Question

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

Answer 1

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

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√(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)`