Section P.6 Homework

1. The Special Factoring Formula for the “difference of squares” is A² − B² 

So 25x² − 4 factors as

2.  Factor out the common factor. (Factor your answer completely.)  4a − 8

3.   Factor out the common factor. (Factor your answer completely.)  y(y − 8) + 2(y − 8)

4.   Factor the difference of squares.  49a² − 4

5.   Factor the perfect square.  w² − 6w + 9

6.   Factor the sum of cubes. 1 + 125y³

^7. Factor the expression completely. Begin by factoring out the lowest power of each common factor.  3x^−1/2 + 4x^1/2 + x^3/2

8.  Factor the expression completely.  x² − 3x − 4

9.   Factor the expression completely.  y² − 8y + 12

10.   Factor the expression completely.  9x² − 54x − 63

11.   Factor the expression completely.  x⁶ − 125y³  

^{12  Factor the expression completely.} y³ − 2y² − 25y + 50

^13.   Factor the expression and simplify.  (a² − 1)b² − 64(a² − 1)

^{14.   Factor the expression completely. (This type of expression arises in calculus in using the “product rule.”)} 3x²(8x − 24)² + x³(2)(8x − 24)(8)

^15.   Factor out the common factor. (Factor your answer completely.)  −6x⁴y² + 48xy³ + 54xy⁴

^16.  Factor the trinomial.  x² + 8x − 65

^17.   Factor the trinomial. 3x² − 2x − 5

^18.   Factor the trinomial.  7x² − 9x − 10

19.   Factor the difference of squares.  a² − 49b²

^20.   Factor the difference of squares.  (x + 9)² − y²

^21.   Factor the difference of cubes.  64r³ − 8t⁶

^22.  Factor the expression by grouping terms. 10x³ + 5x² + 2x + 1

23.   Factor the expression completely. Begin by factoring out the lowest power of each common factor.  4x^−3/2 + 4x^−1/2 + x^1/2

^24.   Factor the expression completely. Begin by factoring out the lowest power of each common factor.  (x − 3)^7/2 − 9(x − 3)^3/2

^25.   Factor the expression completely. Begin by factoring out the lowest power of each common factor.  x^−1/2(x + 5)^1/2 + x^1/2(x + 5)^−1/2

^26.   Factor the expression completely. Begin by factoring out the lowest power of each common factor.  2x^1/3(x − 8)^2/3 − 3x^4/3(x − 8)^−1/3

^27.  Factor the expression completely. Begin by factoring out the lowest power of each common factor. 6x^−1/2(x² + 3)^5/4 − x^3/2(x² + 3)^1/4

^28.   Factor the expression completely. (This type of expression arises in calculus in using the “product rule.”)  3(2x − 9)²(2)(x + 3)^1/2 + (2x − 9)³