Factor the quadratic expression 3x to the 2nd power +9x +6

3(x + 1)(x + 2)

Step-by-step explanation:

Given

3x² + 9x + 6 ← factor out 3 from each term

= 3(x² + 3x + 2) ← factor the quadratic

Consider the factors of the constant term (+ 2) which sum to give the coefficient of the x- term (+ 3)

The factors are + 1 and + 2, since

2 × 1 = 2 and 2 + 1 = 3, thus

x² + 3x + 2 = (x + 1)(x + 2) and

3x² + 9x + 6 = 3(x + 1)(x + 2)

Andre has more money than Bob.  If Andre gave Bob $20, they would have the same amount.  While if Bob gave Andre $22, Andre would then have twice as much as Bob.  How much does each one actually have?

Step-by-step explanation:

Here is the first sentence:

"If Andre gave Bob $20, they would have the same amount."

Algebraically:

1)   x − 20 = y + 20.

(Andre -- x -- has the same amount as Bob, after he gives him $20.)

Here is the second sentence:

"While if Bob gave Andre $22, Andre would then have twice as much

as Bob."

Algebraically:

2)   x + 22 = 2(y − 22).

(Andre has twice as much as Bob -- after Bob gives him $22.)

To solve any system of two equations, we must reduce it to one equation in one of the unknowns.  In this example, we can solve equation 1) for x --

x − 20=y + 20

 implies  x=y + 40

-- and substitute it into equation 2):

y + 40 + 22=2(y − 22).

      That is,

y + 62=2y − 44,

y − 2y=− 44 − 62,

according to the techniques of Lesson 9,

−y=−106

y=106.

Bob has $106.  Therefore, according to the exression for x, Andre has

106 + 40 = $146.

I hope this helps u! :D