(B) Given the polynomial $p(x) = (x - 1)(2 - x)$.Expanding the expression: $p(x) = x(2) - x(x) - 1(2) + 1(x) = 2x - x^2 - 2 + x$.Combining like terms:

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(B) Given the polynomial $p(x) = (x - 1)(2 - x)$.Expanding the expression: $p(x) = x(2) - x(x) - 1(2) + 1(x) = 2x - x^2 - 2 + x$.Combining like terms: $p(x) = -x^2 + 3x - 2$.The highest power (degree) of the variable $x$ in this polynomial is $2$.$A$ polynomial of degree $2$ is known as a quadratic polynomial.

Class 10 Mathematics Polynomials Mix Examples - Polynomials

Easy

Identify the type of the given polynomial based on its degree: $p(x) = (x - 1)(2 - x)$

A
Linear polynomial
B
Quadratic polynomial
C
Cubic polynomial
D
Constant polynomial

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Class 10

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Polynomials

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Mix Examples - Polynomials

Find the division of the following by synthetic division method: $p(x) = x^{4} - a^{4}$ by $x - a$.

Medium

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State the degree of the given polynomial: $p(x) = 5x - 2x^2 + 3$

Easy

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Which of the following statements is true?

Medium

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If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} + x^{2} - 17x + 15$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

Medium

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Examine the validity of the following statement: $(x-2)$ is a factor of $x^{3}+5x^{2}-2x-25$.

Easy

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Identify the type of the given polynomial based on its degree: $p(x) = (x - 1)(2 - x)$

Similar Questions

Find the division of the following by synthetic division method: $p(x) = x^{4} - a^{4}$ by $x - a$.

State the degree of the given polynomial: $p(x) = 5x - 2x^2 + 3$

Which of the following statements is true?

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} + x^{2} - 17x + 15$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

Examine the validity of the following statement: $(x-2)$ is a factor of $x^{3}+5x^{2}-2x-25$.

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