Question

divide: x^4 - 10x^3+27x^2-46x +28 and x -7

Answer 1

Answer:

$(x^{3}-3 x^{2}+6x-4)$

Step-by-step explanation:

$\frac{x^{4}-10x^{3} + 27x^{2} -46x+28}{x-7} \\\frac{(x-7)(x^{3}-3 x^{2}+6x-4) }{(x-7)} \\(x^{3}-3 x^{2}+6x-4)$

Answer 2

Given:

Dividend: $x^4-10x^3+27x^2-46+28$

Divisor: $x-7$

To find:

the quotient of the given division

Solution:

$\frac{ x^4-10x^3+27x^2-46+28}{x-7}$

On factorizing the polynomial in the numerator, we get the following factors,

$x^4-10x^3+27x^2-46+28=(x-7)(x^3-3x^2+6x-4)$

So putting these factors in the numerator, we get,

$\frac{(x-7)(x^3-3x^2+6x-4)}{(x-7)}$

Canceling$(x-7)$ from both the numerator and the denominator since they are the common terms.

We get the quotient as $x^3-3x^2+6x-4$

Hence, the quotient of the given division is$x^3-3x^2+6x-4$.