Question

Which shows one way to determine the factors of x3 – 9x2 5x – 45 by grouping?

a.x2(x – 9) – 5(x – 9)
b.x2(x 9) – 5(x 9)
c.x(x2 5) – 9(x2 5)
d.x(x2 – 5) – 9(x2 – 5)

Answer 1

x(x2 5) – 9(x2 5)
Hope this helps! (:

Answer 2

Option (c) is correct

`x(x^2+5)-9(x^2+5)` is correct way of grouping the terms of given polynomial
`x^3-9x^2+5x -45`

Explanation:

Given polynomial
`x^3-9x^2+5x -45`

We have to write in grouping form and choose the correct from given options.

Grouping of polynomial is expression a polynomial by making pairs such that we can take out some common factor from the paired terms.

Consider the given polynomial
`x^3-9x^2+5x -45`

rewrite the polynomial as
`x^3+5x-9x^2-45`

taking
`x` common from first two terms and -9 common from last two terms, we have,

`\Rightarrow x^3+5x-9x^2 -45`

`\Rightarrow x(x^2+5)-9(x^2+5)`

Thus,
`x(x^2+5)-9(x^2+5)` is correct way of grouping the terms of given polynomial
`x^3-9x^2+5x -45`

Option (c) is correct.