6.3 trinomial squares goals: to recognize a trinomial square and be able to factor it remember to...
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6.3 Trinomial Squares
• Goals: To recognize a trinomial square and be able to factor it
• Remember to always factor out a common factor before you see if it is a trinomial square or not!!
Multiply: (x + 3)2
x2 + 9+ 6x
Multiply: (2x - 5)2
4x2 +25
- 20x
Trinomial SquaresTrinomial Squares
Trinomial Squaresx2 + 6x +9
4x2 – 20x + 25
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
Is 4x2 – 20x + 25 a Trinomial Square?
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
Yes!!
Is x2 + 8x + 16 a Trinomial Square?
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
Yes!!
Is x2 - 12x + 4 a Trinomial Square?
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
no
Is 9x2 - 12x + 16 a Trinomial Square?
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
no
Is 9x2 + 24x - 16 a Trinomial Square?
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
no
Is 16x2 + 40xy + 25y2 a Trinomial Square?
a. Two of the terms must be squares (A2 and B2)
b. No minus sign before A2 and B2
c. If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)
yes
To Factor Trinomial Squares:•A2 + 2AB + B2 (A + B)2
•A2 - 2AB + B2 (A - B)2
Factor: x2 + 10x + 25
(x + 5)2
To Factor Trinomial Squares:•A2 + 2AB + B2 (A + B)2
•A2 - 2AB + B2 (A - B)2
Factor: x2 - 8x + 16
(x - 4)2
To Factor Trinomial Squares:•A2 + 2AB + B2 (A + B)2
•A2 - 2AB + B2 (A - B)2
Factor: 4x2 + 12x + 9
(2x + 3)2
To Factor Trinomial Squares:•A2 + 2AB + B2 (A + B)2
•A2 - 2AB + B2 (A - B)2
Factor: 2x2 + 12x + 18
2(x + 3)2
2(x2 + 6x + 9)
Factor: x2 - 8x + 16
( - )2x 4
Check your answer using FOIL (x – 4)(x – 4)
Factor: 4x2 + 12x + 9
(2x + 3)2
2
first term last term
Factor: 9x2 + 30xy + 25y2
(3x + 5y)2
2
first term last term
Factor: 2x2 + 12x + 18
2(x + 3)2
2(x2 + 6x + 9)
Assignment:Page 2714-42 even