Page 614 - Algebra 1

Checklist Item 3: Look for perfect-square trinomials. Are the first and last terms perfect squares? Is the second term the product of the square roots of the first and last term?
For example, factor x2 + 16x + 64.
10. Is there a common factor for all terms in the polynomial?
11. How many terms exist in the polynomial?
12. Are the first and last terms perfect squares? If so, what are their respective square roots?
13. Notice that the trinomial is of the form a2 + 2ab + b2. What is the value of a? b?
14. Use the formula a2 + 2ab + b2 = (a + b)2 for factoring a perfect-square trinomial.
15. Model Is it possible to factor x2 + 8x + 32 in a similar manner? Explain.
Checklist Item 4: Are there three terms of the polynomial, all of which are
being added? Is the last term not a perfect square?
Some trinomials of the form x2 + bx + c that are not perfect-square trinomials can still be factored as the product of two binomials, such as (x + j) (x + k), where c = jk and b = j + k.
For example, factor x2 + 8x + 15.
16. Is there a common factor for all terms in the polynomial?
17. Is this a perfect-square trinomial? Explain.
18. Is the trinomial of the form x2 + (j + k)x + jk? If so, find two values that add to 8 and multiply to 15. What is the value of j? k?
19. Factor the polynomial using the formula for factoring a trinomial that is not a perfect square.
Checklist Item 5: Are there four terms in the polynomial? If you have four terms with no GCF, try to group the terms into smaller polynomials. Then factor each group by its GCF.
For example, factor x3 + 7x2 + 2x + 14.
20. Is there a common factor for all terms in the polynomial?
21. How many terms are in the polynomial?
22. Use parentheses to group the first two terms and the last two terms. 23. Factor out the GCF of the first group of terms.
24. Factor out the GCF of the second group of terms.
25. Write the polynomial using the factored groups of terms.
26. What factor does each term have in common?
27. Factor out the common term.
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