Solving Polynomials Review

Front

Simplify \( \sqrt{-48} \)

Back

\( 4i\sqrt{3} \)

Front

Solve for \( x^2 - 4 = 77 \)

Back

\( \pm 9 \)

Front

Which of the following is equivalent to \( (3-5i)-(6+2i) \)?

Back

\( -3-7i \)

Front

Is \( (x-2) \) a factor of \( f(x) = x^3 - 8x^2 + 14x - 4 \)?

Back

Yes, \( (x-2) \) is a factor. The remainder is zero.

Front

Calculate \( (-1 + 5i) + (-2 - 3i) \)

Back

\( -3 + 2i \)

Front

What is the definition of a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What is the degree of the polynomial \( 3x^4 - 5x^2 + 2 \)?

Back

The degree is 4.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial \( f(x) \) by \( (x - c) \) is equal to \( f(c) \).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that \( (x - c) \) is a factor of \( f(x) \) if and only if \( f(c) = 0 \).

Front

How do you find the roots of a quadratic equation?

Back

Use the quadratic formula: \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \).