Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$7 x ^ { 2 } - 29 x + 24$
A)(7x - 8)(7x + 3)
B)(7x - 8)(x - 3)
C)7(x - 8)(x - 3)
D)(7x + 3)(x - 8)

Question

Quizplus · Accepted Answer

The correct factorization of $7x^2 - 29x + 24$ is found by looking for two numbers that multiply to $7 \times 24 = 168$ and add to $-29$. These numbers are $-24$ and $-5$, which can be used to split the middle term: $7x^2 - 24x - 5x + 24$. Factoring by grouping, we get $x(7x - 24) - 3(7x - 24)$, which simplifies to $(x - 3)(7x - 8)$, matching option B.

Factor the Polynomial Completely 7x2−29x+247 x ^ { 2 } - 29 x + 247x2−29x+24

Factor the Polynomial Completely $7 x ^ { 2 } - 29 x + 24$