Factoring polynomials 6 problems

Front

What is the definition of factoring in algebra?

Back

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

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a + b)(a - b).

Front

How do you factor a quadratic expression in the form ax² + bx + c?

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers to factor by grouping.

Front

What is the first step in factoring a polynomial completely?

Back

The first step is to look for a greatest common factor (GCF) among all the terms in the polynomial.

Front

How do you factor the expression 3x² + 18x + 15?

Back

First, factor out the GCF, which is 3, to get 3(x² + 6x + 5). Then, factor the quadratic to get 3(x + 5)(x + 1).

Front

What is the factored form of x² - 25?

Back

The factored form is (x + 5)(x - 5), which is derived using the difference of squares formula.

Front

What are the steps to factor k² + 7k + 10?

Back

Identify two numbers that multiply to 10 and add to 7, which are 2 and 5. Rewrite the expression as (k + 2)(k + 5).

Front

How do you factor the expression 2k² - 14k - 60 completely?

Back

First, factor out the GCF, which is 2, to get 2(k² - 7k - 30). Then, factor the quadratic to get 2(k - 10)(k + 3).

Front

What is the factored form of 9x² + 9x - 10?

Back

The factored form is (3x + 5)(3x - 2), which can be found by using the method of grouping or trial and error.

Front

What is the significance of the leading coefficient in factoring quadratics?

Back

The leading coefficient (a) affects the shape of the parabola and can influence the factoring process, especially when a is not equal to 1.