Factorising quadratics

Educational level: this is a secondary education resource.

Quadratic equations are equations of the form ax^2 + bx + c = 0 where a, b and c are constants, a \ne 0 and x is a variable. In other words, a quadratic equation has at least one term of the variable, say x, raised to the exponent 2, e.g. x^2

Subject classification: this is a mathematics resource .

Arranging terms

Arrange the quadratic into order: first the squared number ax2, then the number times x, bx, finally the constant value c.

Factorising quadratics

Form of quadratics: ax^2 + bx + c = 0

To factorise:

  1. split the middle term so it adds to the original number, e.g., let b = (AD + BC), and
  2. multiplies to the constant times the first term, e.g., Ax times Bx equals ABx2, then a = AB,
  3. then bracket so the pronumeral (letter) is like this, e.g., (Ax + C)(Bx + D).

Checking

Multiplying the two terms: (Ax + C) and (Bx + D) with each other becomes:

Ax \times Bx + Ax \times D + C \times Bx + C \times D

which rearranges to:

ABx^2 + (AD + BC)x + CD

The final constant c = CD.

Examples

2m^2 + 11m + 5

= (2m+1)(m+5)

To check it, re-expand the answer to see if we get back to where we started from:

(2M+1)(M+5)

= 2M \times M + 2M \times 5 + 1 \times M +1 \times 5

= 2m^2 + 11m + 5

See also

References

    External links

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