Question

Select the correct steps for factoring the polynomial 27x +8

Answer 1

27x + 8 = (3
`\sqrt[3]{x}` + 2)(
`9\sqrt[3]{x^(2) } - 6\sqrt[3]{x} + 4`) is the final factorized form of the given polynomial.

Explanation:

i) 27x + 8 =
`3^(3)(\sqrt[3]{x} } )^3 + 2^(3)`

ii) From the formula
`a^(3) + b^(3) = (a + b)(a^(2) - ab + b^(2) )` we can write for the given polynomial

iii) therefore 27x + 8 = (
`3\sqrt[3]{x}` + 2)(
`9\sqrt[3]{x^(2) } - 6\sqrt[3]{x} + 4`) is the final factorized form of the given polynomial.