Quadratic Expressions Worksheets Page 9
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36number and algebra
7.3 Factorising expressions with three terms
+ bx + c where a = 1.
2
• A monic quadratic expression is an expression in the form ax
Factorising monic quadratic trinomials
• The area model of binomial expansion can be used to fi nd a pattern for factorising a
general quadratic expression. For example,
(x + f) (x + h) = x
+ fx + hx + fh
(x + 4) (x + 3) = x
+ 4x + 3x + 12
2
2
= x
+ (f + h)x + fh
= x
+ 7x + 12
2
2
+
+
x
4
x
f
x
fx
x
4x
2
2
x
x
+
+
h
hx
f h
3
3x
12
• To factorise a general quadratic, look for factors of c that add to b.
+ bx + c = (x + f) (x + h)
2
x
Factors of c that add to b
+
=
3
4
7
+ 7x + 12 = (x + 3) (x + 4).
2
For example, x
×
=
3
4
12
Maths Quest 10 + 10A
276
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