Chapter SH, Problem 9.17EP

To determine

To solve equation by factoring.

Answer to Problem 9.17EP

  $x=-4,5$

Explanation of Solution

Given information :

The function provided is $(2x+8)(4x-20)$

Formula used :

For some of the equations the solution can be found by factoring. If the factored form of a quadratic equation has real numbers, it will have roots.

  $(x-h)(x-k)=0$

In the factored form it is assumed that at least one of the factors is equal to 0. Therefore, if product if two factors is 0 then at least one of the factors must be zero, this is known as the Zero Product Property

Either,

  $(x-h)=0$

Or,

  $(x-k)=0$

Calculation :

  $(2x+8)(4x-20)$

The above expression is in factored form.

Either,

  $(2x+8)=0$

Or,

  $(4x-20)=0$

Simplifying.

  $x=-4$

The other factor.

  $x=5$

The above expression can be solved to get $x=-4,5$

We get two roots $x=-4,5$ as $(2x+8)(4x-20)$ is not a perfect square.