Polynomial factoring by grouping

[KeenDave]

Hello. I am currently stuck on factoring polynomials by grouping for the following problem:
16x^3 + 24x^2 + 9x

Apparently the answer is x(4x+3)^2, but how?

I took a common factor from the product of A & B whose sum equaled 24, the second term, and got this:

16x^3 + 12x + 12x + 9x , from here I grouped them as such:
(16x^3 + 12x) (12x + 9x)

At this point it becomes a disaster.

I factored to 4x(4x^2 + 3) 3(4x + 3x), umm ???

Any help would be much appreciated, thank you!

 

[BigBeachBanana]

I would start by factoring out the x first.
$$16x^3 + 24x^2 + 9x=x(16x^2+24x+9)$$Can you factor the quadratic?

 

[Otis]

I grouped them as such:
(16x^3 + 12x²) + (12x² + 9x)

Hi KeenDave. Note the missing plus sign and exponents, above.

There is a better approach, however. The first step in factoring polynomials is to check for factors common to all terms.

For a different example:

18x^3 + 24x^2 + 9x

Can you see that 3x may be factored out of each term, first?

What can be factored out of each term, in your polynomial?



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[Otis]

Here's a video showing how to factor a quadratic polynomial when the leading coefficient is not 1, using the Grouping Method.

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[KeenDave]

Here's a video showing how to factor a quadratic polynomial when the leading coefficient is not 1, using the Grouping Method.

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Wonderful video and thank you for sharing!!

 

[KeenDave]

I would start by factoring out the x first.
$$16x^3 + 24x^2 + 9x=x(16x^2+24x+9)$$Can you factor the quadratic?

Thank you for this clue! I was trying a different method and it was not working out haha!