Question

What is the factorization of the polynomial below? -x^2-15x-56

Answer 1

Answer:

Option C. $(x+8)(x+7)$

Step-by-step explanation:

we have

$-x^2-15x-56$

Find the roots of the quadratic equation

equate the equation to zero

$-x^2-15x-56=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-x^2-15x-56=0$

so

$a=-1\\b=-15\\c=-56$

substitute in the formula

$x=\frac{-(-15)\pm\sqrt{-15^{2}-4(-1)(-56)}} {2(-1)}$

$x=\frac{15\pm\sqrt{1}} {-2}$

$x=\frac{15\pm1} {-2}$

$x=\frac{15+1} {-2}=-8$

$x=\frac{15-1} {-2}=-7$

The roots are

x=-8 and x=-7

so

The quadratic equation in factored form is equal to

$-x^2-15x-56=(x+8)(x+7)$