Download Polynomials Review for Test

CC Math I Standards: Unit 6
POLYNOMIALS: ADDITION AND SUBTRACTION
Simplify the following by combining like terms.
1) 3x – 2y + 4y – 6x
3) 4z + 2t + 3z – t
2) 3x – 12y – 2x2 + 6y
5) 8a + 6b + 6a + 2b
4) 5a + 3b – 2c – 8a
ADDING AND SUBTRACTING POLYNOMIALS:
 When adding and subtracting polynomials, you COMBINE LIKE TERMS.
 Be careful of parentheses and positive or negative signs with the operations.
1: (3x2 – 4x + 8) + (2x – 7x2 – 5)
2: (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)
3: (3n2 + 13n3 + 5n) – (7n + 4n3)
4: (7y2 + 2y – 3) + (2 – 4y + 5y2)
5: (2b2 + 8b3 + 4b) – (9b – 5b3)
6: (3x2 + 5x + 2) – (4 – 2x) + (5x2 + 7)
PRACTICE PROBLEMS: Simplify each expression
( 3 x  5)  ( 2 x  3)
1.
x  2x  3  2x 2  7x  9
3.
( 2 x  3)  (4 x  3)
4.
(2 x 2  2 x  4)  ( x 2  3x  7)
5.
(3a 2  a  4)  (a 2  2a  1)
6.
( t 2  1)  ( 2t  3)
2
2.
POLYNOMIALS: Multiplication of Monomial and Polynomial
DISTRIBUTIVE PROPERTY REVIEW
1) -4 (2 – 6x )
2) 3 (5p + q – 3r)
3) -2 (-x - 7y)
SIMPLIFYING PRACTICE PROBLEMS:
1) 3(4x + 7)
2) 2(12 – 5z + 9z2)
3) -7 (– 6m + 11m)
4) 4(11 – 3x)
5) – 5(5a – 3b – 6)
6) -2(x2 - 8x + 3x3 – 6)
LAWS of EXPONENTS REVIEW:
Multiply Coefficients and Add Exponents of Same Variable
1) (3x2)(7x3)
2) 8m5 • m
3) t3 • 6t7
4) (4y4)(-9y2)
5) 3r5 • 2r2 • 7r6
6) (-2p3r)(11r4p6)
7) (6y3x)(5y3)
8) 7c5a3b • 8a2b4c
9) (-3t3u2)(-4u3t)
BINOMIAL #1
POLYNOMIALS: FOIL BOX METHOD Part 1
BINOMIAL #2
FOIL Box Method: The box method does the exact same
F
first
terms
O
outer
terms
I
inner
terms
L
last
terms
multiplications as our standard FOIL method, but gives it in a
graphic organizer.
 Be careful of positive and negatives.
 Combine like terms of boxes to finish.
Exp 1: (x + 2) (x + 1)
Exp 2: (y + 3) (y - 4)
Exp 3: (a – 5) (a – 7 )
Exp 4: (3x + 2) (x + 4)
Exp 5: (5b + 9) (b - 4)
Exp 6: (2n -7) (3n + 3)
Exp 8: (8r2 – 2r) (5r + 4)
Exp 9: (2x + 5y) (7y – 3x)
Exp 7: (2x - 5) (2x - 5)
Practice Problems: Multiply the following binomials.
1. ( x  3)( x  2)
2. ( 2 x  1)( x  1)
3. ( y  4)( y  2)
4. ( x  7)( x  3)
5. ( y  4)( 2 y  3)
6. (4h  3)( 3h  2)
7. ( m  3)( m  1)
8. ( 2a  3)( a  2)
9. ( 3 x  1)( x  2)