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Objectives
Factor perfect-square trinomials.Factor the difference of two
squares.
Page 452 – Factoring Special Polynomials
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Glossary Terms
perfect-square trinomial – a trinomial in the form a² + 2ab + b²
difference of two squares – a polynomial in the form a² - b²
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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
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How to tell if it is a perfect square trinomial
4x² + 12x + 91) 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, equalto the middle term? yes
Since the answer to all the questions is yes, 4x² + 12x + 9 is a perfect square trinomial.
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To factor a perfect square trinomial4x² + 12x + 9
1) Write the square root of the first term.
2x
2) Write the sign of the middle term.
+
3) Write the square root of the last term.
3
4) Put parentheses around it and square it.
( )²
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State whether each term is a perfect square trinomial. If not,
explain.
x² + 8x + 16
yes
3x² + 16x + 16
no , the first term is not a perfect square
x² + 3x + 9
no , the square root of the first times the square root of the last times 2 does not equal the middle term
x² + 10x - 25
no , the last term must always be positive
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Factor each expression
x² - 10x + 25
x - 5( )²
49y4 + 14y² + 1
7y + 1( )²
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Rules and PropertiesRule for Factoring a Difference of Two Squares
a2 – b2 = (a + b)(a – b)
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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.
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How to factor the difference of two squares.
4x² - 49
1) Write the square root of the first term.
2x
2) Plus
+
3) Write the square root of the last term.
9
4) Times (Use parentheses)
( ) (
5) Write the square root of the term.
2x
6) Minus
-
7) Write the square root of the last term and close the parentheses.
9)
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Tell whether each of the following is the difference of two squares
4a² - 25yes
9x² - 15
no, the last term, 15, is not a perfect square
16r² + 49
no, there is not a minus sign between them
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Factor each expression
x² - 4
(x + 2) ( x - 2)
36a² - 49b²
(6a + 7b) (6a - 7b)
25w² - 81
(5w + 9) (5w – 9)
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ASSIGNMENT
Page 455 – 457– # 18 – 38, 44 – 48,