Question #7637

Factor:
1. x2 + 13x + 42
2. x2 + 15x + 54
3. x2 + 7x + 12
4. x2 - 6x + 8
5. m2 + 6m+ 8
Special Factors:
6. x2 + 14x + 49
7. x2 - 20x + 100
8. x2 - 64
Factor out the greatest common monomial factor.
9. 24u3 + 40u2
10. 8x3 + 24x2 + 32x
Solve:
11. x2 + 2x = 0
12. x2 + x - 20 = 0
13. x2 - 4x - 12 = 0
14. x2 - 18x + 81 = 0
15. 8x3 + 24x2 - 32x = 0
16. x2 - 12x = - 20

Expert's answer

1. x2 + 13x + 42=x^2+12x+36+x+6=(x+6)^2+(x+6)=(x+6)(x+6+1)=(x+6)(x+7)

Also you can find zeros of the polynom and factor it with the help of them:

2. x2 + 15x + 54

D=225-54*4=225-216=9

roots: x=(-15+3)/2=-6

x=(-15-3)/2=-9

So we have& x2 + 15x + 54=(x+9)(x+6)

6. x2 + 14x + 49

D=49-49=0

x=-7

x2 + 14x + 49=(x+7)^2

9. 24u3 + 40u2=8u^2(3u+5)

11. x2 + 2x = 0

x(x+2)=0 whence x=0;x=-2

Also you can find zeros of the polynom and factor it with the help of them:

2. x2 + 15x + 54

D=225-54*4=225-216=9

roots: x=(-15+3)/2=-6

x=(-15-3)/2=-9

So we have& x2 + 15x + 54=(x+9)(x+6)

6. x2 + 14x + 49

D=49-49=0

x=-7

x2 + 14x + 49=(x+7)^2

9. 24u3 + 40u2=8u^2(3u+5)

11. x2 + 2x = 0

x(x+2)=0 whence x=0;x=-2

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