Chapter 8: Quadratic Expressions and Equations

Adding and Subtracting Polynomials

100

Find (2a - 5) - (3a + 1)

-a - 6

200

Simplify 3(x^2 + 2x) - x(x - 1)

2x^2 + 7x

300

Find (9t^2 + 4t - 6) - (t^2 - 2t + 4)

8t^2 + 6t - 10

400

Put in standard form: 4x^3 - 6x + 2x^5 + 3

2x^5 + 4x^3 - 6x + 3

500

Simplify: 2a^2(5a - 6) - 5a(a^2 - 3a +4) - 7(a - 5)

5a^3 + 3a^2 - 27a +35

Multiplying polynomials

100

Find 3m^2(2m^2 - m)

6m^4 - 3m^3

200

Find (2n - 3)(n + 4)

2n^2 + 5n - 12

300

Find (3y - 1) ^ 2

9y^2 - 6y + 1

400

Each side of a square x units long is decreased by 9 units. Which expression represents the area of the new square in square units?

x^2 - 18x + 81

500

Simplify: 5n^2(n - 6) - 2n(3n^2 + n - 6) + 7(n^2 - 3)

-n^3 - 25n^2 + 12n - 21

Misc

100

Factor: 12x^3y^2z - 24x^2y^3z + 16x^2y^3z^3

4x^2y^2z(3x - 6y + 4yz^2)

200

Factor - x^2 + 5x + 24

- (x - 8)(x + 3)

300

Factor if possible, if not, write "prime" 10x^2 + 29x - 21

(5x - 3)(2x + 7)

400

If a^2 + b^2 = 11 and ab = 3, find the value of (a - b)^2

5

500

Find an expression for c that will make 9x^2 + 12xy + c a perfect square trinomial.

4y^2

Factoring

100

The area of a rectangle is (y^2 - 8y + 15). Find an expression for the length and width of the rectangle.

(y - 3)(y - 5)

200

Factor xy + 3x - 2x^2 completely

x(y + 3 - 2x)

300

Factor m^2 + 13m + 42

(m + 6)(m + 7)

400

Factor 121r^3 - 64t^2

(11r + 8t)(11r - 8t)

500

Factor: 3x^4 - 73x^2 - 50

(x + 5)(x - 5)(3x^2 + 2)

Solving

100

Solve 6x^2 = 22x

{0, 11/3}

200

Solve x^2 + 8x/3 = -7/9

{-7/3, -1/3}

300

Solve a^2 - 11a/2 + 121/16 = 0

{11/4}

400

Solve (2x - 3)^2 - 25 = 0 by factoring.

{-1, 4}

500

The volume of a box is 96 cubic inches. The length is 8 inches more than the height. The width is 2 inches less than the height. Find the dimensions of the box.

12 in x 2 in x 4 in