Answer:
see explanation
Step-by-step explanation:
(a)
Given
x² + 10x + 16
Consider the factors of the constant term (+ 16) which sum to give the coefficient of the x- term (+ 10)
The factors are + 2 and + 8, since
2 × 8 = 16 and 2 + 8 = 10, thus
x² + 10x + 16 = (x + 2)x + 8)
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(b)
Given
x² + 7x + 12
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)
The factors are + 3 and + 4, since
3 × 4 = 12 and 3 + 4 = 7, thus
x² + 7x + 12 = (x + 3)(x + 4)
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(c)
Given
x² + 13x + 12
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 13)
The factors are + 1 and + 12, since
1 × 12 = 12 and 1 + 12 = 13, thus
x² + 13x + 12 = (x + 1)(x + 12)
