f(x)=x^4-6x^3+x^2+24x-20. If not, give the value of f(k)

Use synthetic division to decide whether k=2, k=-1, or k=0 are zeros of

f(x)=x^4-6x^3+x^2+24x-20. If not, give the value of f(k)

f(x)=x^4-6x^3+x^2+24x-20. If not, give the value of f(k)

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x^4-6x^3+x^2+24x-20

let's try 2

2 1 -6 1 24 -20

2 -8 -14 20

1 -4 -7 10 0

now divide by (x-2)

x^3-4x^2-7x+10

__________________

x-2 / x^4-6x^3+x^2+24x-20

/ x^4-2x^3

________

-4x^3+x^2

-4x^3+8x^2

___________

-7x^2+24x

-7x^2+14x

__________

10x-20

10x-20

_______

0

using x^3-4x^2-7x+10 try 1 using synthetic division

1 1 -4 -7 10

1 -3 -10

1 -3 -10 0

divide x^3-4x^2-7x+10 by x-1

x^2-3x-10

__________________

x-1 / x^3-4x^2-7x+10

/ x^3-x^2

_________

-3x^2-7x

-3x^2+3x

________

-10x+10

-10x+10

_______

0

factor x^2-3x-10 into (x-5)(x+2)

answer (x-2)(x-1)(x-5)(x+2) = x^4-6x^3+x^2+24x-20

Using synthetic division,

2|1 -6 1 24 -20

......2 -8 -14 20---------------------

..1 -4 -7 10|0

In the same way, you can see k = -1 and k = 0 are not zeros.

f(-1) = -36

f(0) = -20

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