Question

Ms. J has been practicing her factoring skills. She factored the following problem by grouping,

but made a mistake.
Example 1: 4x2 + 20x - 3xy - 15y
Ms. J's work:
Step 1: 4x2 + 20x - 3xy - 15y
Step 2: 4x(x + 5) - 3y(x - 5)
Step 3: (x+5)(4x - 3y)
a. What was the mistake?
b. How can she fix the mistake?

Answer 1

a) She did mistake in Step 2

b) when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)

Explanation:

We need to find problem in Ms J solution.

Ms J solution:

`Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5) - 3y(x - 5)\\Step \ 3: (x+5)(4x - 3y)`

She did mistake in Step 2 when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)

Correcting the mistake:

`Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5)\mathbf{- 3y(x +5)}\\Step \ 3: (x+5)(4x - 3y)`