course Mth 158

R.51.If factored completely, 3x^3-12x=?3x(x^2-4)= 3x(x-2)(x+2)

4. True or False: 3x^3-2x^2-6x+4=(3x-2) (x^2+2)..False

Factor each polynomial by removing the common monomial factor.

7.ax^2+a=a(x^2+1) 10.x^3-x^2+x= x(x^2-x+1) 13.3x^2y-6xy^2+12xy= 3xy(x-2y+4)

Factor the difference of two squares

16. x^2-4= (x+2) (x-2) 19.x^2-16= (x-4) (x+4) 22. 36x^2-9= (6x-3) (6x+3)

Factor the perfect squares

25. x^2+4x+4= (x+2)^2 28.x^2+10x+25= (x+5)^2 31.16x^2+8x+1= (4x+1)^2

Factor the sum or difference of two cubes

34.x^3+125= (x+5) (x^2-5x+25) 37.8x^3+27= (2x+3)(4x^2-6x+9)

Factor each polynomial

40. x^2+6x+8= (x+4) (x+2) 43.x^2+7x+10= (x+5) (x+2) 46.x^2-17x+16= (x-16) (x-1)

49. x^2+7x-8= (x+8) (x-1)

Factor by grouping

52. 3x^2-3x+2x-2= 3x(x-1)+2(x-1)= (x-1) (3x+2) 55.6x^2+9x+4x+6= 3x(2x+3)+2(2x+3)= (2x+3) (3x+2)

Factor each polynomial

58. 2x^2+3x+1= x(2x+3)+1=(2x+3)(x+1) 61. 3x^2+2x-8=(3x-4)(x+2) 64.3x^2-10x+8=(3x-4) (x-2)

67.3x^2+10x-8= (3x-2)(x+4)

Factor completely each polynomial. If the polynomial cannot be factored, say it is prime.

70.x^2-9= (x-3) (x+3) 73.x^2+7x+10= (x+2) (x+5) 76.x^2-6x+8= (x-4)(x-2)

79. x^2+4x+16.. prime?no factors of 16, that will get the sum of 4

82. 14+6x-x^2.. prime 85.y^4+11y^3+30y^2=y^2(y^2+11y+30)=y^2(y+5)(y+6)

88.9x^2-12x+4= 3x(3x-4)+4=(3x-4)(3x+4)