Originally Posted by

**stephen_gould** In an explanation text about “The Factor Theorem” the following example is given:

Example: A polynomial is given by f(x) = 2x3 + 13x2 + 13x – 10.

c) Factorise f(x) completely.

Solution:

2x3 + 13x2 +13x – 10 = (x + 2)(ax2 +bx + c).

This is an identity and so the values of a, b and c may be found by comparing coefficients.

Comparing the x3 term gives: a = 2.

Comparing the x2 term gives: 13 = 2a + b → b = 9.

Comparing the constant term gives: c = -5.

If follows that: f(x) = (x + 2)(2x2 + 9x – 5).

Factorising the quadratic part in the usual way gives:

f(x) = (x + 2)(2x – 1)(x + 5).

My questions are:

a) where does the expression “2a + b” come from in the line “comparing the x2 term gives” and

b) how is the c = -5 calculated?