CA Algebra I: Factoring quadratics | Quadratic equations | Algebra I | Khan Academy

TL;DR

This video provides step-by-step solutions to factoring problems involving polynomials.

Transcript

All right, we're on problem 44. And they said, which is the factored form of 3a squared minus 24ab plus 48b squared? And if this confuses you with a's and b's instead of an x there, I just like to think of in this case, this looks like an x squared. So I like to think of it the same way I would think of it in terms of if this was an x squared minus... Read More

Key Insights

• 🧑‍🏭 Factoring involves finding common factors or applying specific patterns to simplify or break down polynomials.
• 🍉 Factoring not only helps in solving equations but also in understanding the properties and relationships between terms.
• 🧰 The difference of squares pattern (a^2 - b^2 = (a + b)(a - b)) is a useful tool for factoring certain polynomials.
• 🧑‍🏭 Polynomials with common factors can be simplified by factoring out the common factor.

Questions & Answers

Q: How do you factor the polynomial 3a^2 - 24ab + 48b^2?

To factor this polynomial, we first look for a common factor, in this case, 3. Then we factor out 3(a - 4b)^2.

Q: What is the factored form of x^2 - 11x + 24?

The polynomial x^2 - 11x + 24 can be factored as (x - 8)(x - 3), using the method of finding two numbers that add up to -11 and multiply to 24.

Q: How do we factor the polynomial 9t^2 + 12t + 4?

The polynomial 9t^2 + 12t + 4 can be factored as (3t + 2)^2, by looking for two numbers that add up to 12 and multiply to 36.

Q: What is the complete factorization of 32 - 8z^2?

The polynomial 32 - 8z^2 can be factored as -8(z + 2)(z - 2), by factoring out a common factor of -8 and using the difference of squares pattern.

Summary & Key Takeaways

• Problem 44: The polynomial 3a^2 - 24ab + 48b^2 can be factored as 3(a - 4b)^2.

• Problem 45: The polynomial x^2 - 11x + 24 can be factored as (x - 8)(x - 3).

• Problem 46: The polynomial 9t^2 + 12t + 4 can be factored as (3t + 2)^2.

• Problem: The polynomial 32 - 8z^2 can be factored as -8(z + 2)(z - 2).