Question

1. What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.(a) Show your work.(b) is the product of 3x-4 and 5x² - 2x + 6 equal to the product of 4 - 3x and 5x² - 2x + 6? Explain

Answer 1

SOLUTIONS

(a) What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.

`(3x-4)(5x^2-2x+6)`
`\begin{gathered} 3x(5x^2-2x+6)-4(5x^2-2x+6) \\ 15x^3-6x^2+18x-20x^2+8x-24 \\ collect\text{ like terms} \end{gathered}`
`15x^3-26x^2+26x-24`

The product is

`15x^3-26x^2+26x-24`
`(4-3x)(5x^2-2x+6)`

The product will be

`\begin{gathered} 4(5x^2-2x+6)-3x(5x^2-2x+6) \\ 20x^2-8x+24-15x^3+6x^2-18x \\ -15x^3+26x^2-26x+24 \end{gathered}`

The product of 4 - 3x and 5x² - 2x + 6 will be equal to the -1 multiply be the product of 3x - 4 and 5x² - 2x + 6, thus the two product are same

Checking

`\begin{gathered} -1(-15x^3+26x^2-26x+24) \\ 15x^3-26x^2+26x-24 \end{gathered}`

Hence the two answer are the same.