Free Pre-Calculus Polynomial Functions Questions and Answers

Question 1

What is the degree of P(x)=3x^4-7x^2-2x^7-x+4 polynomial function?

Accepted Answer

7

Answer

The degree of a polynomial is determined by the highest exponent of the variable in the polynomial expression. In the polynomial P(x) = 3x^4 - 7x^2 - 2x^7 - x + 4, the exponents of x are 4, 2, 7, 1, and 0 (for the constant term). The largest exponent among these is 7, so the degree of the polynomial is 7.

Question 2

The equation f(x) = 5x^4-8x^3+4x^2-6x+3 has how many roots or zeros?

Accepted Answer

4

Answer

According to the Fundamental Theorem of Algebra, a polynomial function of degree 'n' will have exactly 'n' roots or zeros in the complex number system, counting multiplicity. The given polynomial f(x) = 5x^4 - 8x^3 + 4x^2 - 6x + 3 has a highest exponent of 4. Therefore, its degree is 4, meaning it has exactly 4 roots or zeros.

Question 3

P(x) = x^3+6x^2+9x+54 has a polynomial function; find all its zeros.

Accepted Answer

-6, 3i, -3i

Answer

To find the zeros of P(x) = x^3 + 6x^2 + 9x + 54, we can factor by grouping. Grouping the terms gives x²(x+6) + 9(x+6), which factors further into (x²+9)(x+6). Setting each factor to zero, x+6=0 yields x=-6, and x²+9=0 yields x²=-9, so x=±√(-9)=±3i. Thus, the zeros are -6, 3i, and -3i.

Question 4

What is another term for the point where a function intersects the x-axis?

Accepted Answer

All of these

Answer

The point where a function intersects the x-axis is characterized by the y-coordinate being zero. This point is commonly referred to as an x-intercept. It is also called a 'zero' of the function because f(x) equals zero at that point, and a 'root' of the equation f(x)=0. Therefore, all these terms correctly describe the same concept.

Question 5

The polynomial can be represented as...

Accepted Answer

Even degree, positive leading coefficient.

Answer

The end behavior of a polynomial graph is determined by its degree and the sign of its leading coefficient. A polynomial with an even degree and a positive leading coefficient will have both ends of its graph pointing upwards. This means as x approaches positive or negative infinity, y also approaches positive infinity.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

Free Pre-Calculus Polynomial Functions Questions and Answers