Page 452 – Factoring Special Polynomials Objectives Factor perfect-square trinomials. Factor the difference of two squares.

Glossary Terms perfect-square trinomial – a trinomial in the form a² + 2ab + b² difference of two squares – a polynomial in the form a² - b²

Rules and Properties Rule for Factoring a Perfect-Square Trinomial a2 + 2ab + b2 = (a + b)(a + b) = (a + b) 2 a2 – 2ab + b2 = (a – b)(a – b) = (a – b) 2

How to tell if it is a perfect square trinomial 4x² + 12x + 9 1) Are there three terms (trinomial)? yes 2) Is the first term a perfect square? yes 3) Is the last term a perfect square? yes 4) Is the square root of the first term, times the square root of the last term, times 2, equal to the middle term? yes Since the answer to all the questions is yes, 4x² + 12x + 9 is a perfect square trinomial.

To factor a perfect square trinomial 4x² + 12x + 9 1) Write the square root of the first term. 2) Write the sign of the middle term. 3) Write the square root of the last term. 4) Put parentheses around it and square it. ( )² 2x + 3

State whether each term is a perfect square trinomial. If not, explain. x² + 8x + 16 3x² + 16x + 16 yes no , the first term is not a perfect square x² + 3x + 9 x² + 10x - 25 , the square root of the first times the square root of the last times 2 does not equal the middle term no , the last term must always be positive no

Factor each expression x² - 10x + 25 ( )² x - 5 49y4 + 14y² + 1 ( )² 7y + 1

Rules and Properties Rule for Factoring a Difference of Two Squares a2 – b2 = (a + b)(a – b)

How to tell if it’s the difference of 2 squares 4y² - 49 1) Are there two terms? yes 2) Is the first term a perfect square? yes 3) Is the last term a perfect square? yes 4) Is there a minus sign between them? yes Since the answer to all the questions is yes, 4y² - 49 is the difference of two squares.

How to factor the difference of two squares. 4x² - 49 1) Write the square root of the first term. 2) Plus 3) Write the square root of the last term. 4) Times (Use parentheses) 5) Write the square root of the term. 6) Minus 7) Write the square root of the last term and close the parentheses. ( ) ( 2x + 9 2x - 9)

Tell whether each of the following is the difference of two squares yes 9x² - 15 the last term, 15, is not a perfect square no, 16r² + 49 there is not a minus sign between them no,

Factor each expression + 2 ) ( x - 2) 36a² - 49b² (6a + 7b ) ( 6a - 7b) 25w² - 81 (5w + 9) (5w – 9)

ASSIGNMENT Page 455 – 457 # 18 – 38, 44 – 48,