Factoring Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Factor 6x2+11x+36x^2 + 11x + 3.

Solution

  1. 1
    Multiply aโ‹…c=6โ‹…3=18a \cdot c = 6 \cdot 3 = 18. Find two numbers that multiply to 18 and add to 11: 99 and 22.
  2. 2
    Rewrite the middle term: 6x2+9x+2x+36x^2 + 9x + 2x + 3.
  3. 3
    Group: (6x2+9x)+(2x+3)=3x(2x+3)+1(2x+3)(6x^2 + 9x) + (2x + 3) = 3x(2x + 3) + 1(2x + 3).
  4. 4
    Factor out (2x+3)(2x + 3): (3x+1)(2x+3)(3x + 1)(2x + 3).

Answer

(3x+1)(2x+3)(3x + 1)(2x + 3)
When aโ‰ 1a \neq 1, use the AC method: multiply aa and cc, find factors that add to bb, split the middle term, and factor by grouping.

About Factoring

Rewriting an algebraic expression as a product of two or more simpler expressions that multiply to give the original.

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More Factoring Examples

Example 1 easy

Factor [formula].

Example 3 easy

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Example 4 medium

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