Answer:
B: A = –5x; B = –1x; C = 5
Step-by-step explanation:
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The missing values in the division table of Shelia are -5x, -1x and 5 for A, B and C respectively.
Quotient is the resultant number which is obtain by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,
[tex]q=\dfrac{a}{b}[/tex]
Here, (a, b) are the real numbers.
The dividend of the Shelia's problem is,
[tex]x^4 - 4x^3 + 4x^2 - 6x + 5[/tex]
The divisor is given as,
[tex]x-1[/tex]
Divide the dividend with the division as,
[tex]x^3-3x^2 + x - 5[/tex]
[tex]x-1[/tex] _/[tex]\overline{x^4 - 4x^3 + 4x^2 - 6x + 5}[/tex]
[tex]x^4-3x^3 +x^2-5x - 1[/tex]
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[tex]-x^3+3x^2 -1x +5[/tex]
[tex]-x^3+3x^2 +B +C[/tex]
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The Divisor given in the problem is,
[tex]x^4-3x^3 +x^2+A - 1[/tex]
[tex]-x^3+3x^2 +B +C[/tex]
Comparing it with the above division, we get,
[tex]A=-5x\\B=-1x\\C=5[/tex]
Thus, the missing values in the division table of Shelia are -5x, -1x and 5 for A, B and C respectively.
Learn more about the quotient here;
https://brainly.com/question/673545
