Use the Remainder Theorem and synthetic division to find the function value. $$g ( x ) = 3 x ^ { 6 } + 4 x ^ { 4 } - 6 x ^ { 2 } + 4 , \quad g ( 0 )$$
A)4.00
B)1.00
C)-1.00
D)6.00
E)5

Question

Use the Remainder Theorem and synthetic division to find the function value.​ $$g ( x ) = 3 x ^ { 6 } + 4 x ^ { 4 } - 6 x ^ { 2 } + 4 , \quad g ( 0 )$$ ​
A)4.00
B)1.00
C)-1.00
D)6.00
E)5

Quizplus · Accepted Answer

The Remainder Theorem states that if a polynomial $g(x)$ is divided by $x - c$, the remainder is $g(c)$. To find $g(0)$, we substitute $x = 0$ into the polynomial $g(x) = 3x^6 + 4x^4 - 6x^2 + 4$. This gives $g(0) = 3(0)^6 + 4(0)^4 - 6(0)^2 + 4 = 4$.

Use the Remainder Theorem and Synthetic Division to Find the Function