Factor: $7 x ^ { 4 } - 77 x ^ { 3 } + 196 x ^ { 2 }$
A) $7 x ^ { 2 } ( x + 7 ) ( x + 4 )$
B) $7 x ( x - 7 ) ( x - 4 )$
C) $7 x ^ { 2 } ( x - 7 ) ( x - 4 )$
D) $7 \left( x ^ { 2 } + 7 \right) \left( x ^ { 2 } - 4 \right)$
E) Nonfactorable over the integers

Question

Quizplus · Accepted Answer

The first step is to look for a common factor among the three terms. In this case, we can factor out 7x^2:
$$7x^4-77x^3+196x^2=7x^2(x^2-11x+28)$$
Now we need to factor the quadratic expression inside the parentheses. We can do this by looking for two numbers that multiply to 28 and add up to -11. These numbers are -4 and -7, so we have:
$$7x^2(x-4)(x-7)$$
Therefore, the answer is choice C.

Factor 7x4−77x3+196x27 x ^ { 4 } - 77 x ^ { 3 } + 196 x ^ { 2 }7x4−77x3+196x2

Factor $7 x ^ { 4 } - 77 x ^ { 3 } + 196 x ^ { 2 }$