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The Distributive
Law is used in reverse to factorise a quadratic
trinomial, as illustrated below.
Consider the expansion of (x + 2)(x + 3).
We notice that:
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5, the coefficient of x, is the sum of 2 and 3.
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6, the independent term, is the product of 2 and 3.
Note:
The product of two linear factors yields a quadratic
trinomial; and the
factors of a quadratic trinomial are linear factors.
Now consider the expansion of (x + a)(x + b).
Coefficient of x = a + b = Sum of a and b.
Independent term = ab = Product of a and b.
In general:
To factorise 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 12
Solution:
Check:
Key Terms
quadratic trinomial, independent
term, coefficient, linear factor |
