Question

the quotient obtaint when x^4+11x^3-44x^2+76x+48 is divided by x^2-2x+1​

Answer 1

Quotient of polynomial division is $\bf \red{{x}^{2} + 13x - 19}$

Given:

• ${x}^{4} + 11 {x}^{3} - 44 {x}^{2} + 76x + 48$ and ${x}^{2} - 2x + 1$

To find:

• Find the quotient polynomial when former is divided by later polynomial.

Solution:

Divide the polynomial.

$\: \: \: \: \: \: \: \: \: \: {x}^{2} - 2x + 1 \: ) \: {x}^{4} + 11 {x}^{3} - 44 {x}^{2} + 76x + 48 \: ( {x}^{2} + 13x - 19 \\ {x}^{4} - 2 {x}^{3} + {x}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ( - ) \: \: ( + ) \: \: ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - - - - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ 13 {x}^{3} - 45 {x}^{2} + 76x \\ 13 {x}^{3} - 26 {x}^{2} + 13x \\ ( - ) \: \: \: \: ( + ) \: \: \: \: ( - ) \\ - - - - - - - - - - - - \\ - 19 {x}^{2} + 63x + 48 \\ - 19 {x}^{2} + 38x - 19 \\ ( + ) \: \: ( - ) \: \: ( + ) \\ - - - - - - - - \\ 25x + 67 \\ - - - - - - - -$

Quotient of division is ${x}^{2} + 13x - 19$

Remainder is 25x+67

Thus,

Quotient of polynomial division is $\bf {x}^{2} + 13x - 19$

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Answer 2

Given: $x^4+11x^3-44x^2+76x+48$ is divided by $x^2-2x+1$

Quotient is $x^2+13x-19$

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