help please

Question

factor these polynomials completely:

 

A) 8x^3+27

 

B) 16x^4-2x

Answer 1

³³The first one is a cubic polynomial of the form A³+B³, which factors into (A+B)(A²-AB+B²)

 In this case, A = 2x and B = 3 (because (2x)³=8x³  and 3³=27

 

So  8x³+27 = (2x+3)((2x)²-(2x)(3)+3²) = (2x+3)(4x²-6x+9)

 

 

For the second one, don't forget that the first step of every factoring problem is to factor out the GCF, if there is one. In this case, each term is a multiple of 2x, so we factor that out, getting

 

    16x⁴-2x = 2x(8x³-1)   We recognize 8x³ as being  (2x)³, and 1 as being 1³, so we see this as being of the form  A³-B³, which can also be factored.

 

 

   16x⁴-2x = 2x(8x³-1) = 2x(2x-1)(4x²+2x+1)

 

As with all factoring problems, you should multiply your results to see if you get the original expressions.