Question

match each expression to the factored form of the expression.$\boldsymbol{y^2 + 2y - 24}$a. $(y + 2)(y + 3)LXB0\boldsymbol{y^2 + 5y + 6}$c. prime$\boldsymbol{y^2 + 8y + 7}$d. $(y + 7)(y + 1)$

Explanation:

Step1: Factor $y^2+2y-24$

Find two numbers: product = $-24$, sum = $2$. The numbers are $6$ and $-4$.
$\boldsymbol{y^2+2y-24=(y-4)(y+6)}$

Step2: Check $y^2+y+5$

No two integers multiply to $5$ and add to $1$. It cannot be factored, so it is prime.
$\boldsymbol{y^2+y+5 = \text{prime}}$

Step3: Factor $y^2+5y+6$

Find two numbers: product = $6$, sum = $5$. The numbers are $2$ and $3$.
$\boldsymbol{y^2+5y+6=(y+2)(y+3)}$

Step4: Factor $y^2+8y+7$

Find two numbers: product = $7$, sum = $8$. The numbers are $7$ and $1$.
$\boldsymbol{y^2+8y+7=(y+7)(y+1)}$

Answer:

$y^2 + 2y - 24$ → b. $(y - 4)(y + 6)$
$y^2 + y + 5$ → c. prime
$y^2 + 5y + 6$ → a. $(y + 2)(y + 3)$
$y^2 + 8y + 7$ → d. $(y + 7)(y + 1)$