Question

Help I don't understand

Factor Completely

3x^2 + 21x + 30

Answer 1

'Divide and conquer' is a good strategy if possible.

You've probably noticed that the numeric part of each term is divisible by 3; let's start with that. Divide each term by 3.
\[3 ( x ^{2} + 7x + 10 )\]
This is a quadratic (it has an x-squared in it). So we anticipate multiplying two factors (to make up the 2 in the exponent of x).

( x + a ) ( x + b )
If I multiply this out I get \[x ^{2} + ( a + b )x + ab\]
See how the a and b have added together to form the coefficient of x in the multiplied result? See how they are multiplied together to form the constant (ab) in the multiplied result?

In your problem then we need to find two numbers that add to 7 and multiply to 10. These are a and b. What are they? And can you proceed from here?

Answer 2

3x^2+21x+30/3
3(x^2+7+10)
3(x+5)(x+2)

Answer 3

3(x^2+7+10)
3(x+5)(x+2)
(3x+15)(3x+6
)

Answer 4

To save yourself confusion at the end. Divide both sides by 3.

Answer 5

thank you