High School

Which of the following polynomial expressions factors to [tex]x^4(4x - 7)(4x + 7)[/tex]?

A. [tex]- 4x^6− 7x^4[/tex]
B. [tex]- 16x^4-49x^2[/tex]
C. [tex]- 16x^6-49x^4[/tex]
D. [tex]- 16x^6+49x^4[/tex]

Answer :

Answer:

16[tex]x^{6}[/tex] - 49[tex]x^{4}[/tex]

Step-by-step explanation:

given the polynomial expression

[tex]x^{4}[/tex] (4x - 7)(4x + 7)

(4x - 7)(4x + 7) are the factors of a difference of squares , that is

(x - a)(x + a) = x² - a² , then

(4x - 7)(4x + 7) = (4x)² - 7² = 16x² - 49

The polynomial expression can now be expressed as

[tex]x^{4}[/tex] (16x² - 49) ← distribute parenthesis by [tex]x^{4}[/tex]

= 16[tex]x^{6}[/tex] - 49[tex]x^{4}[/tex]

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