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Year 10 Interactive Maths - Second Edition


Quadratic Trinomials

The definition and examples of a quadratic trinomial.


Factors of Quadratic Trinomials of the Type x2 + bx + c

The Distributive Law is used in reverse to factorise a quadratic trinomial, as illustrated below.

The expansion of (x+2)(x+3)= x^2 + 5x +6

We notice that:
  • 5, the coefficient of x, is the sum of 2 and 3.
  • 6, the independent term, is the product of 2 and 3.

To factorise (factorize) x^2 + 5x +6, find two numbers whose sum is 5 and whose product is 6. The two numbers are 2 and 3.


Note:

The product of two linear factors yields a quadratic trinomial; and the factors of a quadratic trinomial are linear factors.


(x+a)(x+b) = x^2 + (a+b)x + ab

Factors of the first term and factors of the last term.

Coefficient of x = a + b.  Independent term = ab.


In general:

To factorise (factorize) a quadratic trinomial, find two numbers whose sum is equal to the coefficient of x and whose product is equal to the independent term.


Example 8

Factorise (factorize) the following two quadratic trinomials.

Solution:

y^2 - 5y + 4 = (y-1)(y-4)

p^2 - p - 6 = (p-3)(p+2)

Check:

To check, expand (p-3)(p+2) to get p^2 - p - 6.


Key Terms

quadratic trinomial, linear factors


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