Beginning Algebra, 11th Edition

360 CHAPTER 6 Factoring and Applications OBJECTIVES Recall from Section 1.1that to factormeans “to write a quantity as a product ...

Finding the Greatest Common Factor for Numbers Find the greatest common factor for each list of numbers. (a)30, 45 45 = 3 # 3 # ...

362 CHAPTER 6 Factoring and Applications NOW TRY EXERCISE 2 Find the greatest common factor for each list of terms. (a) (b)m^3 n ...

(c) Checkmentally by distributing x^3 over each term inside the parentheses. = x 3 1 x^2 + 12 = x 3 1 x^22 + x 3 112 GCF=x^3 x^5 ...

The final result is in factored form because it is a product. CHECK FOIL (Section 5.5) ✓ Rearrange terms to obtain the original ...

Rearranging Terms before Factoring by Grouping Factor by grouping. (a) Factoring out the common factor of 2 from the first two t ...

Concept Check An expression is factored when it is written as a product, not a sum. Which of the following are not factored? ...

68.Concept Check A student factored as follows. The student could not find a common factor of the two terms. WHAT WENT WRONG? Co ...

OBJECTIVE 1 Factor trinomials with a coefficient of 1 for the second- degree term. When factoring polynomials with integer coeff ...

Factoring a Trinomial with All Positive Terms Factor Look for two integers whose product is 14 and whose sum is 9. List pairs of ...

Factoring a Trinomial with Two Negative Terms Factor Find two integers whose product is and whose sum is Because the con- stant ...

Factoring a Trinomial with Two Variables Factor Here, the coefficient of zin the middle term is so we need to find two expressio ...

6.Concept Check InExercise 5,what must be true of aand bif the coefficient of the con- stant term is positive? 7.What is meant b ...

56. 57. 58. 59. 60. 61. 62. Brain Busters Factor each polynomial. 13 m-n 2 k^2 - 1313 m-n 2 k+ 4013 m ...

NOTE In the preceding example, we could have written 7xas rather than as 3 x+ 4 x.Factoring by grouping would give the same answ ...

Factoring a Trinomial with a Common Factor by Grouping Factor Factor out the greatest common factor, To factor find two integers ...

NOTE In Example 4,we might also realize that our initial attempt to factor as cannotbe correct, since the terms of have a common ...

SECTION 6.3 More on Factoring Trinomials^377 Factoring a Trinomial with a Negative Constant Term by Using FOIL Factor The intege ...

This leads to the completely factored form. CHECK FOIL; Combine like terms. = 15 y^3 + 55 y^2 + 30 y ✓ Distributive property = 5 ...

9.Concept Check Which pair of integers would be used to rewrite the middle term when one is factoring by grouping? A. 3 B.8, C. ...