Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

Front

What is a polynomial?

Back

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

Front

What does it mean to factor a polynomial completely?

Back

Factoring a polynomial completely means expressing it as a product of its irreducible factors, which cannot be factored further.

Front

What is the difference between a prime polynomial and a reducible polynomial?

Back

A prime polynomial cannot be factored into simpler polynomials with real coefficients, while a reducible polynomial can be factored into simpler polynomials.

Front

How do you factor a quadratic polynomial of the form ax^2 + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Use these numbers to split the middle term and factor by grouping.

Front

Factor the polynomial: -8x^2 + 10x + 3

Back

-1 (2x - 3) (4x + 1)

Front

Factor the polynomial: 2x^2 + 7x + 6

Back

(2x + 3) (x + 2)

Front

Factor the polynomial: 4x^2y - 12xy + 5y

Back

y (2x - 1) (2x - 5)

Front

Factor the polynomial: y^2 - 7y + 12

Back

(y - 3) (y - 4)

Front

What is the area of a circle formula?

Back

The area of a circle is given by the formula A = πr^2, where r is the radius.