Polynomial Operations

All About Polynomials

100

What type of polynomial is this?

4x²+6x+7

Trinomial

200

What is the degree of this polynomial?

3x⁵+6x³-x²

5

300

Write this polynomial in standard form.

x²-3x+11x⁵-7+14x³

11x⁵+14x³+x²-3x-7

400

What type of polynomial is this?

15-2x²

Binomial

500

What degree is this polynomial?

5x²+4x³y⁴-7xy⁵

7

Addition and Subtraction

100

Simplify the following:

(x²+2x)+(6x²-5)

7x²+2x-5

200

Simplify the following:

(3x²+4x)-(6x²-2)

-3x²+4x+2

300

Simplify the following:

(5-9x²)+(4x²+6x-3)

-5x²+6x+2

400

Simplify the following:

(-s²-3)-(2s²+10s)

-3s²-10s-3

500

Simplify the following:

(x²-2x+3)+(4x+1)-(3x²-2x)

-2x²+4x+4

Monomial X Polynomial

100

Simplify the following:

2(3x-5)

6x-10

200

Simplify the following:

-4x²(3x+11)

-12x³-44x²

300

Simplify the following:

2xy(5x²-7)

10x³y-14xy

400

Simplify the following:

-3x(6x³-2xy+10)

-18x⁴+6x²y-30x

500

Simplify the following:

5x²(x³+4x-3)+2x³(6x-7x²-4)

-9x⁵+2x⁴+12x³

Polynomial Multiplication

100

Simplify the following:

(x+3)(x-2)

x²+x-6

200

Simplify the following:

(x-3)(2x+3)

2x²-3x-9

300

Simplify the following:

(-11x+3)(-10x²-7x-9)

110x³+47x²+78x-27

400

Simplify the following:

(-6x⁴+5x²+3x)(x+4)

-6x⁵-24x⁴+5x³+23x²+12x

500

Simplify the following:

(2x²+3x+4)(x²+2x+6)

2x⁴+7x³+22x²+26x+24

Special Cases &Word Problems

100

Find the product.

(2x-3)²

4x²-12x+9

200

Find the product.

(5x+3)(5x-3)

25x²-9

300

Use the difference of two squares to find the product of 22 and 18.

(20+2)(20-2)=(20)²-(2)²=396

400

A portrait without its frame has a height 3 times its width w, in inches. Its frame is 1 in. wide all along its perimeter. What is an expression for the area of the framed portrait in terms of w?

3w²+8w+4

500

A square picture has a 2-inch frame around it. If the area of the frame alone is 48 in.², what is the area of the picture?

16in²