In this lesson we will factor polynomials

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Presentation transcript:

In this lesson we will factor polynomials To factor polynomials, we must first learn to divide monomials

Simplify the expression Write the expression without exponents

Now cancel to simplify the expression 4

Next, we will factor polynomials What does each term in the polynomial have in common? 3x3 + 6x2 + 9x

Each term is divisible by 3 and x We can ‘factor out’ the greatest common factor. 3x3 + 6x2 + 9x 3x(x2 + 2x + 3)

Factor out the greatest common factor in this polynomial 15x2 – 12x3 Each term contains the factor 3x2 3x2(5 – 4x)

The polynomial is modeled x2 + 4x + 3 What are the factors?

Place x’s and 1’s on the top and left side to model the factors x2 + 4x + 3 x + 3 x +1

Write the polynomial as the product of two binomials x + 3 x2 + 4x + 3 x +1 (x + 3)(x + 1)

Factor the polynomial x2 + 6x + 9

Write as a product of binomials x2 + 6x + 9 (x + 3)(x + 3) or (x + 3)2

Factor out the greatest common factor -15x2 + 35x Since the expression begins with a negative, factor out –5x -5x(3x – 7)

We can also factor with a box 6x2 + 4x + 3x + 2 First, place the polynomial in a box 6x2 4x 3x 2

Next factor out the greatest common factor 6x2 + 4x + 3x + 2 3x + 2 2x +1 6x2 4x 3x 2

Write the polynomial as the product of two binomials 6x2 + 4x + 3x + 2 (3x + 2)(2x + 1) 3x + 2 2x +1 6x2 4x 3x 2

Complete Activity 9c Divide Monomials Factor out the Greatest Common Factor Factor Polynomials with Algebra tiles Factor Polynomials with a box