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What are the factors of 8q³ +27
A.(2q - 3) (4q² - 6q + 9)
B.(2q + 3) (4q²-6q+9)
C. (2q-3) (4q² + 6q+9)
D.(2q+3) (4q²+ 6q + 9) ​

Sagot :

RhoZetaidn

✏️ Sum or Difference of Two Cubes

[tex] {\Large{\overline{\underline{\sf{\hookrightarrow Answer:}}}}} [/tex]

  • The correct answer is letter B. The factors of 8q³ + 27 are (2q + 3) and (4q² - 6q + 9).

Solution:

The pattern of factoring the sum or difference of two cubes is:

  • [tex] \sf{ a^3 + b^3 = (a + b)(a^2 - ab + b^2) } [/tex], and
  • [tex] \sf{ a^3 - b^3 = (a - b)(a^2 + ab + b^2) } [/tex]

First find the cube root of the two terms.

  • [tex] \sf{ \sqrt [3] {8q^3} = 2q } [/tex]
  • [tex] \sf{ \sqrt [3] {27} = 3 } [/tex]

The sign of [tex] \sf{ b } [/tex] in the linear factor is the same as the sign in the middle of the expression being factored. Thus [tex] \sf{ \sf b } [/tex] is positive, and the linear factor is [tex] \sf{ \sf 2q + 3 } [/tex].

Now follow the pattern for the quadratic factor.

  • [tex] \sf{ a^2 - ab + b^2 } [/tex]
  • [tex] \sf{ \rightarrow (2q)^2 - (2q)(3) + (3)^2 } [/tex]
  • [tex] \sf{ \rightarrow 4q^2 - 6q + 9 } [/tex]

Note that the sign of [tex] \sf{ \sf ab } [/tex] in the quadratic factor is the opposite of the sign of [tex] \sf{ \sf b } [/tex] in the linear factor, and the sign of [tex] \sf{ \sf b^2 } [/tex] is always positive.

Thus, the factored form of [tex] \sf{ 8q^3 + 27 } [/tex] is [tex] {\underline{\green{\sf{(2q + 3)(4q^2 - 6q + 9)}}}} [/tex]. The correct answer is letter B.

[tex]{\: \:}[/tex]

[tex] {\huge{\overline{\sf{Hope\:It\:Helps}}}} [/tex]

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