathrm {~cm}38 cm and 31 cm31 \mathrm {~cm}31 cm . The area of the picture inside the frame is 690 square centimeters. Find the width of the frame.

Solve. -A flagpole is supported by a wire fastened 27 feet from its base. The wire is 9 feet longer than the height it reaches on the flagpole. Find the length of the wire.

Match the polynomial function with its graph. - f(x) =(x−4) (x−3) (x−1) f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 ) f(x) =(x−4) (x−3) (x−1)

Solve. -A window washer accidentally drops a bucket from the top of a 64-foot building. After t seconds, the height h(t) is given by the function h(t) = -16t2 + 64. Find how long it takes the bucket to hit the ground.

Solve. -One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Fill in the blank with one of the words or phrases listed below. -A is a polynomial with one term.

Match the polynomial function with its graph. - f(x) =x(x−1) (x+1) f ( x ) = x ( x - 1 ) ( x + 1 ) f(x) =x(x−1) (x+1)

Solve. -A certain rectangle's length is 3ft3 \mathrm { ft }3ft longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.

Match the polynomial function with its graph. - $f ( x ) = ( x - 5 ) ( x - 2 )$

Match the polynomial function with its graph. - $f ( x ) = 2 x ^ { 2 } - 9 x + 10$

Solve. -The force in newtons needed to stretch a certain spring $x$ centimeters from its resting position is given by the polynomial function $f ( x ) = 6 x ^ { 2 }$ , where 6 is the spring constant. If a force of 150 newtons is applied, how far will the spring be stretched?

Match the polynomial function with its graph. - $f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 )$

Match the polynomial function with its graph. - $f ( x ) = x ( x - 1 ) ( x + 1 )$

Solve. -A certain rectangle's length is $3 \mathrm { ft }$ longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.