Question

Please help me folks.

Answer 1

3
`x^(5)` (x + 2)(3x + 5)

Explanation:

Given

9
`x^(7)` + 33
`x^(6)` + 30
`x^(5)` ← factor out 3
`x^(5)` from each term

= 3
`x^(5)` (3x² + 11x + 10) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × 10 = 30 and sum = + 11

The factors are 6 and 5

Use these factors to split the x- term

3x² + 6x + 5x + 10 ( factor the first/second and third/fourth terms )

= 3x(x + 2) + 5(x + 2) ← factor out (x + 2) from each term

= (x + 2)(3x + 5), thus

3x² + 11x + 10 = (x + 2)(3x + 5)

and

9
`x^(7)` + 33
`x^(6)` + 30
`x^(5)` = 3
`x^(5)` (x + 2)(3x + 5)