4.1-4.4 Review

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree three, which means its highest exponent is three. It can be expressed in the form: ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

How do you factor the expression 8x^3 - 1?

Back

The expression 8x^3 - 1 can be factored using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, it factors to (2x - 1)(4x^2 + 2x + 1).

Front

What is the sum of (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The sum is obtained by combining like terms: (2x^2 - 4x^2) + (5x + 6x) + (3 - 7) = -2x^2 + 11x - 4.

Front

How do you simplify (5x + x^2 - 4) - (4x - x^2 + 6)?

Back

To simplify, distribute the negative sign and combine like terms: (x^2 + x - 4 - 4x + x^2 - 6) = 2x^2 + x - 10.

Front

What is the result of dividing (3x^3 + 5x - 1) by (x + 1)?

Back

Using polynomial long division, the result is 3x^2 - 3x + 8 - \frac{9}{x+1}.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (indeterminates) raised to non-negative integer powers and coefficients. It can be expressed in the form: a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 - 2x^2 + 7x - 3, the degree is 3.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, in the expression 3x^2 + 5x^2 - 2x, the terms 3x^2 and 5x^2 are like terms.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a - b)(a + b). This is used to factor expressions that are the difference of two perfect squares.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent. For example, 3x + 5x = 8x.