6A The language of polynomials

6A
The language of polynomials

​6 POLYNOMIALS

POLYNOMIALS

POLY =many | Nomial = term

POLYNOMIAL = many terms

POLYMER = many monomers

​STRATEGY: Find the term with the highest exponent/power/degree = the shape of the graph

Multiple Choice

What type of graph would the following function represent?

$$f\left(x\right)=x^2-3x$$

• Linear

• Parabola / Quadratic

• Cubic

• Quartic

Multiple Choice

What type of graph would the following function represent?

$$f\left(x\right)=3x^3+2x^2−x−3$$

• Linear

• Parabola / Quadratic

• Cubic

• Quartic

Multiple Choice

What type of graph would the following function represent?

$$f\left(x\right)=5−3x+2x^2$$

• Linear

• Parabola / Quadratic

• Cubic

• Quartic

Multiple Choice

What type of graph would the following function represent?

$$f\left(x\right)=2−7x^3+25x$$

• Linear

• Parabola / Quadratic

• Cubic

• Quartic

Multiple Choice

What type of graph would the following function represent?

$$f\left(x\right)=3x^4+8x^3$$

• Linear

• Parabola / Quadratic

• Cubic

• Quartic

Multiple Choice

What type of graph would the following function represent?

$$f\left(x\right)=2x^3−3x^4+2x^2−1$$

• Linear

• Parabola / Quadratic

• Cubic

• Quartic

Give it a try

Give it a try

Math Response

Let $$P(x)=x^3−3x^2−2x+1.$$

Find $$P\left(1\right)$$

Type answer here

Correct Answer: -3

Deg^°

Rad

Math Response

Let $$P(x)=x^3−3x^2−2x+1.$$

Find $$P\left(-1\right)$$

Type answer here

Correct Answer: -1

Deg^°

Rad

Math Response

Let $$P(x)=x^3−3x^2−2x+1.$$

Find $$P\left(2\right)$$

Type answer here

Correct Answer: -7

Deg^°

Rad

Math Response

Let $$P(x)=x^3−3x^2−2x+1.$$

Find $$P\left(-2\right)$$

Type answer here

Correct Answer: -15

Deg^°

Rad

Give it a try

Give it a try

Math Response

Let $$f(x)=x^3−2x^2+x$$
$$g(x)=2−3x$$

$$h(x)=x^2+x$$

Simplify the following:

$$f(x)+g(x)$$

Type answer here

Correct Answer: x^3-2x^2-2x+2

Deg^°

Rad

Math Response

Let $$f(x)=x^3−2x^2+x$$
$$g(x)=2−3x$$

$$h(x)=x^2+x$$

Simplify the following:

$$3f(x)$$

Type answer here

Correct Answer: 3x^3-6x^2+3x

Deg^°

Rad

Math Response

Let $$f(x)=x^3−2x^2+x$$
$$g(x)=2−3x$$

$$h(x)=x^2+x$$

Simplify the following:

$$g(x)h(x)$$

Type answer here

Correct Answer: -3x^3-x^2+2x

Deg^°

Rad

Equating coefficcients

Give it a try