A1 MP4 Polynomials Operations

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 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. For example, factoring 2x^2 + 4x as 2x(x + 2).

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 + 5, the degree is 3.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 3x^4 + 2x^3 - x + 7 is in standard form.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2. For example, (x + 3)^2 = x^2 + 6x + 9.

Front

What is the difference of squares?

Back

The difference of squares is a special product that states a^2 - b^2 = (a - b)(a + b). For example, x^2 - 9 = (x - 3)(x + 3).

Front

How do you factor a quadratic polynomial?

Back

To factor a quadratic polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b. For example, to factor x^2 - 5x + 6, use -2 and -3: (x - 2)(x - 3).