Question

Please help me folks.

Answer 1

Answer:

3$x^{5}$ (x + 2)(3x + 5)

Step-by-step 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)