Question

Divide p(x)=x⁴-5x+6 by g(x)=2-x². check your answer by division algorithm of polynomial

Answer 1

Answer:

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Answer 2

Answer:

Quotient = $-(x^2+2)$

Reminder = $-5x+10$

Step-by-step explanation:

Given:

$p(x)=x^4-5x+6$

$g(x)=2-x^2$

To find:

Quotient and reminder

Solution:

The idea of polynomial division serves as the foundation for this kind of query. Either the long division method or the long method of algebra can be used to answer this question. We merely proceed to divide the polynomial that has to be divided by its first term by the first term of the divisor. This provides us the quotient's first term. Until no more division is conceivable, we keep doing this.

Students should be cautious while subtracting the terms from the product after multiplying by the divisor because any confusion over the sign during subtraction could result in an incorrect response. This type of problem can also be solved through factorization, although that is a more difficult approach to finding the answer.

$\begin{array}{r}-x^{2}-2\phantom{)} \\-x^{2}+2{\overline{\smash{\big)}\,x^4-5x+6\phantom{)}}}\\\underline{-~\phantom{(}(x^4-2x^2)\phantom{-b)}}\\2x^2-5x+6\phantom{)}\\ \underline{-~\phantom{()}(2x^2-4)}\\ -5x+10\phantom{)}\end{array}$

Thus the quotient is $-(x^2+2)$ and the reminder $-5x+10$

On dividing a polynomial p(x) by x2 - 4, quotient and remainder

found to be x and 3 respectively. The polynomial p(x) is

https://brainly.in/question/15921981

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in

each of the following :

(i) p(x) = x³ – 3x² + 5x – 3, g(x) = x² – 2

(ii) p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

(iii) p(x) = x⁴ – 5x + 6, g(x) = 2 – x²

https://brainly.in/question/5482808

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