question\nfactor completely.\n4x² + 7x - 2

Explanation:

Step1: Multiply leading and constant terms

Multiply $4$ and $- 2$, we get $4\times(-2)=-8$.

Step2: Find two numbers

Find two numbers that multiply to $-8$ and add up to $7$. The numbers are $8$ and $-1$ since $8\times(-1)=-8$ and $8+( - 1)=7$.

Step3: Rewrite the middle - term

Rewrite $7x$ as $8x - x$. So, $4x^{2}+7x - 2=4x^{2}+8x - x - 2$.

Step4: Group the terms

Group the terms: $(4x^{2}+8x)+(-x - 2)$.

Step5: Factor out the GCF from each group

Factor out the GCF from each group. From $4x^{2}+8x$, the GCF is $4x$, so $4x^{2}+8x = 4x(x + 2)$. From $-x - 2$, the GCF is $-1$, so $-x - 2=-1(x + 2)$.

Step6: Factor out the common binomial factor

We have $4x(x + 2)-1(x + 2)=(4x - 1)(x + 2)$.

Answer:

$(4x - 1)(x + 2)$