Question

$2 {x}^{4} - x {3} + 3 {x}^{2} - x + 1 \div x {2} + 1$
2x⁴-x³+3x²-x+1
$2 {x}^{4} - x {3} + 3 {x}^{2} - x + 1 \div x {2} + 1$
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Answer 1

Answer:

u

Let f(x)=2x

4

−4x

3

−3x−1

First see how many times 2x

4

is of x.

x

2x

4

=2x

3

Now multiply (x−1)(2x

3

)=2x

4

−2x

3

Then again see the first term of the remainder that is −2x

3

. Now do the same.

Here the quotient is 2x

3

−2x

2

−2x−5 and the remainder is −6.

Now, the zero of the polynomial (x−1) is 1.

Put x=1 in f(x),f(x)=2x

4

−4x

3

−3x−1

f(1)=2(1)

4

−4(1)

3

−3(1)−1

2(1)−4(1)−3(1)−1

=2−4−3−1

=−6