Math 152
Chapter 5 Handout
Helene Payne
Name:
1. For the following polynomial,
3x3 − x2 + 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) 8x3 − 3x2 y + 5y 4
Leading Coefficient:
Degree of polynomial:
(b) 10x7 y 3 + 12x6 y 2 + 2x5 y − 19x4 y 5
Leading Coefficient:
Degree of polynomial:
3. Add the polynomials:
(2x6 − 5x5 + 3x2 − 7x + 3) + (3x6 − 8x4 − x2 − 11x + 2)
Math 152
Chapter 5 Handout
Helene Payne
4. Subtract the polynomials:
(a) (4x2 + 3x + 7) − (2x2 − x − 5)
(b) (7x3 y 2 − 6x2 y + 6x2 − 9xy + 8) − (12x3 y 2 − 13x2 y 2 − 14x2 y − 11xy + 2)
5. Multiply the polynomials:
(a) (−8x3 y 4 )(−4xy 2 )
(b) 2xy(5xy 2 + 6x2 y − 3xy)
(c) (a − 9)(a2 + 3a − 4)
(d) (y + 9)(y − 9)
(e) (2x + 3)(3x − 2)
Page 2
Math 152
Chapter 5 Handout
Helene Payne
(f) (y + 7)2
(g) (5x + y)2
(h) (3a + 7b)(3a − 7b)
6. Factor out the greatest common factor from each polynomial:
(a) 15x3 − 10x2 + 25x
(b) 36a2 b3 − 18a3 b + 27a4 b2
7. Factor out the negative of the greatest common factor:
(a) −9x2 + 36y
(b) −x2 + 7x − 5
Page 3
Math 152
Chapter 5 Handout
Helene Payne
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) x2 − xy + 4x − 4y
(c) 15x2 + 6x − 40xy − 16y
10. Factor each polynomial completely, or state that the polynomial is prime.
(a) x2 + 4x + 3
(b) y 2 + 3y − 18
Page 4
Math 152
Chapter 5 Handout
(c) 3x2 + 27x + 24
(d) 2x2 + 3x + 1
(e) 12x2 − 4x − 5
(f) a2 − 3ab − 10b2
11. Factor each difference of two squares.
(a) x2 − 36
(b) 16x2 − 25y 2
(c) x2 − 1
Page 5
Helene Payne
Math 152
Chapter 5 Handout
Helene Payne
12. Factor each perfect square trinomial.
(a) a2 − 20a + 100
(b) 4x2 + 12x + 9
(c) 16a2 − 40ab + 25b2
13. Factor each polynomial using the formula for the sum or difference of two
cubes.
a3 + b3 = (a + b)(a2 − ab + b2 )
a3 − b3 = (a − b)(a2 + ab + b2 )
(a) x3 + 27
(b) y 3 − 64
(c) 27x3 + 8y 3
Page 6
Math 152
Chapter 5 Handout
14. Use factoring to solve each polynomial equation.
(a) x2 − 6x + 8 = 0
(b) 6x2 + 27x = 0
(c) x3 + x2 = 12x
(d) (x + 9)(x + 1) = 33
(e) 3x4 − 12x2 = 0
Page 7
Helene Payne
Math 152
Chapter 5 Handout
Helene Payne
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 = −16t2 + 48t +
160. When will the object hit the ground?
Page 8
Math 152
Chapter 5 Handout
Helene Payne
Name:
1. For the following polynomial,
3x3 − x2 + 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) 8x3 − 3x2 y + 5y 4
Leading Coefficient:
Degree of polynomial:
(b) 10x7 y 3 + 12x6 y 2 + 2x5 y − 19x4 y 5
Leading Coefficient:
Degree of polynomial:
3. Add the polynomials:
(2x6 − 5x5 + 3x2 − 7x + 3) + (3x6 − 8x4 − x2 − 11x + 2)
4. Subtract the polynomials:
(a) (4x2 + 3x + 7) − (2x2 − x − 5)
(b) (7x3 y 2 − 6x2 y + 6x2 − 9xy + 8) − (12x3 y 2 − 13x2 y 2 − 14x2 y − 11xy + 2)
5. Multiply the polynomials:
(a) (−8x3 y 4 )(−4xy 2 )
(b) 2xy(5xy 2 + 6x2 y − 3xy)
(c) (a − 9)(a2 + 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)
Math 152
Chapter 5 Handout
6. Factor out the greatest common factor from each polynomial:
(a) 15x3 − 10x2 + 25x
(b) 36a2 b3 − 18a3 b + 27a4 b2
7. Factor out the negative of the greatest common factor:
(a) −9x2 + 36y
(b) −x2 + 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) x2 − xy + 4x − 4y
(c) 15x2 + 6x − 40xy − 16y
10. Factor each polynomial completely, or state that the polynomial is prime.
(a) x2 + 4x + 3
(b) y 2 + 3y − 18
(c) 3x2 + 27x + 24
(d) 2x2 + 3x + 1
(e) 12x2 − 4x − 5
(f) a2 − 3ab − 10b2
11. Factor each difference of two squares.
(a) x2 − 36
(b) 16x2 − 25y 2
(c) x2 − 1
Page 2
Helene Payne
Math 152
Chapter 5 Handout
Helene Payne
12. Factor each perfect square trinomial.
(a) a2 − 20a + 100
(b) 4x2 + 12x + 9
(c) 16a2 − 40ab + 25b2
13. Factor each polynomial using the formula for the sum or difference of two cubes.
a3 + b3 = (a + b)(a2 − ab + b2 )
a3 − b3 = (a − b)(a2 + ab + b2 )
(a) x3 + 27
(b) y 3 − 64
(c) 27x3 + 8y 3
14. Use factoring to solve each polynomial equation.
(a) x2 − 6x + 8 = 0
(b) 6x2 + 27x = 0
(c) x3 + x2 = 12x
(d) (x + 9)(x + 1) = 33
(e) 3x4 − 12x2 = 0
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 = −16t2 + 48t + 160. When will the object hit the
ground?
Page 3
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