The degree of the polynomial obtained when $8 - 6 x + x^{2} - 7 x^{3} + x^{5}$ is subtracted from $x^{4} - 6 x^{3} + x^{2} - 3 x + 1$ is

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Solution

The correct option is A
5

$(x^{4} - 6 x^{3} + x^{2} - 3 x + 1) - (x^{5} - 7 x^{3} + x^{2} - 6 x + 8)$
$= x^{4} - 6 x^{3} + x^{2} - 3 x + 1 - x^{5} + 7 x^{3} - x^{2} + 6 x - 8$
$= - x^{5} + x^{4} + x^{3} + 3 x - 7$

Degree of the polynomial(that contains only one variable) is the highest exponent of its various terms. The terms of the polynomial obtained are $x^{5}$ , $x^{4}$ , $x^{3}$ , $3 x$ and $7$ . Here, the term $x^{5}$ has the highest exponent for the variable $x$ and hence the degree of the given polynomial is 5.

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The degree of the polynomial obtained when $8 - 6 x + x^{2} - 7 x^{3} + x^{5}$ is subtracted from $x^{4} - 6 x^{3} + x^{2} - 3 x + 1$ is:

Subtract $(8 - 6 x + x^{2} - 7 x^{3} + x^{5})$ from $(x^{4} - 6 x^{3} + x^{2} - 3 x + 1)$ .

Find the polynomial from the given information.

Quotient = x^{3} + 2 x

Divisor = x^{2} + \frac{1}{2} x

Remainder = 5

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x^{2} + 2 x^{2} y^{3} + 3 y^{2}

is _____

The expression that should be subtracted from the polynomial f(x) = x⁴ + 2x³ -13x² - 12x + 21 so that the resulting polynomial is exactly divisible by g(x) = x² – 4x + 3 is

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The degree of the polynomial obtained when 8−6x+x2−7x3+x5 is subtracted from x4−6x3+x2−3x+1 is

The degree of the polynomial obtained when $8 - 6 x + x^{2} - 7 x^{3} + x^{5}$ is subtracted from $x^{4} - 6 x^{3} + x^{2} - 3 x + 1$ is