Question

the polynomial which when divided by minus x square + X - 1 gives a question x minus 2 and remainder 3 is​

Answer 1

Step-by-step explanation:

what we have to solve???

Answer 2

Hint: In this problem, we are required to calculate the polynomial. We are given a divisor, quotient and remainder. So, by using the basic definition of dividend we can easily evaluate the required polynomial.

Complete step-by-step answer:

According to the problem statement, we are given a divisor −x2+x−1 of a polynomial. This divisor when divided from the dividend polynomial leaves x - 2 as quotient and 3 as remainder. We are required to find the final expression of a polynomial.

As we know that, the product of divisor and quotient add to the remainder gives the dividend of a number or an expression. This can be mathematically expressed as:

Let f(x) be the dividend polynomial having a divisor p(x) and a quotient q(x). The polynomial also leaves a remainder r(x) upon division. Therefore,

f(x)=p(x)⋅q(x)+r(x)

By using this basic definition of dividend, and putting p(x)=−x2+x−1, q(x)=x−2 and r(x)=3, we get

f(x)=(−x2+x−1)⋅(x−2)+3f(x)=(−x2)⋅(x−2)+x⋅(x−2)−1⋅(x−2)+3f(x)=−x3+2x2+x2−2x−x+2+3f(x)=−x3+3x2−3x+5

So, the required polynomial is −x3+3x2−3x+5.

Therefore, option (c) is the correct answer.

Note: This is a direct problem which can be easily solved by the knowledge of expression of dividend in terms of divisor, quotient and remainder. Students must take care while multiplying the exponents of x and the negative sign respective to each term as silly mistakes due to calculation error are bound to occur.