Grade 10 Academic (MPM2D) · Quadratic Relations of the Form y = ax^2 + bx + c

Factor a difference of squares or a complex trinomial

Factor a difference of squares, or a trinomial ax^2+bx+c where a is not 1, using the decomposition method. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MPM2D-QR1.3

Try one

Factor the difference of squares.

9x2 - 4
  • (3x + 2)(3x + 2)
  • (x - 2)(x + 2)
  • (3x - 2)(3x + 2)
  • (3x - 2)(3x - 2)

Answer: (3x - 2)(3x + 2)

See one solved, step by step

Factor completely.

2x2 - 9x - 5
  • (2x - 5)(x + 1)
  • (2x - 1)(x - 5)
  • (2x + 1)(x + 5)
  • (2x + 1)(x - 5)
📘 Worked solution
12x2 - 9x - 5With a = 2 (not 1), look for factors of a: 2 and 1, since 2 * 1 = 2.
2Try (2x ? )(x ? ), where the missing numbers multiply to −5.The constant term -5 must come from multiplying the two missing numbers.
3Check 1 and −5: (2x + 1)(x - 5) expands to 2x2 - 9x - 5.Multiply it back out (FOIL) to confirm the middle term matches -9x.
4(2x + 1)(x - 5)That's the fully factored form — always double check by expanding it back out.

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