When [tex]10x^4-14x^3-10x^2+6x-10[/tex] is divided by [tex]x^3-3x^2+x-2[/tex],
The quotient is: [tex]10x + 16[/tex]
The remainder is: [tex]28x^2 + 10x+ 22[/tex]
The correct form of the question is:
divide [tex]10x^4-14x^3-10x^2+6x-10[/tex] by [tex]x^3-3x^2+x-2[/tex]
This can be represented using the following long division.
[tex]x^3-3x^2+x-2 \left|\begin{array}{c}10x^4-14x^3-10x^2+6x-10\end{array}[/tex]
Step 1: Divide [tex]10x^4[/tex] by [tex]x^3[/tex]
[tex]\frac{10x^4}{x^3} = 10x[/tex]
Step 2.1 : Multiply [tex]10x[/tex] by [tex]x^3-3x^2+x-2[/tex],
[tex]10x \times (x^3-3x^2+x-2) = (10x^4 - 30x^3 + 10x^2 - 20x)[/tex]
Step 2.2: Subtract the result from the quotient
[tex](10x^4-14x^3-10x^2+6x-10) - (10x^4 - 30x^3 + 10x^2 - 20x) = 16x^3 - 20x^2 +26x - 10[/tex]
Step 3: Divide [tex]16x^3[/tex] by [tex]x^3[/tex]
[tex]\frac{16x^3}{x^3} = 16[/tex]
Step 4.1: Multiply [tex]16[/tex] by [tex]x^3-3x^2+x-2[/tex],
[tex]16 \times (x^3-3x^2+x-2) = 16x^3 - 48x^2 + 16x - 32[/tex]
Step 4.2: Subtract the result from the quotient
[tex](10x^4-14x^3-10x^2+6x-10) - (16x^3 - 48x^2 + 16x - 32) = 28x^2 + 10x +22[/tex]
Step 5: Divide [tex]28x^2[/tex] by [tex]x^3[/tex]
The exponent of [tex]28x^2[/tex] is less than [tex]x^3[/tex].
So, the division ends here.
The quotient of the division is:
[tex]Q = 10x + 16[/tex]
The remainder of the division is:
[tex]R = 28x^2 + 10x+ 22[/tex]
See attachment for the steps
Read more about polynomial division at:
https://brainly.com/question/11735499
