Polynomials

Which statement best summarizes the chapter "Polynomials"?

1. Every polynomial has exactly one zero.
2. Polynomials are expressions with only negative powers.
3. Polynomials are algebraic expressions with non-negative integer powers, and their degree, zeroes, graphs, and relationships between coefficients and zeroes are fundamental concepts used in algebra.
4. Every polynomial is quadratic.

A quadratic polynomial can have at most:

1. One zero
2. Two zeroes
3. Three zeroes
4. Four zeroes

If the zeroes of a quadratic polynomial are 2 and 5, the quadratic polynomial is:

1. x^2 - 7x + 10
2. x^2 + 7x + 10
3. x^2 - 3x + 10
4. x^2 + 10

Which polynomial is linear?

1. 6x + 5
2. x^2 - 4
3. 2x^3 + 1
4. 9

Which statement about the graph of a polynomial is correct?

1. Every zero corresponds to a point where the graph cuts or touches the x-axis.
2. Every zero lies on the y-axis.
3. Zeroes are always positive.
4. A polynomial has infinitely many zeroes.

If one zero of the polynomial x^2 - 7x + 12 is 3, the other zero is:

1. 2
2. 3
3. 4
4. 5

Which of the following is a cubic polynomial?

1. 5x^2 + 1
2. 2x^3 - x + 4
3. 7x - 3
4. 9

Which polynomial has degree zero?

1. 4x + 2
2. 7
3. 3x^2 + 1
4. 5x^3

The product of the zeroes of 2x^2 - 5x + 3 is:

1. 5/2
2. 3/2
3. -3/2
4. 3

If the zeroes of a quadratic polynomial are alpha and beta, then the sum of the zeroes is:

1. alpha * beta
2. -b/a
3. c/a
4. a/b

The maximum number of zeroes of a polynomial of degree 5 is:

1. 3
2. 4
3. 5
4. 6

If x = 2 is a zero of the polynomial x^2 - 5x + 6, which statement is correct?

1. p(2) = 4
2. p(2) = 2
3. p(2) = 0
4. p(2) = -2

What is the degree of the polynomial 5x^4 - 3x^2 + 7x - 9?

1. 2
2. 3
3. 4
4. 5

If p(x) = x, then zero is:

1. 0
2. 1
3. −1
4. 2

A cubic polynomial can have maximum zeros:

1. 1
2. 2
3. 3
4. 4

Degree of a non-zero constant polynomial is:

1. 0
2. 1
3. 2
4. Undefined

If sum of zeros of a quadratic polynomial is 0, then:

1. b = 0
2. c = 0
3. a = 0
4. discriminant = 0

Zeros of x² − 4 are:

1. 2, 2
2. −2, 2
3. 4, −4
4. 1, −1

A polynomial with all coefficients zero is called:

1. Linear polynomial
2. Constant polynomial
3. Zero polynomial
4. Quadratic polynomial

If a polynomial p(x) is divided by (x − a), the remainder is:

1. p(0)
2. p(a)
3. a
4. 0

If (x − a) is a factor of p(x), then p(a) equals:

1. a
2. 1
3. 0
4. −a

Zeros of a polynomial are the points where its graph:

1. Intersects y-axis
2. Intersects x-axis
3. Touches origin
4. Becomes constant

Maximum number of zeros of a quadratic polynomial is:

1. 1
2. 2
3. 3
4. 4

A linear polynomial has how many zeros?

1. 0
2. 1
3. 2
4. Infinite

Product of zeros of x² − 7x + 10 is:

1. 7
2. −7
3. 10
4. −10

Sum of zeros of x² − 5x + 6 is:

1. 5
2. −5
3. 6
4. −6

If p(x) = x − 7, then its zero is:

1. 0
2. 7
3. −7
4. 1

The degree of the polynomial 5x³ + 4x² − 7x + 9 is:

1. 1
2. 2
3. 3
4. 4