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Factoring trinomials with a leading coefficient worksheets Grades 8–9

Factor ax² + bx + c by splitting the middle term and grouping.

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How to do it

For ax² + bx + c, find two numbers that multiply to a × c and add to b. Split the middle term and group.

3x2+8x+5=(3x+5)(x+1)3x^{2} + 8x + 5 = (3x + 5)(x + 1)
a ×c=3×5=15;multiply to 15, add to 8:3 and 5\text{a }\times c = 3 \times 5 = 15;\quad \text{multiply to }15,\ \text{add to }8:\quad 3\ \text{and }5
3x2+8x+5=3x2+3x+5x+5=3x(x+1)+5(x+1)=(3x+5)(x+1)3x^{2} + 8x + 5 = 3x^{2} + 3x + 5x + 5 = 3x(x + 1) + 5(x + 1) = (3x + 5)(x + 1)split the middle, then group

Example problems

  1. 2x2+5x+3=2x^{2} + 5x + 3 =
  2. 3x2+7x−6=3x^{2} + 7x - 6 =
  3. 2x2+5x−3=2x^{2} + 5x - 3 =
  4. 6x2−5x−21=6x^{2} - 5x - 21 =

Polynomials and factoring

  1. Exponent rules
  2. Adding and subtracting polynomials
  3. Multiplying a monomial by a polynomial
  4. Multiplying binomials (FOIL)
  5. Special products
  6. Factoring out the GCF
  7. Factoring trinomials
  8. Factoring trinomials with a leading coefficient
  9. Factoring the difference of squares