A Guide To Factoring Algebraic Expressions: Simplify Complex Equations & Find Prime Factors

Factor

When two or more integers are multiplied, each number is a factor of the product. To factor means to write the number or term as a product of its factors.

Factoring is the process of breaking down an expression into its factors. Factors are the terms that are multiplied together to produce a given expression.

For example, consider the expression 6x^2 + 11x – 10. To factor this expression, we first need to look for two numbers that multiply to -60 (the product of the coefficient of the x^2 term and the constant term), but add up to the coefficient of the x term (11 in this case). These numbers are 15 and -4.

We can then split the middle term in the expression using these numbers as coefficients. This gives us:

6x^2 + 15x – 4x – 10

We can then factor each pair of terms separately:

3x(2x + 5) – 2(2x + 5)

Notice how the terms in the parentheses are the same. We can now factor out this common factor to get:

(2x + 5)(3x – 2)

So the factored form of 6x^2 + 11x – 10 is (2x + 5)(3x – 2).

Factoring is an important tool in mathematics as it allows us to simplify complex expressions, solve equations, and find prime factors of numbers.

More Answers: