To factor the polynomial x2 + bx + c, you need to identify integers with the sum of
and the product of c. Understanding the relationship between b and c is essential
o factoring polynomials. When two numbers have a sum of b and a product of c,
hey are called factor pairs.
1. Let c> 0. Investigate how c is affected by changes in b. Complete the table.
b
2
3
4
5
6
7
8
Factor pair Product (c) Polynomial
1
x²+2x+1
x² + 3x +2
x² + 4x +3
x² + 4x + 4
x2+5x+1
x2+5x+6
1.1
1.2
1.3
2.2
1,4
2,3
2
3
4
4
6
Factored form
(x + 1)(x + 1)
(x+1)(x+2)
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(x + 1)(x+3)
(x+2)(x+2)
(x+1)(x+4)
(x+2)(x+3)