SOLUTION: Rewrite the function as a product of factors, and state all zeros. 1. R(x) =x^3+13x^2+48x+36 2. M(x) =3x^4-3x^2 3. N(x) =x^3+5x^2-8x-12 4. P(x) =x^3-8 5. B(x) =x^4-81 6. T(x

Question 1108150: Rewrite the function as a product of factors, and state all zeros.
1. R(x) =x^3+13x^2+48x+36
2. M(x) =3x^4-3x^2
3. N(x) =x^3+5x^2-8x-12
4. P(x) =x^3-8
5. B(x) =x^4-81
6. T(x) =15x^3+27x^2-6x
Answer by rumessa(13) (Show Source): You can put this solution on YOUR website!
1. R(x) =x^3+13x^2+48x+36
sol
x^3+13x^2+48x+36 = 0
put x =-1 we get eqution 0 so first factor is x +1
dived equation by x+1
x+1) x^3+13x^2+48x+36( x^2 +12x +36
x^3+x^2
_ _
________________________
12x^2 +48x + 36
12x^2 +12x
- -
______________________--
36x + 36
36x + 36
- -
_________________
0
x^3+13x^2+48x+36 = ( x +1)( x^2 +12x +36)

2. M(x) =3x^4-3x^2
3x^4-3x^2 = 0
3x^2 ( x^2 -1) =0
3x^2 ( x+1)(x-!)
3. N(x) =x^3+5x^2-8x-12
x^3+5x^2-8x-12 =0
put x =-1 we get equation 0 so first factor is x +1
dived equation by x+1
x+1) x^3+5x^2-8x-12 ( x^2 + 4x -12
x^3+x^2
- -
_________________________
4x^2 -8x -12
4x^2 +4x
- -
_____________________
-12x - 12
-12x -12
+ +
_____________________________
0

x^3+5x^2-8x-12 = (x+1)(x^2 + 4x -12)
= (x+1)(x^2 + 6x - 2x -12)
= (x+1)x(x+6)-2(x+6)
= (x+1)(x-2)(x+6)
4. P(x) =x^3-8
x^3-8 =0
x^3 - 2^3=0
(x-2)(x^2-2x+4)
5. B(x) =x^4-81
x^4-81 = 0
x^4 - 3^4 = 0
(x^2)^2 - (3^2)^2 =0
(x^2 - 3^2)(x^2 + 3^2) =0
(x+3)(x-3)(x^2 + 9)

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