College

What is the product?

[tex]\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)[/tex]

A. [tex]14x^5 - x^4 - 46x^3 - 58x^2 - 20x - 45[/tex]

B. [tex]14x^6 - 56x^5 - 91x^4 - 140x^3 - 315x^2[/tex]

C. [tex]14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2[/tex]

D. [tex]14x^{12} - 182x^6 + 35x^4 - 455x^2[/tex]

Answer :

Answer:

C

Step-by-step explanation:

Given the product of factors

(7x² )(2x³ + 5 )(x² - 4x - 9 )

distribute the middle factor by 7x²

= (14[tex]x^{5}[/tex] + 35x² )(x² - 4x - 9 )

Each term in the second factor is multiplied by each term in the first factor, that is

14[tex]x^{5}[/tex] (x² - 4x - 9 ) + 35x² (x² - 4x - 9 ) ← distribute parenthesis

= 14[tex]x^{7}[/tex] - 56[tex]x^{6}[/tex] - 126[tex]x^{5}[/tex] + 35[tex]x^{4}[/tex] - 140x³ - 315x²

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