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Multiply (x+3)(2x-7) Factor 3. 42x – 7
Warm-Up Multiply (x+3)(2x-7) Factor 3. 42x – 7
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Homework Check
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Factoring Trinomials and Difference of Two Perfect Squares
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Sign Rule for Factoring Trinomials:
When the last term is POSITIVE… The signs inside the parenthesis will be the SAME as the middle number’s sign
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x2 +7x + 6 ( )( ) x x + 6 + 1
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x2 + 9x + 14 ( )( ) x x + 7 + 2
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x2 – 6x + 8 ( )( ) x x – 4 – 2
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x2 – 10x + 16 ( )( ) x x – 8 – 2
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Sometimes you can factor out a GCF 1st!
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2x2 – 16x + 24 2(x2 – 8x +12) 2( )( ) x x – 6 – 2
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You Try... 3y2 + 36y + 60 3(y +10)(y +2) 4x2 +24x + 32 4(x + 2)(x + 4)
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Sign Rule for Factoring Trinomials:
When the last term is NEGATIVE… The parenthesis will have DIFFERENT SIGNS. The larger factor will have the SAME sign as the middle number
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n2 + 2n – 48 ( )( ) n n + 8 – 6
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x2 + 8x – 20 ( )( ) x x – 2 + 10
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x2 – 4x – 21 ( )( ) x x + 3 – 7
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x2 – 9x – 36 ( )( ) x x + 3 – 12
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2x3 + 18x2 + 28x
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c4 + 2c3 – 80c2
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3x2 + 6x – 24
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5x2 + 5x – 10
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3x3 – 6x2 – 45x
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3x3 – 39x x
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Difference of Two Perfect Squares
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Factoring Difference of Two Squares
Both terms must be Perfect Squares and have a MINUS between them Check the binomial for GCF Use two sets of parenthesis (one’s a plus, one’s a minus) Split up what it takes to make the 1st a perfect square and what it takes the 2nd to be a perfect square
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Difference of Two Squares
Factor
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Difference of Two Squares
Factor
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2x3 – 162x
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16x2 – 36
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Factoring Trinomials when a is not equal to 1 Guess & Check Method
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How to Factor a Trinomial
Check for GCF 1st. Divide out the GCF of each term if one exists. When factoring ax2 + bx + c, first find factors of a and c. Check the products of the inner and outer terms to see if the sum is b. When c is POSITIVE, both signs inside the parentheses will be the same as the middle term.
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1. x2 + 9x + 14 +1 +2 +14 +7 1x ( )( ) x x
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2. 2x2 – 5x + 3 1x 2x -1 -3 ( – )( – ) x x
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3. 5x2 + 11x + 2 1x 5x +1 +2 ( )( ) x x
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4. 3x2 – 10x + 3 1x 3x -1 -3 ( – )( – ) x x
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5. 2x2 – 7x + 5 1x 2x -1 -5 ( – )( – ) x x
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6. 6x2 – 11x + 3 1x 2x 6x 3x -1 -3 ( – )( – ) 2x x
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7. 4x2 + 16x + 15 +1 +15 +3 +5 1x 2x 4x ( )( ) 2x x
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8. 3x2 – 20x – 7 1x 3x 1 7 ( )( ) x x –
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9. 2x2 + 3x – 5 1x 2x 1 5 ( )( ) x x –
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10. 5m2 + 14m – 3 1m 5m 1 3 ( )( ) m m –
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11. 2x2 – 11x – 21 1x 2x 1 3 7 21 ( )( ) x x –
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Sometimes you can factor out a GCF 1st!
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12. 14x2 – 32x + 18 2(7x2 – 16x + 9) 2( – )( – ) x 7x 1 9 1x 7x -1 -9
-3 2( – )( – ) x x
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Work Factoring WS
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