4/15 Alg2: Checking for Factors of Polynomials

Checking for Factors of Polynomials

The remainder tells all!

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can check whether or not a binomial is a factor of a polynomial.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Is it a factor?

If it is a factor, what is the remainder?

Let's use synthetic division to divide together.

This is one of two methods we can use!

Multiple Choice

What is the remainder, according to our work?

• 0

• 1

• -6

• 6

Multiple Choice

Is the binomial, (x - 6), a factor of the polynomial, P(x)?

• Yes, because the remainder is zero.

• No, because the remainder is NOT zero.

Let's use direct substitution to determine if the binomial is a factor.

This is the second method we can use! Does P(a) = 0?

Multiple Choice

Is the binomial, (x - 6), a factor of the polynomial, P(x)?

• Yes, because  $P\left(6\right)\ =\ 0$  

• No, because  $P\left(6\right)\ne0$  

Another Example

We won't do both methods again, but think... How do I know if it is a factor?

Here is the work. Now think to yourself, answer on the next slide: Is (x+3) a factor of P(x)?

Multiple Choice

Is (x+3) a factor of P(x)?

• Yes, because $P\left(-3\right)=0$

• No, because $P\left(-3\right)\ne0$

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can check whether or not a binomial is a factor of a polynomial.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Debrief

• Learning Target: I can check whether or not a binomial is a factor of a polynomial.

• Use synthetic division OR direct substitution.

• If the remainder from synthetic division is 0, it IS a factor.

• If P(a) = 0 from direct substitution, it IS a factor.

Great work! Complete your exit ticket and enjoy your Thursday!!!!