Answer:
3[tex]x^{5}[/tex] (x + 2)(3x + 5)
Step-by-step explanation:
Given
9[tex]x^{7}[/tex] + 33[tex]x^{6}[/tex] + 30[tex]x^{5}[/tex] ← factor out 3[tex]x^{5}[/tex] from each term
= 3[tex]x^{5}[/tex] (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[tex]x^{7}[/tex] + 33[tex]x^{6}[/tex] + 30[tex]x^{5}[/tex] = 3[tex]x^{5}[/tex] (x + 2)(3x + 5)
