Chapter 4 Section 4.AFactor polynomials in the form ax^2+bx+c

In this assignment, you will be able to...

1.Factor polynomials in the form ax^2+bx+c

3. Factor the difference of perfect squares.

4. Factor perfect square polynomials.

2. Factor monomials first.

Factor the expression. If the expression cannot be factored, say so.

1.) 2x^2+5x+3

Answer:

Original Expression2x^2+5x+3

2x^2+5x+3 Multiply the 2 and 3x^2+5x+6 Now factor

(x+2)(x+3) Now divide factors by 2

(x+2)(x+3)__

(x+1)(2x+3)

__2 2

Reduce, if you can't, put divisor in front of x.

Final factors.

(x+1)(2x+3)

Factor the expression. If the expression cannot be factored, say so.

2.) 3n^2+7n+4

Answer:

Original Expression

Multiply the 3 and 4n^2+7n+12 Now factor

(n+4)(n+3) Now divide factors by 3

(n+4)(n+3)__

(3n+4)(n+1)

__3 3

Reduce, if you can't, put divisor in front of x.

Final factors.

3n^2+7n+4

3n^2+7n+4

(3n+4)(n+1)

Factor the expression. If the expression cannot be factored, say so.

3.) 4r^2+5r+1

(4r+1)(r+1)Answer:

Factor the expression. If the expression cannot be factored, say so.

4.) 6p^2+5p+1

(3p+1)(2p+1)Answer:

Factor the expression. If the expression cannot be factored, say so.

5.) 11z^2+2z-9

(11z-9)(z+1)Answer:

Factor the expression. If the expression cannot be factored, say so.

6.) 15x^2-2x-8

(5x-4)(3x+2)Answer:

Factor the expression. If the expression cannot be factored, say so.

7.) 4y^2-5y-4

Cannot be factored.Answer:

Factor the expression. If the expression cannot be factored, say so.

8.) 14m^2+m-3

(7m-3)(2m+1)Answer:

Factor the expression. If the expression cannot be factored, say so.

9.) 9d^2-13d-10

(9d+5)(d-2)Answer:

Factor the expression. If the expression cannot be factored, say so.

10.) 5x^2+14x-3

(5x-1)(x+3)Answer:

Factor the expression. If the expression cannot be factored, say so.

11.) 9x^2-1

(3x+1)(3x-1)Answer:

9x^2-1 Original expression

(3x)(3x) (1)(-1)(3x)(3x)=9x^2

(1)(-1)=-1

(3x+1)(3x-1) Factors.

Factor the expression. If the expression cannot be factored, say so.

12.) 4r^2-25

(2r+5)(2r-5)Answer:

4r^2-25 Original expression

(2r)(2r) (5)(-5)(2r)(2r)=4r^2

(5)(-5)=-25

Factors.(2r+5)(2r-5)

Factor the expression. If the expression cannot be factored, say so.

13.) 49n^2-16

(7n+4)(7n-4)Answer:

Factor the expression. If the expression cannot be factored, say so.

14.) 25x^2+4

Cannot be factored.Answer:

Factor the expression. If the expression cannot be factored, say so.

15.)16s^2+8s+1

(4s+1)^2Answer:

Factor the expression. If the expression cannot be factored, say so.

16.) 64w^2-144w+81

(8w-9)^2Answer:

Factor the expression. If the expression cannot be factored, say so.

17.) 12x^2-4x-40

Answer:

Original Expression

Multiply the 3 and 10x^2-x-30 Now factor

(x+5)(x-6) Now divide factors by 3

(x+5)(x-6)__

4(3x+5)(x-2)

__3 3

Reduce, if you can't, put divisor in front of x.

Final factors. Don't forget to put the 4 back in.

3x^2-x-10

12x^2-4x-40

4(3x^2-x-10)Factor common monomials first

4(3x+5)(x-2)

Factor the expression. If the expression cannot be factored, say so.

18.)18z^2+36z+16

Answer:

Original Expression

Multiply the 9 and 8z^2+18z+72 Now factor(z+12)(z+6) Now divide factors by 9(z+12)(z+6)__

2(3z+4)(3z+2)

__9 9

Put divisors in front of x.

Final factors. Don't forget to put the 2 back in.

9z^2+18z+8

2(9z^2+18z+8)Factor common monomials first

18z^2+36z+16

Reduce.

(z+4)(z+2)3 3

____

2(3z+4)(3z+2)

Factor the expression. If the expression cannot be factored, say so.

19.) 32v^2-2

2(4v+1)(4v-1)Answer:

20.)Factor 21x^2-77x-28. Describe each step.

You are a factoring machine.