Polynomial Review Sheet Answers
I. Degree (find each monomial’s degree and take the highest degree)
1. 5
2. 3
3. 0
4. 7
II. Add/Subtract Polynomials (you can only add like terms; do not change the exponents!!!!)
5. –5x2y + 8xy – 1xy2
6. change subtraction to addition (“keep/change/opposite”):
(7m3 + 5m2 – 8m + 3) + (–10m3 + –3m2 + 8m + 3)
–3m3 + 2m2 + 6
7. 13x2 + 5x – 4
8. (“subtracted from”) (3p2 + p – 5) – (p2 – 4p + 1)  “keep/change/opposite”
(3p2 + p – 5) + (–p2 + 4p + –1)
2p2 + 5p – 6
III. Properties of Powers
 Adding/subtracting – add/subtract coefficients; keep exponents the same
 Multiplying – multiply coefficients; add exponents
 Dividing – divide coefficients; subtract exponents
 Power to a power (exponent outside a monomial) – raise coefficients to exponent; multiply exponents
 Negative exponents – take the exponent and base “across the road” (fraction bar)
9. (Square everything up top remembering to multiply the exponents)
9x8
 subtract exponents; there are more x’s up top, so leave them in the top of your answer
x3
9x5
10. (multiply coefficients, add exponents of like bases)
–15x5y–3  do not leave negative exponents in your final answer! Take the y and –3 to the bottom!!
 15 x 5
y3
11. (square everything in the parentheses – multiply exponents)
9 6
x
16
12. (divide the coefficients; subtract the exponents leaving the variables where there are more of them)
4x 2 z 4
y
IV. Multiplying Polynomials
 You may use the BOX or the distributive property (also called FOIL only with multiplying binomials)
13.
x2
3x
5
3x3
5x2
14.
3xy2
3x3 + 5x2
15.
4xy3
xy
2
12x2y5
3x2y3
6xy2
12x2y5 + 3x2y3 + 6xy2
x
6
2x
2x2
12x
–3
–3x
–18
16.
3m
1
4m
12m2
4m
5
15m
5
2x2 + 9x – 18
12m2 + 19m + 5
17. (DO NOT JUST SQUARE BOTH TERMS!!!! Write it out, and either FOIL or BOX it out.)
(2x – 7)2 = (2x – 7)(2x – 7)
2x
–7
2x
4x2
–14x
–7
–14x
49
4x2 – 28x + 49
4a
9
4a
16a2
36x
–9
–36x
–81
18.
16a2 – 81
VI. Applications
19. If the perimeter of a square (4 equal sides) is 16x + 28, then each side is
Area of a square = bh = (4x + 7)(4x + 7)  BOX or FOIL
= 16x2 + 56x + 49
16 x  28
, which is 4x + 7.
4
20. Original room:
11
New room (adding x + 8 to both sides)
11 + x + 8  x + 19
Area = 66 feet2
6
6 + x + 8  x + 14
New Area = (x + 14)(x + 19)  BOX or FOIL
= x2 + 33x + 266
He added (New area – Original area)
= (x2 + 33x + 266) – (66)
= x2 + 33x – 200 feet2
21. Area of rectangle (WHOLE)
A = bh
A = (3x – 4)(x + 6)  BOX or FOIL
A = 3x2 +14x – 24
Area of shaded = WHOLE – INSIDE
= (3x2 + 14x – 24) – (x2 + 3x + 4)
= 2x2 + 11x – 28
22.
2x – 5
3x + 7
8
Volume = Lwh
= (8)(3x + 7)(2x – 5)  BOX or FOIL
= (8) (6x2 – 1x – 35)  distribute
= 48x2 – 8x – 280
Area of triangle (INSIDE)
A = (1/2) bh
A = (1/2) (x + 2)(2x + 4)  BOX or FOIL
A = (1/2) (2x2 + 6x + 8)  distribute ½
A = x2 + 3x + 4