Factor Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of simpler polynomials or factors.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring formula: a² - b² = (a - b)(a + b).

Front

Factor the polynomial: x² - 16

Back

(x - 4)(x + 4) - This is an example of the difference of squares.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)² = a² + 2ab + b².

Front

Find the product: (x + 7)²

Back

x² + 14x + 49 - This is an application of the square of a binomial.

Front

What is the standard form of a quadratic polynomial?

Back

The standard form of a quadratic polynomial is ax² + bx + c, where a, b, and c are constants.

Front

Factor the polynomial: 2m² + 3m - 9

Back

(m + 3)(2m - 3) - This involves finding two numbers that multiply to ac and add to b.

Front

What is the product-sum method in factoring?

Back

The product-sum method involves finding two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle coefficient.

Front

Factor the polynomial: 4a² - 25

Back

(2a + 5)(2a - 5) - This is another example of the difference of squares.