Question

Will factored 7x^67x 6 7, x, start superscript, 6, end superscript as (3x^2)(4x^4)(3x 2 )(4x 4 )left parenthesis, 3, x, squared, right parenthesis, left parenthesis, 4, x, start superscript, 4, end superscript, right parenthesis. Olivia factored 7x^67x 6 7, x, start superscript, 6, end superscript as (7x^2)(x^3)(7x 2 )(x 3 )left parenthesis, 7, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis. Which of them factored 7x^67x 6 7, x, start superscript, 6, end superscript correctly?

Answer 1

None of them factored 7x^6 correctly.

Question:

Will factored 7x^6 as (3x^2)(4x^4), Olivia factored 7x^6 as (7x^2)(x^3). Which of them factored 7x^6 correctly?

Explanation:

Given;

Will factored 7x^6 as (3x^2)(4x^4)

To verify;

(3x^2)(4x^4) = 3 × 4 × x^2 × x^4 = 12 × x^(2+4) = 12x^6

(3x^2)(4x^4) = 12x^6

Wrong

Olivia factored 7x^6 as (7x^2)(x^3)

To verify;

(7x^2)(x^3) = 7 × x^2 × x^3 = 7 × x^(2+3) = 7x^5

(7x^2)(x^3) = 7x^5

Wrong

Both Will and Olivia are wrong. So,

None of them factored 7x^6 correctly.

Answer 2

None of them factored
`7x^6` correctly.

Explanation:

• Will factored
  `7x^6` as
  `(3x^2)(4x^4)`
• Olivia Factored
  `7x^6` as
  `(7x^2)(x^3)`

We are to determine which of them factored correctly. We will do this by backward expansion of the factored terms.

For Will

• 
  `(3x^2)(4x^4)`
  `=12x^8`

For Olivia

• 
  `(7x^2)(x^3)=7x^5`

We conclude therefore that none factored it correctly.