Polynomial Review

Classify

100

What do we use to classify polynomials?

What is highest degree and number of terms

200

Write each polynomial in standard form. Then classify. 7x + 3x + 5

10x + 5, linear binomial

300

Write each polynomial in standard form. Then classify. -4p + 3p + 2p^2

2p^2 - p, quadratic binomial

400

Write each polynomial in standard form. Then classify. 7x^3 - 10x^3 + x^3

-2x^3, cubic monomial

500

7x^3 + 6x^5 - 4x^2 - 3x^4 + 2

6x^5 - 3x^4 + 7x^3 - 4x^2 + 2, quintic poly of five terms

End Behavior

100

What do we look at to describe end behavior?

leading coefficient and degree

200

If the leading coefficient is positive and the degree is even, what is the end behavior?

f(x)--- + infinity, as x --- + infinity f(x)--- + infinity, as x --- - infinity

300

If the leading coefficient is negative and the degree is odd, what is the end behavior?

f(x) --- + infinity, as x --- - infinity f(x) --- - infinity, as x --- + infinity

400

What is the leading coefficient and end behavior? y = -7x^3 + 8x^2 + x

-7x^3 f(x) --- + infinity, as x --- - infinity f(x) --- - infinity, as x --- + infinity

500

What is the leading coefficient and the end behavior? -14x^6 +11x^5 - 11

-14x^6 f(x) --- - infinity, as x --- - infinity f(x) --- - infinity, as x --- + infinity

Roots/Zeros

100

Write each polynomial in factored form. x^3 + 7x^2 + 10x

x(x+5)(x+2)

200

Write the polynomial in factored form. x^3 - 36x

x(x-6)(x+6)

300

Write the zeros of the function. y = (x-1)(x+2)

x = 1, -2

400

Find the zeros of the function. y = (x+1)(x-1)(x-2)

x = -1, 1, 2

500

Write a polynomial function with the given zeros. x = 5, 6, 7

y = x^3 -18x^2 +107x -210

Equations

100

Find all possible solutions to the equation. 64x^3 -1 = 0

see board for answer

200

Find all possible solutions of the equation. x^4 -10x^2 = -9

x = 1, -1, 3, -3

300

Find all the possible solutions of the equation. x^4 - 8x^2 = -16

x = 2, -2, 2i, -2i

400

Find all real solutions of the following equation x^4 - 4x^3 - x^2 + 16x = 12

x = -2, 1, 2, 3

500

Find all real solutions of the following equation. x^3 - x^2 - 16x = 20

x = -2, 5

Dividing

100

(2x^2 + 7x + 11) divided by (x + 2)

2x + 3 + 5/(x+2)

200

(x^3 + 5x^2 +11x + 15) divided by (x+3)

x^2 + 2x + 5

300

(x^3 - x^2 - 4x +4) divided by (x - 2)

x^2 + x - 2

400

(4x^3 +21x^2 - x - 24) divide by (x+5)

4x^2 + x - 6 + 26/(x+5)

500

(9x^3 -15x^2 + 4x) divided by (x-3)

9x^2 + 12x + 40 + 120/(x-3)