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Expression Formation

The degree of...

Question

The degree of $x^{3} - 3 x^{2} + 1$

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Solution

The highest power of the variable $x$ in the given expression is $3$ .
$⟹$ the degree is $3$

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Q. The degree of

(6 x^{4} - 7 x^{3} + 3 x^{2} + 2 x - 1)

p (x) = x^{2} - 2 x + 1

q (x) = x^{3} - 3 x^{2} + 2 x - 1

p (x) \times q (x)

and check the degree of

p (x) \times q (x)

Find the cube of $x + \frac{1}{x}$

Q. Find the product of the following polynomials and state the degree of their product.

(i) x² + 3x + 1; 2x

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3
(ii) 3x² + 5x ; x² + 2x + 1
(iii) x³ + 4x + 2 ; x² + x + 5
(iv) x³

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x + 4
(v) 2y² + 3 ; 3y³ + 1

Q. What must be added to

6 x^{4} - x^{3} + 3 x^{2} + 4 x - 2

, so that the result is exactly divisible by

3 x^{2} - 2 x + 4

? Also find the degree of the quotient.

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