Example 1: Factoring trinomials with a common factor | Algebra II | Khan Academy

TL;DR

Factorizing a quadratic expression by simplifying through division and grouping.

Transcript

Factor 8k squared minus 24k minus 144. Now the first thing we can do here, just eyeballing each of these terms, if we want to simplify it a good bit is all of these terms are divisible by 8. Clearly, 8k squared is divisible by 8, 24 is divisible by 8, and 144-- it might not be as obvious is divisible by 8-- but it looks like it is. 8 goes into one ... Read More

Key Insights

• 😑 Dividing each term by a common factor simplifies the expression.
• 🍹 Finding two numbers whose sum and product matches the coefficients simplifies factoring.
• 🧑‍🏭 Grouping terms and factoring out common factors aids in further simplification.
• 😑 The final factorized expression has the form (constant)(binomial)(binomial).

Questions & Answers

Q: How can we simplify the expression 8k^2 - 24k - 144?

We can simplify the expression by dividing each term by 8 and factoring out the common factor of 8, resulting in 8(k^2 - 3k - 18).

Q: How do we factorize the expression further?

To factorize the expression, we need to find two numbers whose sum is equal to the coefficient on x (in this case, -3) and whose product is equal to the constant term (in this case, -18). The numbers are 3 and -6.

Q: Can we simplify the expression further after finding the two numbers?

Yes, we can simplify the expression further by grouping the terms with common factors. We can group k^2 - 3k and -6 to get (k^2 - 3k) - 6.

Q: What is the final factorized expression?

The final factorized expression is 8(k + 3)(k - 6), obtained by factoring out the common factors from the grouped terms.

Summary & Key Takeaways

• The expression 8k^2 - 24k - 144 is simplified by dividing each term by 8 and factoring out the common factor of 8.

• The resulting expression is then further simplified by factoring out two numbers whose sum is equal to the coefficient on x and whose product is equal to the constant term.

• By grouping and factoring out the common factors, the expression is finally written as 8(k + 3)(k - 6).