5.2 Lesson on "U" substitution

"U" substitution

Recognizing the bigger patterns.

First we have to recognize factoring of a quadratic and rewriting forms!

Be ready!

The next questions are about the conceptual parts of "U" substitution.

Multiple Choice

How do you factor a quadratic?
ex:

x² - 10x + 16

• Factors of "c" that add to "b"

• GCF

• factor by grouping

• Elimination

Multiple Select

Select the factors of the following quadratic

x² - 10x + 16

• (x - 2)

• (x + 2)

• x²(10x + 16)

• (x - 8)

Math Response

Rewrite the following as a square.

64x⁸

Type answer here

Correct Answer: \left(8x^4\right)^2

Deg^°

Rad

Don't forget everything has it's own exponent! Even numbers have an exponent.

Own exponents!

When we have a term in parenthesis and a power is outside, the power applies to all things inside.

(8x⁴)² = 64x⁸

Power of a Power

Don't forget the power rules!

Math Response

Rewrite the following as a square!


81x¹⁶

Type answer here

Correct Answer: \left(9x^8\right)^2

Deg^°

Rad

Starting "U" Substitution

Recognize the structure, identify "U"

x⁴ - 7x² + 10 = 0

u - 2 = 0

Since u = x² replace u with x²

Solve both cases!

u - 5 = 0

Replace "U" at the end
u² - 7u + 10 = 0

This one I'll do!

Follow along! Write it down!

(y² - 17)² - 16(y² - 17) + 64 = 0

You do this one!

x⁴ - 36x² = -35