Question

factor the trinomial completely.

\\22x^2 - 25xy + 7y^2\\

select the correct choice below and fill in any answer box within your choice.

a. \\22x^2 - 25xy + 7y^2 = \\

b. \\22x^2 - 25xy + 7y^2\\ is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

Find two numbers that multiply to \( a \cdot c \) and add to \( b \):

$$ a = 22, \quad b = -25, \quad c = 7 $$

$$ a \cdot c = 22 \cdot 7 = 154 $$

$$ b = -25 $$

Step 2: Find factors of 154 that add to -25

$$ -11 \cdot -14 = 154 $$

$$ -11 + (-14) = -25 $$

Step 3: Rewrite and factor by grouping

$$ 22x^2 - 11xy - 14xy + 7y^2 $$

$$ 11x(2x - y) - 7y(2x - y) $$

$$ (2x - y)(11x - 7y) $$

Answer:

A. \( 22x^2 - 25xy + 7y^2 = (2x - y)(11x - 7y) \)