Home work 4 and project

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c). It is faster and more efficient than traditional long division.

Front

How do you evaluate a polynomial function at a specific value?

Back

To evaluate a polynomial function f(x) at a specific value a, substitute x with a in the polynomial expression and simplify.

Front

What is the value of f(5) if f(x) = 3x^2 - 9x - 20?

Back

f(5) = 10.

Front

What is the process to find f(3) + g(2) if f(x) = x + 2 and g(x) = 5x - 1?

Back

Evaluate f(3) = 5 and g(2) = 9, then add them: f(3) + g(2) = 5 + 9 = 14.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition g(f(x)) means to apply f first and then g.

Front

What is the result of g(f(x)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

g(f(x)) = 8x^2 - 1.

Front

What does it mean for a number to be a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) equals zero. It is the x-intercept of the graph of the function.

Front

How do you determine if a value is a zero of the function b(x) = x^3 + 3x^2 - x - 3?

Back

Substitute the value into the function and check if the result equals zero.

Front

What is the significance of the left box in synthetic division?

Back

The left box in synthetic division contains the value of the divisor (the root of the linear factor) that is being used for the division.

Front

What is the value that is not a zero of the function b(x) = x^3 + 3x^2 - x - 3?

Back

x = 3 is not a zero of the function.