Name: 2. Determine (a) the leading coefficient and (b) the degree of the polynomials
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1 Name: 1. For the following polynomial, 3x 3 x 2 + 4x 6 (a) List the terms: (b) List the coefficient of each term: (c) List the degree of each term: (d) Find the degree of the polynomial. 2. Determine (a) the leading coefficient and (b) the degree of the polynomials below. (a) 8x 3 3x 2 y + 5y 4 Leading Coefficient: Degree of polynomial: (b) 10x 7 y x 6 y 2 + 2x 5 y 19x 4 y 5 Leading Coefficient: Degree of polynomial: 3. Add the polynomials: (2x 6 5x 5 + 3x 2 7x + 3) + (3x 6 8x 4 x 2 11x + 2)
2 4. Subtract the polynomials: (a) (4x 2 + 3x + 7) (2x 2 x 5) (b) (7x 3 y 2 6x 2 y +6x 2 9xy +8) (12x 3 y 2 13x 2 y 2 14x 2 y 11xy +2) 5. Multiply the polynomials: (a) ( 8x 3 y 4 )( 4xy 2 ) (b) 2xy(5xy 2 + 6x 2 y 3xy) (c) (a 9)(a 2 + 3a 4) (d) (y + 9)(y 9) (e) (2x + 3)(3x 2) Page 2
3 (f) (y + 7) 2 (g) (5x + y) 2 (h) (3a + 7b)(3a 7b) 6. Factor out the greatest common factor from each polynomial: (a) 15x 3 10x x (b) 36a 2 b 3 18a 3 b + 27a 4 b 2 7. Factor out the negative of the greatest common factor: (a) 9x y (b) x 2 + 7x 5 Page 3
4 8. Factor the greatest common binomial factor from each polynomial: (a) 4x(2y + 1) 5(2y + 1) (b) 2y(x 8) (x 8) 9. Factor by grouping. (a) ab 7a + 6b 42 (b) x 2 xy + 4x 4y (c) 15x 2 + 6x 40xy 16y 10. Factor each polynomial completely, or state that the polynomial is prime. (a) x 2 + 4x + 3 (b) y 2 + 3y 18 Page 4
5 (c) 3x x + 24 (d) 2x 2 + 3x + 1 (e) 12x 2 4x 5 (f) a 2 3ab 10b Factor each difference of two squares. (a) x 2 36 (b) 16x 2 25y 2 (c) x 2 1 Page 5
6 12. Factor each perfect square trinomial. (a) a 2 20a (b) 4x x + 9 (c) 16a 2 40ab + 25b Factor each polynomial using the formula for the sum or difference of two cubes. a 3 + b 3 = (a + b)(a 2 ab + b 2 ) a 3 b 3 = (a b)(a 2 + ab + b 2 ) (a) x (b) y 3 64 (c) 27x 3 + 8y 3 Page 6
7 14. Use factoring to solve each polynomial equation. (a) x 2 6x + 8 = 0 (b) 6x x = 0 (c) x 3 + x 2 = 12x (d) (x + 9)(x + 1) = 33 (e) 3x 4 12x 2 = 0 Page 7
8 15. Solve each word problem below, using only one variable. Draw a picture!! (a) The length of a rectangle storage room is 9 feet longer than its width. If the area of the room is 162 square feet, find the dimensions of the room. (b) An object is thrown upward from the top of a 160 foot building with an initial velocity of 48 feet per second. The height, h of the object after t seconds is given by the quadratic equation: h = 16t 2 +48t When will the object hit the ground? Page 8
9 1. For the following polynomial, 3x 3 x 2 + 4x 6 (a) List the terms: (b) List the coefficient of each term: (c) List the degree of each term: Name: (d) Find the degree of the polynomial. 2. Determine (a) the leading coefficient and (b) the degree of the polynomials below. (a) 8x 3 3x 2 y + 5y 4 Leading Coefficient: Degree of polynomial: (b) 10x 7 y x 6 y 2 + 2x 5 y 19x 4 y 5 Leading Coefficient: Degree of polynomial: 3. Add the polynomials: (2x 6 5x 5 + 3x 2 7x + 3) + (3x 6 8x 4 x 2 11x + 2) 4. Subtract the polynomials: (a) (4x 2 + 3x + 7) (2x 2 x 5) (b) (7x 3 y 2 6x 2 y + 6x 2 9xy + 8) (12x 3 y 2 13x 2 y 2 14x 2 y 11xy + 2) 5. Multiply the polynomials: (a) ( 8x 3 y 4 )( 4xy 2 ) (b) 2xy(5xy 2 + 6x 2 y 3xy) (c) (a 9)(a 2 + 3a 4) (d) (y + 9)(y 9) (e) (2x + 3)(3x 2) (f) (y + 7) 2 (g) (5x + y) 2 (h) (3a + 7b)(3a 7b)
10 6. Factor out the greatest common factor from each polynomial: (a) 15x 3 10x x (b) 36a 2 b 3 18a 3 b + 27a 4 b 2 7. Factor out the negative of the greatest common factor: (a) 9x y (b) x 2 + 7x 5 8. Factor the greatest common binomial factor from each polynomial: (a) 4x(2y + 1) 5(2y + 1) (b) 2y(x 8) (x 8) 9. Factor by grouping. (a) ab 7a + 6b 42 (b) x 2 xy + 4x 4y (c) 15x 2 + 6x 40xy 16y 10. Factor each polynomial completely, or state that the polynomial is prime. (a) x 2 + 4x + 3 (b) y 2 + 3y 18 (c) 3x x + 24 (d) 2x 2 + 3x + 1 (e) 12x 2 4x 5 (f) a 2 3ab 10b Factor each difference of two squares. (a) x 2 36 (b) 16x 2 25y 2 (c) x 2 1 Page 2
11 12. Factor each perfect square trinomial. (a) a 2 20a (b) 4x x + 9 (c) 16a 2 40ab + 25b Factor each polynomial using the formula for the sum or difference of two cubes. a 3 + b 3 = (a + b)(a 2 ab + b 2 ) a 3 b 3 = (a b)(a 2 + ab + b 2 ) (a) x (b) y 3 64 (c) 27x 3 + 8y Use factoring to solve each polynomial equation. (a) x 2 6x + 8 = 0 (b) 6x x = 0 (c) x 3 + x 2 = 12x (d) (x + 9)(x + 1) = 33 (e) 3x 4 12x 2 = Solve each word problem below, using only one variable. Draw a picture!! (a) The length of a rectangle storage room is 9 feet longer than its width. If the area of the room is 162 square feet, find the dimensions of the room. (b) An object is thrown upward from the top of a 160 foot building with an initial velocity of 48 feet per second. The height, h of the object after t seconds is given by the quadratic equation: h = 16t t When will the object hit the ground? Page 3
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