Factoring Trinomials Math Example 2

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

Example 2

hard
Factor 2x2+7x+32x^2 + 7x + 3 using the AC method.

Solution

  1. 1
    Step 1: Find AC=2ร—3=6AC = 2 \times 3 = 6. Find two numbers that multiply to 6 and add to 7.
  2. 2
    Step 2: 1ร—6=61 \times 6 = 6 and 1+6=71 + 6 = 7. Split the middle term: 2x2+x+6x+32x^2 + x + 6x + 3.
  3. 3
    Step 3: Group: (2x2+x)+(6x+3)=x(2x+1)+3(2x+1)(2x^2 + x) + (6x + 3) = x(2x + 1) + 3(2x + 1).
  4. 4
    Step 4: Factor: (x+3)(2x+1)(x + 3)(2x + 1).
  5. 5
    Check: (x+3)(2x+1)=2x2+x+6x+3=2x2+7x+3(x+3)(2x+1) = 2x^2 + x + 6x + 3 = 2x^2 + 7x + 3 โœ“

Answer

(x+3)(2x+1)(x + 3)(2x + 1)
The AC method handles trinomials with leading coefficient aโ‰ 1a \neq 1. Multiply aโ‹…ca \cdot c, find the factor pair that sums to bb, split the middle term, then factor by grouping.

About Factoring Trinomials

Factoring a trinomial of the form ax2+bx+cax^2 + bx + c into a product of two binomials by finding two numbers that multiply to acac and add to bb.

Learn more about Factoring Trinomials โ†’

More Factoring Trinomials Examples

Example 1 easy

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Example 3 easy

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Example 4 medium

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โ† All Factoring Trinomials Examples Factoring Trinomials Concept