Question

factor:

1. $-7x^2 + 7x + 14$

Explanation:

Step1: Factor out -7

First, we can factor out the greatest common factor (GCF) from the polynomial \(-7x^{2}+7x + 14\). The GCF of \(-7x^{2}\), \(7x\), and \(14\) is \(-7\). So we have:
\(-7x^{2}+7x + 14=-7(x^{2}-x - 2)\)

Step2: Factor the quadratic

Now we need to factor the quadratic \(x^{2}-x - 2\). We need two numbers that multiply to \(-2\) and add up to \(-1\). The numbers are \(-2\) and \(1\) because \((-2)\times1=-2\) and \(-2 + 1=-1\). So we can factor \(x^{2}-x - 2\) as \((x - 2)(x+1)\).
Putting it all together, the factored form of the original polynomial is \(-7(x - 2)(x + 1)\)

Answer:

\(-7(x - 2)(x + 1)\)