factor the following expression.\n7x² + 6x - 16\n(x + ?)( x - )

Explanation:

Step1: Multiply leading - coefficient and constant

For the quadratic expression (ax^{2}+bx + c=7x^{2}+6x - 16), where (a = 7), (b = 6), (c=-16). Calculate (a\times c=7\times(-16)=-112).

Step2: Find two numbers that multiply to (ac) and add to (b)

We need two numbers (m) and (n) such that (m\times n=-112) and (m + n=6). The numbers are (14) and (-8) since (14\times(-8)=-112) and (14+( - 8)=6).

Step3: Rewrite the middle term

Rewrite (6x) as (14x-8x). So, (7x^{2}+6x - 16=7x^{2}+14x-8x - 16).

Step4: Group the terms

((7x^{2}+14x)-(8x + 16)).

Step5: Factor out the greatest - common factor from each group

From the first group (7x^{2}+14x), the GCF is (7x), so (7x^{2}+14x = 7x(x + 2)). From the second group (8x + 16), the GCF is (8), so (8x + 16=8(x + 2)). Then (7x(x + 2)-8(x + 2)=(x + 2)(7x-8)).

Answer:

((x + 2)(7x-8))