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.