6 Questions
Which theorem states that if a polynomial $f(x)$ is divided by $x - c$, the remainder is $f(c)$?
Remainder Theorem
What is the degree of the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$?
4
What is the sum of the coefficients of the polynomial $2x^3 - 5x^2 + 3x - 7$?
3
What is the value of the polynomial $2x^3 - 5x^2 + 3x - 7$ when $x = 4$?
The value of the polynomial $2x^3 - 5x^2 + 3x - 7$ when $x = 4$ is $f(4) = 2(4)^3 - 5(4)^2 + 3(4) - 7 = 113$.
What is the remainder when the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$ is divided by $x + 2$?
The remainder when the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$ is divided by $x + 2$ is $f(-2) = 3(-2)^4 - 2(-2)^3 + 5(-2)^2 - 7(-2) + 1 = 201$.
What is the product of the roots of the polynomial $4x^2 - 5x + 1$?
The product of the roots of the polynomial $4x^2 - 5x + 1$ is given by the formula $r_1 \cdot r_2 = \frac{c}{a} = \frac{1}{4}$, where $r_1$ and $r_2$ are the roots and $c$ and $a$ are the constant and leading coefficients, respectively.
Test your knowledge of polynomials with this Class 10 standard question quiz. Determine the degree of a given polynomial, identify the theorem related to polynomial division, and calculate the sum of coefficients in a polynomial expression.
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