Polynomial Review Sheet Answers



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)

[pic] ( subtract exponents; there are more x’s up top, so leave them in the top of your answer

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!!

[pic]

11. (square everything in the parentheses – multiply exponents)

[pic]

12. (divide the coefficients; subtract the exponents leaving the variables where there are more of them)

[pic]

IV. Multiplying Polynomials

▪ You may use the BOX or the distributive property (also called FOIL only with multiplying binomials)

13. 14.

3x3 + 5x2 12x2y5 + 3x2y3 + 6xy2

15. 16.

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)

4x2 – 28x + 49

18.

16a2 – 81

VI. Applications

19. If the perimeter of a square (4 equal sides) is 16x + 28, then each side is [pic], which is 4x + 7.

Area of a square = bh = (4x + 7)(4x + 7) ( BOX or FOIL

= 16x2 + 56x + 49

20. Original room: New room (adding x + 8 to both sides)

Area = 66 feet2

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) Area of triangle (INSIDE)

A = bh A = (1/2) bh

A = (3x – 4)(x + 6) ( BOX or FOIL A = (1/2) (x + 2)(2x + 4) ( BOX or FOIL

A = 3x2 +14x – 24 A = (1/2) (2x2 + 6x + 8) ( distribute ½

A = x2 + 3x + 4

Area of shaded = WHOLE – INSIDE

= (3x2 + 14x – 24) – (x2 + 3x + 4)

= 2x2 + 11x – 28

22.

Volume = Lwh

= (8)(3x + 7)(2x – 5) ( BOX or FOIL

= (8) (6x2 – 1x – 35) ( distribute

= 48x2 – 8x – 280

-----------------------

3x3

5x2

x2

3x

5

xy

4xy3

3xy2

3x2y3

12x2y5

6xy2

2

2x2

12x

–3x

–18

x

6

2x

–3

5

4m

1

3m

5

15m

4m

12m2

–7

2x

–7

2x

49

–14x

–14x

4x2

–9

4a

9

4a

–81

–36x

36x

16a2

2x – 5

3x + 7

8

6 + x + 8 ( x + 14

11 + x + 8 ( x + 19

11

6

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