factoring lesson + rational discontinuities

Factoring Rationals

Factoring Technique

Divide and Slide

I want to try out another factoring technique to see if that helps with factoring. It is called the "divide and slide". The steps will be on the next page

​1. list out a, b, and c
2. multiple a and c and factor the product
3. find the sum to make b
4. Do the "divide and slide"

Dropdown

Identify the values for a, b, and c

$$x^2+8x+15$$

a=​

Select answer

b=​

Select answer

c=​

Select answer

Math Response

$$x^2+8x+15$$

if a = 1, b = 8, and c = 15, what is

$$a\cdot c=$$

Type answer here

Correct Answer: 15

Deg^°

Rad

Math Response

$$x^2+8x+15$$

What are the factors for this quadratic?

Type answer here

Correct Answer: \left(x+3\right)\left(x+5\right)

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Rad

Math Response

$$3x^2+11x+6$$

What are the factors for this polynomial?

Type answer here

Correct Answer: \left(3x+2\right)\left(x+3\right)

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Math Response

Factor

$$x^2-19x+18$$

Type answer here

Correct Answer: \left(x-1\right)\left(x-18\right)

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Math Response

Factor

$$2x^2+11x+5$$

Type answer here

Correct Answer: \left(2x+1\right)\left(x+5\right)

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Rad

Math Response

Factor the following rational equation

$$\frac{x^2-4}{x^2-6x-16}$$

Type answer here

Correct Answer: \frac{\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-8\right)}

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Rad

Math Response

If

$$\frac{x^2-4}{x^2-6x-16}=\frac{\left(x+2\right)\left(x-2\right)}{\left(x-8\right)\left(x+2\right)_{ }}$$ At what x value will there be a removable discontinuity?

Be sure to answer as "x=a"

Type answer here

Correct Answer: x=-2

Deg^°

Rad

Math Response

If

$$\frac{x^2-4}{x^2-6x-16}=\frac{\left(x+2\right)\left(x-2\right)}{\left(x-8\right)\left(x+2\right)_{ }}$$ At what x value will there be a vertical asymptote?

Be sure to answer as "x=a"

Type answer here

Correct Answer: x=8

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Rad

Math Response

Factor the following rational equation entirely

$$\frac{2x^2+5x-3}{3x^2+5x-12}$$

Type answer here

Correct Answer: \frac{\left(2x-1\right)\left(x+3\right)}{\left(x+3\right)\left(3x-4\right)}

Deg^°

Rad

Math Response

If

$$\frac{2x^2+5x-3}{3x^2+5x-12}=\frac{\left(2x-1\right)\left(x+3\right)}{\left(x+3\right)\left(3x-4\right)}$$ Then at what x value will there be a removable discontinuity? be sure to answer in the format "x=a":

Type answer here

Correct Answer: x=-3

Deg^°

Rad

Math Response

If

$$\frac{2x^2+5x-3}{3x^2+5x-12}=\frac{\left(2x-1\right)\left(x+3\right)}{\left(x+3\right)\left(3x-4\right)}$$ Then at what x value will there be a vertical asymptote? be sure to answer in the format "x=a":

Type answer here

Correct Answer: x=\frac{4}{3}

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Rad

Open Ended

Given that $$f\left(x\right)=\frac{x^2-16}{x^2-x-12}$$ , how many removable discontinuities does f(x) have? How many vertical asymptotes are in f(x)? Be sure to explain what how you knew those discontinuities existed. [Answer in complete sentences]