Polynomials

Polynomial End Behavior

100

The leading coefficient is positive when this end behavior is seen. (2 answers)

x -> \infty, y -> \infty

Drawing acceptable.

200

The degree of a polynomial is this when both ends of a polynomial point up or down.

What is even

300

This is the degree and this the leading coefficient of the polynomial x²-5x⁴-7x⁸

What is Degree 8 and LC -7?

400

This is the end behavior of the polynomial 3x⁴+5x²+2

What is x -> \infty, y -> infty and x -> - \infty, y -> \infty?

Drawing acceptable.

500

This is the end behavior to the polynomial 2x³-5x⁵-(1/3)x⁷

What is x -> \infty, y -> - \infty and x -> - \infty, y -> \infty?

Drawing acceptable.

Synthetic Division

100

(x²-x+1) divided by (x-1) has this remainder

What is one.

200

This is (x^3+3x^2+3x+1) divided by (x+1).

What is (x^2+2x+1).

300

Show that (x+2) is a factor of (x²+4x+4).

See work.

400

This is (x²+2x+1) divided by (x+1).

What is (x+1)?

500

This is (3x³+2x²+x+7) divided by (x-2).

What is 3x²+8x+17+(41/x-2)

Polynomial Long Division

100

This is (x²-2x+2) divided by (x-1).

What is x-1+(1/x-1)

200

Show that (x+3) is a factor of x^2+6x+9.

See work.

300

This is (x³+x²+x+1) divided by (x+2)

What is x²-x+3-(5/x+2)

400

This is x²+2x+1 divided by x+1

What is x+1?

500

This is 4x³+2x²+5 divided by (x-2)

What is 4x²-10x+20+(45/x-2)

Factoring Polynomials

100

This is the fully factored form of 4x²-9

What is (2x+3)(2x-3)?

200

This is the fully factored form of x²-6x+5.

What is (x-5)(x-1)?

300

This is the fully factored form of 4x⁴-9x²

What is x²(2x-3)(2x+3)?

400

This is the fully factored form of 8x³+8x²+2x.

What is x(4x+2)(2x+1)?

500

(x²+5x+4)(x²+3x+2) is this in its fully factored form.

What is (x+4)(x+1)(x+1)(x+2)

Solving Polynomials

100

These are the solutions to x(x+1)(x+2).

What are 0,-1, -2?

200

These are the solutions to x²+2x+1

What is -1

300

This is the equation to polynomial with roots 0, -2, 3/2, and 3/2

What is x(x+2)(2x-3)²?

400

This is an equation for polynomial with solutions 10, 1/2, 4/5, and -2

What is (x-10)(2x-1)(4x-5)(x+2)?

500

This is an equation for polynomial with repeated solutions whose graph touches but does not pass through the x axis at x=-2.

What is (x+2)ⁿ

where n is an even number.