Factoring Special Factoring Special PolynomialsPolynomials

Holt Text pages 452-454Holt Text pages 452-454

Perfect Square PolynomialsPerfect Square Polynomials

ExamplesExamples(x+2)(x+2)22

(x-3)(x-3)22

TerminologyTerminology

Perfect Square PolynomialsPerfect Square PolynomialsFirst term is a perfect squareFirst term is a perfect square

Last term is also a perfect squareLast term is also a perfect square

Middle Term: Multiply the square root of Middle Term: Multiply the square root of the first and last terms, then double it.the first and last terms, then double it.

Is Is xx22 + 12x + 36 + 12x + 36 a perfect square a perfect square polynomial?polynomial?

xx22+8+8x+16x+16

What is the square root of:What is the square root of:xx22??

16?16? What is 2(x)(4)?What is 2(x)(4)? Is Is xx22+8+8x+16 a perfect square.x+16 a perfect square.

3x3x22+3+3x+16x+16

What is the square root of:What is the square root of:3x3x22??

16?16?

Is 3Is 3xx22+16+16x+16 a perfect square?x+16 a perfect square?

xx22+3+3x+9x+9

What is the square root of:What is the square root of:xx22??

16?16? What is 2(x)(4)?What is 2(x)(4)? Is Is xx22+8+8x+16 a perfect square?x+16 a perfect square?

Factor 9xFactor 9x22+24+24x+16x+16

Since the sq. root of 9xSince the sq. root of 9x2 2 is 3xis 3x Since the sq. root of 16 is 4Since the sq. root of 16 is 4 (3x+4)(3x+4)22 equals the above polynomial. equals the above polynomial.

Factor 64xFactor 64x44-16-16xx22y+yy+y22

Since the sq. root of 64xSince the sq. root of 64x4 4 is 3xis 3x Since the sq. root of ySince the sq. root of y22 is 4 is 4 (8x(8x22+y)+y)22 equals the above equals the above

polynomial.polynomial.

Difference of Two SquaresDifference of Two Squares

Factor 4xFactor 4x22-25-25 Negative constants have a negative Negative constants have a negative

and positive factorand positive factor Positive square numbers have two Positive square numbers have two

positive factorspositive factors

Factor 4xFactor 4x22-25-25

The square root of the first term: 4xThe square root of the first term: 4x The positive and negative factors of -The positive and negative factors of -

25 are -5 and +525 are -5 and +5 This converts to (2x-5)(2x+5)This converts to (2x-5)(2x+5) Notice the only difference between Notice the only difference between

the difference of two squares and the difference of two squares and (2x+5)(2x+5).(2x+5)(2x+5).

Factor 16xFactor 16x22-49-49

The square root of the first term: 4xThe square root of the first term: 4x The positive and negative factors of -The positive and negative factors of -

49 are -7 and +749 are -7 and +7 This converts to (4x-7)(4x+7)This converts to (4x-7)(4x+7)

Factor xFactor x22-4-4

The square root of the first term: xThe square root of the first term: x The positive and negative factors of -The positive and negative factors of -

49 are -2 and +249 are -2 and +2 This converts to (x-2)(x+2)This converts to (x-2)(x+2)

Factor 81xFactor 81x22-64-64

The square root of the first term: 9xThe square root of the first term: 9x The positive and negative factors of -The positive and negative factors of -

64 are -8 and +864 are -8 and +8 This converts to (9x-8)(9x+8)This converts to (9x-8)(9x+8)