In the exit slip, Brady factored the expressions wrong. He needed to factor x^2−10x+25 and 16c^2−9This is his work.

Question

In the exit slip, Brady factored the expressions wrong. He needed to factor x^2−10x+25 and 16c^2−9This is his work.

Identify Brady's error(s). Write the correct solution.

(3 points)

Answer:
The correct factorization of x^2−10x+25 is (x−5)^2 and the correct factorization of 16x2−9 is (4c+3)(4c-3).

Brady made mistakes in factoring the expressions. Here's the correct explanation and work:
Step 1: Factoring
x^2−10x+25:
Brady's mistake: He factored it as x^2−10x+5^2, which is incorrect.
Correct factorization:
x^2−10x+25=(x−5)(x−5)
or
(x−5)^2.
Step 2: Factoring
16c^2−9:
Brady's mistake: He factored it as(4c)^2−(3)^2,which is incorrect.
Correct factorization:
16c^2−9=(4c+3)(4c−3)

Answer 1

Therefore, Brady's errors were not recognizing that x^2−10x+25 can be factored as a perfect square trinomial and not recognizing that 16c^2−9 is a difference of squares where 16c^2 can be written as (4c)^2 and 9 can be written as (3)^2. The correct factorizations are (x−5)^2 for x^2−10x+25 and (4c+3)(4c−3) for 16c^2−9.