2. Chapter 7
Factoring

3. A General Approach to Factoring
7.4
A General Approach to Factoring

4. 7.4 A General Approach to Factoring
Objectives
Factor out any common factor.
Factor binomials.
Factor trinomials.
Factor polynomials with more than three terms.
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5. 7.4 A General Approach to Factoring
Factoring a Polynomial
A polynomial is completely factored when
it is written as a product of prime polynomials with integer coefficients, and
none of the of polynomial factors can be factored further.
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6. 7.4 A General Approach to Factoring
Factoring Out a Common Factor
This step is always the same, regardless of the number of terms in the polynomial.
Factor each polynomial.
(a)
(b)
(c)
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7. 7.4 A General Approach to Factoring
Factoring Binomials
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8. 7.4 A General Approach to Factoring
Factoring Binomials
Use one of the rules to factor each binomial if possible.
(a)
(b)
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9. 7.4 A General Approach to Factoring
Factoring Binomials
Use one of the rules to factor each binomial if possible.
(c)
(d)
Sum of cubes
is prime.
It is the sum of squares.
The binomial 25m is the sum of squares. It can be factored, however as 25(m2 + 25) because it has a common factor, 25.
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10. 7.4 A General Approach to Factoring
Factoring Trinomials
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11. 7.4 A General Approach to Factoring
Factoring Trinomials
Factor each trinomial.
(a)
(b)
(c)
The numbers -6 and 1 have a product of -6 and a sum of -5.
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12. 7.4 A General Approach to Factoring
Factoring Trinomials
Factor each trinomial.
(d)
(e)
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13. 7.4 A General Approach to Factoring
Factoring Polynomials with More than Three Terms
Factor each polynomial. Consider factoring by grouping.
(a)
(b)
Group the terms.
Factor each group.
5k + 1 is a common factor.
Difference of squares
Group the first three terms.
Perfect square trinomial
Difference of squares
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14. 7.4 A General Approach to Factoring
Factoring Polynomials with More than Three Terms
Factor each polynomial. Consider factoring by grouping.
(a)
Rearrange and group the terms.
Factor each group.
Factor out 2m – n.
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