Polynomial Operations and Binomial Theorem

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 5 is a polynomial.

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 + 7, the degree is 3.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 2x^3 + 3x^2 + x + 5 is in standard form.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the Binomial Theorem?

Back

The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Front

What is Pascal's Triangle?

Back

Pascal's Triangle is a triangular array of binomial coefficients. Each number is the sum of the two directly above it. It is used to find coefficients in binomial expansions.

Front

Expand (x + 2)^2.

Back

The expansion is x^2 + 4x + 4.

Front

What is the result of (y - 3)(y + 7)?

Back

The result is y^2 + 4y - 21.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to each term of the polynomial being subtracted and then combine like terms.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.