math homework

INSTRUCTOR GUIDANCE EXAMPLE: Week Five Discussion

Factoring

Since there are several different types of factoring problems assigned from pages 345-

346, four types will be demonstrated here to offer a selection, even though individual

students will only be working two from these pages.

#73. x 3 – 2x

2 – 9x + 18 Four terms means start with grouping

x 2 (x – 2) – 9(x – 2) The common factor for each group is (x – 2)

(x – 2)(x 2 – 9) Notice the difference of squares in second group

(x – 2)(x – 3)(x -+ 3) Now it is completely factored.

#81. 6w 2 – 12w – 18 Every term has a GCF of 6

6(w 2 – 2w – 3) Common factor is removed, now have a trinomial

Need two numbers that add to -2 but multiply to -3

Try with -3 and +1

6(w – 3)(w + 1) This works, check by multiplying it back together

#97. 8vw 2 + 32vw + 32v Every term has a GCF of 8v

8v(w 2 + 4w + 4) The trinomial is in the form of a perfect square

8v(w + 2)(w + 2) Showing the squared binomial

8v(w + 2) 2 Writing the square appropriately

#103. -3y 3 + 6y

2 – 3y Every term has a GCF of -3y

-3y(y 2 – 2y + 1) Another perfect square trinomial

-3y(y – 1)(y – 1) Showing the squared binomial

-3y(y – 1) 2 Writing the square appropriately

Here are two examples of problems similar to those assigned from page 353.

5b 2 – 13b + 6 a = 5 and c = 6, so ac = 5(6) = 30. The factor pairs of 30

are 1, 30 2, 15 3, 10 5,6 -3(-10)=30 while -3+(-10)= -13 so replace -13b by -3b and -10b 5b

2 – 3b – 10b + 6 Now factor by grouping.

b(5b – 3) – 2(5b – 3) The common binomial factor is (5b – 3).

(5b – 3)( b – 2) Check by multiplying it back together.

3x 2 + x – 14 a = 3 and c = -14, so ac =3(-14)= -42. The factor pairs of – 42 are

1, -42 -1, 42 3, -14 -3, 14

2, -21 -2, 21 6, -7 -6, 7

We see that -6(7) = -42 while -6 + 7 = 1 so replace x with -6x + 7x.

3x 2 – 6x + 7x – 14 Factor by grouping.

3x(x – 2) + 7(x – 2) The common binomial factor is (x – 2).

(x – 2)(3x + 7) Check by multiplying it back together.