1. Find the quotient: e^2-e-12/e-4

A. e+3/e-4
b. e^2+3
C. e-3
D. e+3

2. Find the quotient: (a^2+11a+30) / (a + 5)

A. a+6
B. a^2 + 10a+25
C. a^2 + 11a + 25
D. a+6/a+5

3. Find the LCM for x^2+3x+2 and x^2 +5x+6.

A. (x+1)(x+2)(x+3)
B. x+1
C. x+3
D. (x+1)(x+3)

Need help with these 3 questions please

e^2-e-12 = (e-4)(e+3)

dividing by e-4 leaves e+3

similarly,
a^2+11a+30 = (a+5)(a+6)

x^2+3x+2 = (x+1)(x+2)
x^2+5x+6 = (x+2)(x+3)
now the LCM should be easy

Thank you

Sure! I'll explain how to solve each of these questions step by step.

1. Find the quotient: e^2-e-12/e-4

To find the quotient, we need to divide the numerator (e^2-e-12) by the denominator (e-4). We can do this by performing long division or simplifying the expression:

Factor the numerator: (e-4)(e+3)
Now the expression becomes: (e-4)(e+3)/(e-4)

Cancel out the common factor (e-4):
e+3

So, the answer is D. e+3

2. Find the quotient: (a^2+11a+30) / (a + 5)

To find the quotient, we need to divide the numerator (a^2+11a+30) by the denominator (a + 5). We can do this by performing long division or simplifying the expression:

Factor the numerator: (a+5)(a+6)
Now the expression becomes: (a+5)(a+6)/(a+5)

Cancel out the common factor (a+5):
a+6

So, the answer is A. a+6

3. Find the LCM for x^2+3x+2 and x^2 +5x+6.

To find the LCM (Least Common Multiple), we need to factor both expressions and then multiply together the highest powers of each factor.

Factor the first expression: (x+1)(x+2)
Factor the second expression: (x+2)(x+3)

Now, we can see that both expressions have a common factor of (x+2). To find the LCM, we multiply together the highest powers of each factor.

The LCM for (x+1)(x+2) and (x+2)(x+3) is (x+1)(x+2)(x+3).

So, the answer is A. (x+1)(x+2)(x+3).

I hope this helps! Let me know if you have any further questions.