Q21. - Algebra 1

Question

Factor each polynomial.

$x^2-10x+24$

Step-by-Step Solution

Answer

The factors of the given polynomial are $\left(x-4\right)\left(x-6\right)$.

Step 1. Compare.

Compare a given trinomial to $a{x}^2+bx+c$ and write the values of $a,b$ and $c$.

 $$\begin{gathered} a=1 \\ b=-10 \\ c=24 \end{gathered}$$

Step 2. List the factors.

List the factors of 24. Look for the pair of factors with a sum of $-10$.

Factors of 24	Sum of factors
1,24	25
2,12	14
$-3,-8$	$-11$
$-4,-6$	$-10$

 

Therefore, correct factors are $-4$ and $-6$.

Step 3. Apply factoring pattern of a x 2 + b x + c .

There are two numbers having a product of 24 and some of $-10$. The numbers are $-4$ and $-6$.

$$\begin{gathered} x^2-10x+24=\left(x+m\right)\left(x+p\right) \\ =\left(x-4\right)\left(x-6\right) \end{gathered}$$

Therefore, the factors of $x^2-10x+24$ are $\left(x-4\right)\left(x-6\right)$.