Algebra: A complete introduction by P. Abbott & Hugh Neill

Author:P. Abbott & Hugh Neill
Language: eng
Format: epub
Tags: Algebra: A complete introduction
Publisher: Hodder Education, Part of Hachette Livre UK
Published: 2013-05-02T16:00:00+00:00

13.7 Worked examples

Example 13.6

Factorize x2 + 13x + 36.

There are several pairs of factors of 36 − namely (1 × 36), (2 × 18), (3 × 12), (4 × 9) and (6 × 6).

Look for the pair whose sum is +13; this pair is (9, 4).

Example 13.7

Factorize x2 − 13x + 36.

In this case, the sign of the middle term is − and of the last term is +.

In this case, look for two negative factors of 36 whose sum is −13. These are −9 and −4.

Example 13.8

Factorize x2 − 5x − 36.

When the last term is negative the factors of 36 must have opposite signs.

The coefficient of x is the sum of a positive and negative number, and the negative number must be the greater numerically; or alternatively, 5 is the difference of the two factors numerically.

The required factors of −36 are −9 and +4.

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