Factoring by Grouping: Rewriting Trinomials

This lesson teaches how to rewrite trinomials by factoring using grouping. It begins with a review of multiplying linear expressions to form quadratics and then explains factoring by grouping when the leading coefficient is 1. The lesson progresses to more complex cases where the leading coefficient is not 1, detailing the steps to determine replacement terms and factor the expression. Advanced examples are provided to reinforce the core lesson, demonstrating how to handle higher-degree polynomials and different coefficients.

What is the result when you multiply two linear expressions?

• A cubic expression

• A quadratic expression

• A linear expression

• A constant

In factoring by grouping, what must the product of the replacement terms equal?

• The sum of the coefficients

• The middle term

• The value of the constant term

• The leading coefficient

How do you determine the replacement terms for the middle term in a trinomial?

• By finding two numbers whose sum is the leading coefficient and product is the middle term coefficient

• By finding two numbers whose product is the leading coefficient and sum is the constant term

• By finding two numbers whose sum is the constant term and product is the middle term coefficient

• By finding two numbers whose product is the constant term and sum is the middle term coefficient

What is the first step in factoring by grouping?

• Combine like terms

• Factor out the greatest common factor

• Multiply the linear expressions

• Rewrite the trinomial as a four-term polynomial

When the leading coefficient is not 1, what is the product value used for determining replacement terms?

• The middle term

• The product of the leading coefficient and the constant

• The sum of the coefficients

• The constant term

In advanced factoring by grouping, what is the first step after rewriting the expression like a quadratic?

• Combine like terms

• Multiply the linear expressions

• Factor out the greatest common factor

• Determine two terms to substitute for the middle term

What is the greatest common factor in the expression 3x to the 10th minus 17x to the fifth plus 10?

• 3

• Negative 5

• 3x to the fifth

• x to the fifth