Factor the following expression completely: x2 + 5x – 36
Slide: 5
Factoring Trinomials – Hints When both b and c are positive, both values will be positive.
Factor x2 + 9x + 8
Therefore:
8×1=8
8+1=9
x2 + 9x + 8 = (x + 8)(x + 1)
When b is negative and c is positive, both values will be negative.
Factor x2 – 13x + 42
Therefore: Slide: 6
–6 × –7 = 42
–6 + (–7) = –13
x2 – 13x + 42 = (x – 6)(x – 7)
Factoring Trinomials – Hints When c is negative, one value will be positive and the other value will be negative. Pay careful attention to which value gets which sign!
Factor x2 + 6x – 16
Therefore:
Slide: 7
8 + (–2) = 6
x2 + 6x – 16 = (x + 8)(x – 2)
Factor x2 – x – 12
Therefore:
8 × –2 = –16
3 × –4 = –12
3 + (–4) = –1
x2 – x – 12 = (x + 3)(x – 4)
Factoring General Trinomials To factor a trinomial expression in the form of ax2 + bx + c, we will combine our methods for factoring ordinary trinomials and factoring by grouping.
Example:
Factor the following expression:
2x2 + 13x + 15
Step 1: Find 2 numbers which multiply to a × c and add to b. What two numbers multiply to 30 (2 × 15), and add to 13?
10 × 3 = 30
Slide: 8
10 + 3 = 13
Factoring General Trinomials To factor a trinomial expression in the form of ax2 + bx + c, we will combine our methods for factoring ordinary trinomials and factoring by grouping.
Example:
Factor the following expression:
2x2 + 13x + 15
Step 2: Replace b with the two determined values.
2x2 + 13x + 15 = 2x2 + 10x + 3x + 15
10 × 3 = 30 Slide: 9
10 + 3 = 13
Factoring General Trinomials To factor a trinomial expression in the form of ax2 + bx + c, we will combine our methods for factoring ordinary trinomials and factoring by grouping.