Chapter 6.2, Problem 12MRE

To determine

To calculate: The factors of the trinomial $y^2-5y-24$.

Answer to Problem 12MRE

The trinomial $y^2-5y-24$ is factored as $\left(y-8\right)\left(y+3\right)$.

Explanation of Solution

Given information:

The trinomial $y^2-5y-24$.

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the trinomial $y^2-5y-24$.

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial $-8$ and $3$ are two numbers such that their sum is $-5$ and product is $-24$.

Therefore, the trinomial is rewritten as,

  $y^2-5y-24=y^2-8y+3y-24$

Take out the common terms,

  $\begin{array}{c}{y}^2-5y-24=y^2-8y+3y-24\\ =y\left(y-8\right)+3\left(y-8\right)\\ =\left(y-8\right)\left(y+3\right)\end{array}$

Thus, thetrinomial $y^2-5y-24$ is factored as $\left(y-8\right)\left(y+3\right)$.