Binomial Theorem (Intro)

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Q1. Which expression represents the factored form of x^2 + 5x + 6?

Solution:

The expression factors to (x + 2)(x + 3) since 2 and 3 add to 5 and multiply to 6.

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Q2. Which expression represents the factored form of x^2 - 16?

Solution:

This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).

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Q3. What is the value of x in the equation 3(x + 2) = 21?

Solution:

Divide both sides by 3: x + 2 = 7. Then subtract 2: x = 5.

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Q4. What is the solution set for the inequality 2x + 3 ≥ 7?

Solution:

Subtract 3 from both sides: 2x ≥ 4. Then divide by 2: x ≥ 2.

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Q5. What is the solution to the inequality 2x + 1 ≥ 3?

Solution:

Subtract 1 from both sides: 2x ≥ 2. Divide by 2: x ≥ 1.