factoring by gcf
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Factoring by GCF. Factoring. Put the expression in a division tower Continue to divide by numbers or variables until there is no number or variable common to all terms. Put the numbers and variables along the side on the outside of the parentheses. - PowerPoint PPT PresentationTRANSCRIPT
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Factoring by GCFFactoring by GCF
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FactoringFactoring
Put the expression in a division towerPut the expression in a division towerContinue to divide by numbers or Continue to divide by numbers or variables until there is no number or variables until there is no number or variable common to all terms.variable common to all terms.Put the numbers and variables along Put the numbers and variables along the side on the outside of the the side on the outside of the parentheses.parentheses.Put the top expression on the inside of Put the top expression on the inside of parentheses.parentheses.
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Example 1Example 156x4 – 32x3 – 72x2
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Factor each expression.
A. 5(x + 2) + 3x(x + 2)
5(x + 2) + 3x(x + 2)
(x + 2)(3x + 5)
The terms have a common binomial factor of (x + 2).
Factor out (x + 2).
B. –2b(b2 + 1)+ (b2 + 1)
–2b(b2 + 1) + (b2 + 1)
–2b(b2 + 1) + 1(b2 + 1)
(b2 + 1)(–2b + 1)
The terms have a common binomial factor of (b2 + 1).
(b2 + 1) = 1(b2 + 1)
Factor out (b2 + 1).
Example 2: Factoring Out a Example 2: Factoring Out a Common Binomial FactorCommon Binomial Factor
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Example 3: Factoring by GroupingExample 3: Factoring by Grouping
Factor each polynomial by grouping. Check your answer.
6h4 – 4h3 + 12h – 8
(6h4 – 4h3) + (12h – 8)
2h3(3h – 2) + 4(3h – 2)
2h3(3h – 2) + 4(3h – 2)
2(3h – 2)(h3 + 2)
Group terms that have a common number or variable as a factor.
Factor out the GCF of each group.
(3h – 2) is another common factor.
Factor out (3h – 2).
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Example 4: Factoring by GroupingExample 4: Factoring by Grouping
Factor each polynomial by grouping. Check your answer.
5y4 – 15y3 + y2 – 3y
(5y4 – 15y3) + (y2 – 3y)
5y3(y – 3) + y(y – 3)
5y3(y – 3) + y(y – 3)
y(y – 3)(5y2 + 1)
Group terms.
Factor out the GCF of each group.
(y – 3) is a common factor.
Factor out (y – 3).
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Example 5: Factoring with Example 5: Factoring with OppositesOpposites
Factor 2x3 – 12x2 + 18 – 3x
2x3 – 12x2 + 18 – 3x
(2x3 – 12x2) + (18 – 3x)
2x2(x – 6) + 3(6 – x)
2x2(x – 6) + 3(–1)(x – 6)
2x2(x – 6) – 3(x – 6)
(x – 6)(2x2 – 3)
Group terms.
Factor out the GCF of each group.
Simplify. (x – 6) is a common factor.
Factor out (x – 6).
Write (6 – x) as –1(x – 6).
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Example 6Example 6
Factor each polynomial. Check your answer.
15x2 – 10x3 + 8x – 12
(15x2 – 10x3) + (8x – 12)
5x2(3 – 2x) + 4(2x – 3)
5x2(3 – 2x) + 4(–1)(3 – 2x)
5x2(3 – 2x) – 4(3 – 2x)
-1(2x - 3)(5x2 – 4)
Group terms.Factor out the GCF of
each group.
Simplify. (3 – 2x) is a common factor.
Factor out (3 – 2x).
Write (2x – 3) as –1(3 – 2x).
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Try these…Try these…
Factor each polynomial. Check your answer.
1. 16x + 20x3
2. 4m4 – 12m2 + 8m
Factor each expression.
3. 7k(k – 3) + 4(k – 3)
4. 3y(2y + 3) – 5(2y + 3)
(2y + 3)(3y – 5)
(k – 3)(7k + 4)
4m(m3 – 3m + 2)
4x(4 + 5x2)
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Try these (cont)…Try these (cont)…Factor each polynomial by grouping. Check your answer.
5. 2x3 + x2 – 6x – 3
6. 7p4 – 2p3 + 63p – 18
7. A rocket is fired vertically into the air at 40 m/s.
The expression –5t2 + 40t + 20 gives the
rocket’s height after t seconds. Factor this
expression.
–5(t2 – 8t – 4)
(7p – 2)(p3 + 9)
(2x + 1)(x2 – 3)