Chapter 5 Polynomial Functions

Operations With Polynomials

100

Simplify 

(10x² + 5x) + (13x² + 4x +3)

What is 

23x² + 9x + 3

200

Simplify 

(7x³ - 2x² + x) - (4x³ + 5x² -4)

What is 

3x³ - 7x² + x + 4

300

Simplify 

(5x³)³(2y²)

What is 

250x⁶y2          

400

Simplify 

3xy² (5x² + 3y - 2)               

What is 

15x³y² + 9xy³ - 6xy²

500

Simplify 

(24x²y⁴ - 12x³y³ +6xy²) / (3x²y²)

What is

8y² - 4xy + 2/x 

Dividing Polynomials

100

Find the quotient of 

(a² - 8a - 26) / (a + 2)

What is 

a - 10 - (6/a+2)

200

Simplify 

(z⁴ - 3z³ + 2z² - 4z + 4) / (z - 1)

What is 

z³ - 2z² - 4

300

Simplify 

(y³ + 11y² - 10y + 6) / (y + 2)

What is 

y² + 9y - 28 + (62/y + 2)

400

Simplify 

(x⁵ - 4x³ + 4x²)(x - 4)^-1

What is 

x⁴ + 4x³ + 12x² +52x + 208 + (832/x - 4)

500

CURVE BALL

Simplify Using Long Division

(x⁴ + x³ - 6x² - 4x +14) / (x² + x - 2)

What is

x² - 4 + (6/(x² + x - 2))

End Functions

100

What is g(3) of g(x)=x^2-8x+6?

-9

200

What is g(3) and g(-4) of the function g(x)=x^6-4x^4+3x^2-10?

422 and 3110

300

What is the remaining factors of the polynomial x^3+x62-16x-16 if x+4 is a factor?

x-4 and x+1

400

What is the remaining factors of the polynomial 16x^5-32x^4-81x+162 if x-2 is a factor?

2x-3, 2x+3, 4x^2+9

500

What is when a certain type of plastic is cut into sections, the length of each section determines its strength? The function f(x) = x^4-14x^3+69x^2-140x+100 can describe the relative strength of a section of length x feet. Sections of plastics x feet long, where f(x) = 0, are extremely weak. After testing the plastic, engineers discovered that sections 5 feet long are extremely weak. Are there other lengths of plastic that are extremely weak? If so what are they?

What is (x-2) x=2 feet

Types of Roots

100

What is the number and type of roots of x²+5x-6=0?

Waht is

2 real roots, 1 and -6

200

What is type and number of real roots of x^2-8x+16=0?

Two real roots, double root, -4

300

What is type and number of roots of x^3+2x=0?

One real root, 0, and to two imaginary roots, plus or minus i square root of  2

400

What is type and number of roots of x^4-1=0?

Two real roots, 1 and -1, and two imaginary roots, i and -i

500

What is the number of positive and negative zeros of x^5-6x^4-3x^3+7x^2-8x+1?

There are 4, 2, or 0 positive roots and exactly 1 negative real root.

Zeros

100

What are all the roots of g(x) = x^4-6x^3+12x^2+6x-13?

3-2i, 3+2i, -1, 1

200

What are the roots of f(x)=2x^3-17x^2+90x-41?

1/2, 4+5i, 4-5i

300

What is the polynomial of least degree with integral coefficients that has the given zeros of 9, 1+2i?

f(x)=x^3-11x^2+23x-45

400

What is polynomial function of least degree with integral coefficients that has the given zeros of -2, 2, 4, 6?

f(x)=x^4-10x^3+20x^2+40x-96

500

What are all the rational zeros of 

4x³ - 3x² - 100x + 75

What is 

-5,5, 3/4