Polynomials

Q. If f(x) = 3x^2 + 2x - 1, what is f(2)?

Solution

f(2) = 3(2)^2 + 2(2) - 1 = 3(4) + 4 - 1 = 12 + 4 - 1 = 15.

Correct Answer: A — 5

Q. If g(x) = x^3 - 3x^2 + 4, what is g(1)?

Solution

g(1) = (1)^3 - 3(1)^2 + 4 = 1 - 3 + 4 = 2.

Correct Answer: C — 4

Q. If h(x) = 2x^2 - 3x + 1, what is h(-1)?

Solution

h(-1) = 2(-1)^2 - 3(-1) + 1 = 2 + 3 + 1 = 6.

Correct Answer: A — 0

Q. If p(x) = x^2 + 3x + 2, what is p(-1)?

Solution

p(-1) = (-1)^2 + 3(-1) + 2 = 1 - 3 + 2 = 0.

Correct Answer: A — 0

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

Solution

The degree of a polynomial is the highest power of x. Here, the highest power is 4.

Correct Answer: B — 4

Q. What is the product of the roots of the polynomial x^2 + 5x + 6?

Solution

The product of the roots of ax^2 + bx + c is c/a. Here, 6/1 = 6.

Correct Answer: A — 6

Q. What is the sum of the roots of the polynomial x^2 - 4x + 3?

Solution

The sum of the roots of ax^2 + bx + c is -b/a. Here, -(-4)/1 = 4.

Correct Answer: B — 2

Q. What is the value of x if 2x^2 - 8 = 0?

Solution

2x^2 - 8 = 0 => 2x^2 = 8 => x^2 = 4 => x = ±2. The positive value is 2.

Correct Answer: C — 2

Q. Which of the following is a factor of the polynomial x^2 - 5x + 6?

Solution

x^2 - 5x + 6 = (x - 2)(x - 3). So, x - 3 is a factor.

Correct Answer: B — x - 3

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