SF ALG2H Midterm Review

Front

What is the result of expanding (5x+2)(x^2-3x+6)?

Back

5x^3 - 13x^2 + 24x + 12

Front

How do you write a polynomial function of least degree with integral coefficients that has the zeros -1, 5, and -3+2i?

Back

x^4 + 2x^3 - 16x^2 - 82x - 65

Front

What transformation occurs from f(x) = 12x + 2 to g(x) = 6x - 2?

Back

Vertical shift down 4, half the slope

Front

What is the vertex of the parabola represented by y=3(x-2)^2+3?

Back

(2,3)

Front

How do you use Pascal's Triangle to expand (2x+5)^4?

Back

16x^4 + 160x^3 + 600x^2 + 1000x + 625

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

What is the relationship between the roots of a polynomial and its factors?

Back

If r is a root of the polynomial, then (x - r) is a factor of the polynomial.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a) for a quadratic equation ax^2 + bx + c = 0.