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Perform the indicated operation.
1. (x + 2 – x2) + (3x2 + 4x + 5)
= x + 2 – x2 + 3x2 + 4x + 5
= 2x2 + 5x + 7
take out parentheses (no signs change)
combine like terms
2. (15 + 3x – x2) + (4x2 – 2x – 10)
= 15 + 3x – x2 + 4x2 – 2x – 10
= 3x2 + x + 5
Algebra 1
Section 10.8
Review for Test
take out parentheses (no signs change)
combine like terms
© Mr. Sims
3. (x2 + 3x – 1) – (4x2 – 5x + 6)
= x2 + 3x – 1 – 4x2 + 5x – 6
= - 3x2 + 8x – 7
take out parentheses (watch signs)
combine like terms
4. (3x2 – 2x + 4) – (-x3 + 2x – 6)
= 3x2 – 2x + 4 + x3 – 2x + 6
= x3 + 3x2 – 4x + 10
take out parentheses (watch signs)
combine like terms
© Mr. Sims
5.
(x – 5)(x – 10)
= x(x) + x(-10) – 5(x) – 5(-10) FOIL method
= x2 – 10x – 5x + 50
= x2 – 15x + 50 combine like terms
6. (6 + x)(x2 – 2x + 3)
= 6(x2) + 6(-2x) + 6(3) + x(x2) + x(-2x) + x(3)
= 6x2 – 12x + 18 + x3 – 2x2 + 3x
= x3 + 4x2 – 9x + 18 combine like terms and
distributive property
list in decreasing order of exponents
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Factor the expression.
7. x2 – 2x – 15
=
x- 5
8. x2 + 10x + 25
x + 3
9. 2x2 – x – 21
= 2x - 7
x+3
= x + 5 x+ 5
10. 4x2 – 32x + 60
= 4(x2 – 8x + 15)
factor 4 out 1st
=4 x - 5 x - 3
© Mr. Sims
Factor the expression.
11. x2 – 9
= x + 3
12. 5x2 + 16x + 3
x - 3
13. x2 – 12x + 36
= x - 6 x - 6
= 5x + 1 x + 3
14. x2 – 3x – 40
= x - 8 x + 5
© Mr. Sims
Solve the equation by factoring.
15. x2 – 2x – 8 = 0
x - 4 x + 2 = 0
x–4=0
+4
or
+4
x=4
x+2=0
-2
or
factor into two binomials
set each factor equal to 0
-2
x=-2
16. x2 + 4x – 12 = 0
x+6
x+6=0
or
x - 2 = 0
x–2=0
set each factor equal to 0
+2 +2
-6 -6
x=-6
factor into 2 binomials
or
x=2
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17. 4x2 + 5x + 1 = 0
4x + 1 x + 1 = 0
4x + 1 = 0
or
factor into 2 binomials
x+1=0
-1 -1
4x = -1
x = -1/4 or
-1
set each factor equal to 0
-1
x=-1
18. 9x2 – 5x – 4 = 0
9x + 4 x - 1
= 0
factor into 2 binomials
9x + 4 = 0 or x – 1 = 0
-4 -4
set each factor equal to 0
+1 +1
9x = - 4
x=1
x = - 4/9 or
© Mr. Sims
Perform the indicated operations.
1.) (x4 + 3x2 + 2) + (2x4 – 3x2 + 6)
3.) (5x – 4)(5x + 4)
2.) (5x3 + 2x – 4) – (4x3 + 2x2 – 5x)
4.) (3x + 5)2
Algebra 1
Section 10.8
Assignment
5.) (2x – 1)(13x + 5)
6.) (4x3 – 6x + 7) (x + 1)
Factor the expression.
7.) 36x2 – 25
8.) x2 + 10x + 25
9.) 5x2 – 3x – 2
12.) x2 + 6x – 91 = 0
13.) 4x2 – 10x – 36 = 0
10.) 2x2 – 28x + 96
Solve the equation.
11.) x2 – 7x + 6 = 0
© Mr. Sims
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