Question

factor the trinomial, or state that the trinomial is prime. check the factorization using foil multiplication.
$y^2 - 10y + 21$
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. $y^2 - 10y + 21 = \square$
b. the polynomial is prime.

Explanation:

Step1: Find pair of factors of 21

We need two numbers that multiply to $21$ and add to $-10$. These numbers are $-7$ and $-3$, since $(-7)\times(-3)=21$ and $(-7)+(-3)=-10$.

Step2: Factor the trinomial

Write the trinomial as a product of two binomials using the found factors:
$y^2 - 10y + 21=(y-7)(y-3)$

Step3: Verify with FOIL method

First terms: $y\times y = y^2$
Outer terms: $y\times(-3) = -3y$
Inner terms: $(-7)\times y = -7y$
Last terms: $(-7)\times(-3) = 21$
Combine like terms: $y^2 -3y -7y +21 = y^2 -10y +21$, which matches the original trinomial.

Answer:

A. $y^2 - 10y + 21 = (y-7)(y-3)$