Warm Up Determine whether the following are perfect squares. If so, find the square root. 64 yes; 8 2. 36 yes; 6 3. 45 no 4. x2 yes; x 5. y8 yes; y4 6. 4x6 yes; 2x3 7. 9y7 no 8. 49p10 yes;7p5

Find the degree of each polynomial. A. 11x7 + 3x3 D. x3y2 + x2y3 – x4 + 2 7 5 B. 4 C. 5x – 6 1 The degree of a polynomial is the degree of the term with the greatest degree.

Objectives Factor perfect-square trinomials. Factor the difference of two squares.

A trinomial is a perfect square if: • The first and last terms are perfect squares. • The middle term is two times one factor from the first term and one factor from the last term. 9x2 + 12x + 4 3x 3x 2(3x 2) 2 2 •

Determine whether each trinomial is a perfect square. If so, factor Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9x2 – 15x + 64 8 8 3x 3x 2(3x 8)  2(3x 8) ≠ –15x.  9x2 – 15x + 64 is not a perfect-square trinomial because –15x ≠ 2(3x  8).

The trinomial is a perfect square. Factor. Determine whether each trinomial is a perfect square. If so, factor. If not explain. 81x2 + 90x + 25 5 5 9x 9x 2(9x 5) ● The trinomial is a perfect square. Factor. 81x2 + 90x + 25

Determine whether each trinomial is a perfect square. If so, factor Determine whether each trinomial is a perfect square. If so, factor. If not explain. 36x2 – 10x + 14 The trinomial is not a perfect-square because 14 is not a perfect square.

The trinomial is a perfect square. Factor. Determine whether each trinomial is a perfect square. If so, factor. If not explain. x x 2 2  2(x 2) x2 + 4x + 4 The trinomial is a perfect square. Factor.

A rectangular piece of cloth must be cut to make a tablecloth A rectangular piece of cloth must be cut to make a tablecloth. The area needed is (16x2 – 24x + 9) in2. The dimensions of the cloth are of the form cx – d, where c and d are whole numbers. Find an expression for the perimeter of the cloth. Find the perimeter when x = 11 inches. 16x2 – 24x + 9 16x2 – 24x + 9

A polynomial is a difference of two squares if: In Chapter 7 you learned that the difference of two squares has the form a2 – b2. The difference of two squares can be written as the product (a + b)(a – b). You can use this pattern to factor some polynomials. A polynomial is a difference of two squares if: There are two terms, one subtracted from the other. Both terms are perfect squares. 4x2 – 9 2x 2x 3 3 

Recognize a difference of two squares: the coefficients of variable terms are perfect squares, powers on variable terms are even, and constants are perfect squares. Reading Math

Determine whether each binomial is a difference of two squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 3p2 – 9q4 3p2 is not a perfect square. 3p2 – 9q4 is not the difference of two squares because 3p2 is not a perfect square.

Determine whether each binomial is a difference of two squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 100x2 – 4y2 2y 2y  10x 10x The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). 100x2 – 4y2 = (10x + 2y)(10x – 2y)

Determine whether each binomial is a difference of two squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. x4 – 25y6 5y3 5y3  x2 x2 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). x4 – 25y6 = (x2 + 5y3)(x2 – 5y3)

Determine whether each binomial is a difference of two squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 1 – 4x2 The polynomial is a difference of two squares. 2x 2x  1 1 Write the polynomial as (a + b)(a – b). 1 – 4x2 = (1 + 2x)(1 – 2x)

Determine whether each binomial is a difference of two squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. p8 – 49q6 7q3 7q3 ● p4 p4 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). p8 – 49q6 = (p4 + 7q3)(p4 – 7q3)

Check It Out! Example 3c Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 16x2 – 4y5 16x2 – 4y5 4x  4x 4y5 is not a perfect square. 16x2 – 4y5 is not the difference of two squares because 4y5 is not a perfect square. HW pp. 562-564/13-29 odd,46-50,55-64