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Given g(x) = x4 + 2x3 - 7x2 - 8x + 12. When g(x) is divided by x - 1, which conclusion about g(x) is true?

1.9(1) = 0
2.9(-1) = 0
3.x + 1 is a factor of g(x).
4. No conclusion can be made regarding g(x).

Given gx x4 2x3 7x2 8x 12 When gx is divided by x 1 which conclusion about gx is true 191 0 291 0 3x 1 is a factor of gx 4 No conclusion can be made regarding g class=

Respuesta :

Answer:

g(1) = 0

There is a remainder of 10 so you can automatically cross out 3 and 4.

When [tex]g(x) = x^4 + 2x^3-7x^2-8x+12[/tex] is divided by x - 1, the only true conclusion is g(1) = 0

The given equation is:

[tex]g(x) = x^4 + 2x^3-7x^2-8x+12[/tex]

x- 1 is a factor of [tex]g(x) = x^4 + 2x^3-7x^2-8x+12[/tex] only if g(1) = 0

Let us find g(1) by substituting x = 1 into [tex]g(x) = x^4 + 2x^3-7x^2-8x+12[/tex]

[tex]g(x) = x^4 + 2x^3-7x^2-8x+12[/tex]

[tex]g(1) = 1^4+2(1^3)-7(1^2)-8(1)+12\\\\g(1) = 1 + 2 - 7 - 8 + 12\\\\g(1) = -12 + 12\\\\g(1) = 0[/tex]

Therefore, when [tex]g(x) = x^4 + 2x^3-7x^2-8x+12[/tex] is divided by x - 1, the only true conclusion is g(1) = 0

Learn more here: https://brainly.com/question/24437791

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