AAC #3 Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is expressed as a sum of terms in descending order of the degree of the variable, e.g., a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest polynomial that divides all terms of a polynomial without leaving a remainder.

Front

How do you apply the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern expressed as a^2 - b^2 = (a - b)(a + b).

Front

What is the process of expanding a binomial?

Back

Expanding a binomial involves using the binomial theorem or distributive property to write it as a sum of terms, e.g., (a + b)^n.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c).

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).