Factoring polynomials using complex numbers | Khan Academy

TL;DR

Amat made a mistake in factoring the quadratic expression by treating the square root of three as three.

Transcript

• [Instructor] We're told that Amat tried to write x to the fourth plus 5x squared plus 4 as a product of linear factors. This is his work. And then they'd tell us all of the steps that he did. And then they say, in what step did Amat make his first mistake? So pause this video and see if you can figure that out. All right, now let's work through t... Read More

Key Insights

• 🧑‍🏭 Factoring quadratic expressions involves identifying common factors and applying factorization rules.
• 😑 The quadratic expression x to the fourth plus 5x squared plus 4 can be factored into x squared plus 9 times x squared plus 1.
• 🥺 Treating the square root of a number incorrectly can lead to mistakes in the factoring process.
• ❎ The concept of difference of squares and sum of squares can be applied when factoring quadratic expressions.

Questions & Answers

Q: What expression did Amat try to factor?

Amat attempted to factor x to the fourth plus 5x squared plus 4.

Q: How did Amat correctly factor x to the fourth plus 5x squared plus 4?

Amat factored x to the fourth plus 5x squared plus 4 into x squared plus 9 times x squared plus 1.

Q: Why did Amat make a mistake in the factoring process?

Amat made a mistake by treating the square root of three as three when factoring x squared plus 9.

Q: What was Amat's mistake in step three?

Amat took the square root of three, instead of three, when factoring x squared plus 9, resulting in an error.

Summary & Key Takeaways

• The instructor analyzes Amat's attempt to factor x to the fourth plus 5x squared plus 4 as a product of linear factors.

• Amat correctly factors x to the fourth plus 5x squared plus 4 into x squared plus 9 times x squared plus 1.

• However, Amat mistakenly treats the square root of three as three when factoring x squared plus 9.