Quiz 5-3 1. Simplify: 2. Simplify: Simplify (special pattern):

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Presentation transcript:

Quiz 5-3 1. Simplify: 2. Simplify: Simplify (special pattern):

Section 5-4 Factor and solve Polynomial Equations

Vocabulary Prime Polynomial: A polynomial where the coefficient of each term has no common factor with any other coefficients and… it cannot be factored into polynomials of lesser degree. (There is no number (other than +1 or -1) that is common to all of these terms.) This is important because if you can factor out the common term, it will end up being easier to factor the polynomial.

NOT a prime polynomial 3 is a common factor of each term We can “factor out” the 3

Prime vs. Not Prime Polynomials: Example: is prime because it cannot be factored. Example: is not prime because it can be factored.

Your Turn: Are these prime polynomials or not? If not, write it in factored form. 1. 2.

More Vocabulary Factored completely: a polynomial is factored completely if it is written as the product of a monomial and one or more prime polynomials. Example: Can this be factored?

Your Turn: 3. Factor this polynomial completely

Move Vocabulary Factor by grouping: some polynomials can be factored easily if they have pairs of terms that have a common monomial factor. What’s the common monomial factor here? What’s the common monomial factor here? Are both of these factors prime? Do these two expressions have a common factor?

Hints on factoring by grouping You need two pairs of terms in order to factor by grouping If they give you a 4 term polynomial, try factoring by grouping.

Your turn: (problems 2 and 3 in the green book) 4. Factor

Special Patterns (we learned these last time) Sum of 2 “cubes” Difference of 2 “cubes” Difference of 2 “squares”

Your turn: Factor completely (special pattern) 5. 6. (prob. #1 pg 143 green book) 5. 6.

What does solving a polynomial mean? Where does the polynomial cross the x-axis.

Solve by factoring Solve  rewrite the equation so that it = 0 Factor the polynomial Use the Zero product rule to find the solution. How many times does this polynomial cross the x-axis? x = 3, -3, 1, -1

Your turn: 7. Solve the polynomial. (problem #4 on green book page 143)