Polynomials Quiz

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Questions and Answers

Which theorem states that if a polynomial $f(x)$ is divided by $x - c$, the remainder is $f(c)$?

Remainder Theorem (correct)
Fundamental Theorem of Algebra
Factor Theorem
Rational Root Theorem

What is the degree of the polynomial $3x^4 - 2x^3 + 5x^2 - 7x + 1$?

3
5
4 (correct)
2

What is the sum of the coefficients of the polynomial $2x^3 - 5x^2 + 3x - 7$?

-5
2
-7
3 (correct)

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 $f(4) = 2(4)^3 - 5(4)^2 + 3(4) - 7 = 113$. Signup and view all the answers

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 $f(-2) = 3(-2)^4 - 2(-2)^3 + 5(-2)^2 - 7(-2) + 1 = 201$. Signup and view all the answers

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. Signup and view all the answers