factor the following special cases x 2 – 36 4x 2 – 49 x 2 + 6x + 9 x 2 + 16x + 64 warm up
TRANSCRIPT
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FACTOR THE FOLLOWING SPECIAL CASES
X2 – 364X2 – 49
X2 + 6X + 9 X2 + 16X + 64
warm up
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Factoring Test tomorrow
30 questions totalFactor using the GCF (greatest common
factor) 6 questions
Factor the trinomial with a lead coefficient of 1 (easy problem) ( short problem) 8 questions
Factor the trinomial with a lead coefficient not 1 (harder problem) ( longer problem) 4 questions
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Factoring Test tomorrow
Factoring polynomials with special cases (look for perfect squares) 6 questions
Factor completely, you need to choose the appropriate method or combinations of methods 6 questions
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Ways to factor
Factor GCFFactor trinomial lead coefficient 1 (easy)Factor trinomial lead coefficient not 1 (hard)Factor perfect square trinomialFactor difference of squares
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1. Always check for GCF first2. Two or three terms?
1. Two terms check to see if both perfect squares
1. If yes then factor using difference of squares
2. if no then prime
2. Three terms check to see if first and last perfect squares
1. If yes then factor perfect square trinomial
2. If no then check lead coefficient1. If it equals 1 then easy method2. if not 1 then hard method
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Factor using the greatest common factor
Decide what the greatest common factor isDivide each term by that greatest common
factor Divide the coefficients Subtract the exponents
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Factor using the greatest common factor
4x - 8
12x2 + 4x
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Factor using the greatest common factor
6x + 3
-4x3 + 2x2
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Factor using the greatest common factor
28a2b + 56abc2
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Factor 20x2 - 24xy
1. x(20 – 24y)
2. 2x(10x – 12y)
3. 4(5x2 – 6xy)
4. 4x(5x – 6y)
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Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
Factoring Trinomials
X2 + 8x + 12
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Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
Factoring Trinomials
X2 + 8x + 15
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Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
Factoring Trinomials
X2 - 4x + 3
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Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
Factoring Trinomials
X2 - 5x + 6
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Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
Factoring Trinomials
X2 + 2x - 8
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Step one – write factors of last term
Step two – find the factors that add to get you middle number
Step three – write factors you found as binomials
Factoring Trinomials
X2 - x - 12
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Factor each trinomial, if possible. The first four do NOT have leading coefficients, the last two DO have leading coefficients. Watch out for signs!!
1) t2 – 4t – 21
2) x2 + 12x + 32
3) x2 –10x + 24
4) x2 + 3x – 18
Factor These Trinomials!
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2x2 + 7x + 3
• 1) multiply first coefficient with the last coefficient• 2) list the factors of that multiplication• 3) Find the factors that add to the middle term• 4) List out 4 terms• 5) factor by grouping
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3x2 - 8x + 4
• 1) multiply first coefficient with the last coefficient• 2) list the factors of that multiplication• 3) Find the factors that add to the middle term• 4) List out 4 terms• 5) factor by grouping
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Factoring Polynomials where the lead coefficient isn’t one
Example2x2 - 11x + 15
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Factoring Polynomials where the lead coefficient isn’t one
Example3x2 + 7x - 20
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Factor using the perfect square trinomial method
x2 + 12x + 36
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Factor using the perfect square trinomial method
x2 + 4x + 4
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Factor using the perfect square trinomial method
x2 - 14x + 49
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Factor using the perfect square trinomial method
9x2 - 6x + 4
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Factoring Difference of Squares
X2 - 16 X2 - 36
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Factoring Difference of Squares
4X2 - 25 25X2 - 36