Factor Completely: 3x2 + 21x + 36
Responses
A 3(x + 3)(x + 4)3(x + 3)(x + 4)
B (x + 4)(3x + 9)(x + 4)(3x + 9)
C (x + 9)(3x + 4)(x + 9)(3x + 4)
D (x + 3)(3x + 12)
To factor the expression 3x^2 + 21x + 36 completely, we can look for common factors and then use the distributive property.
First, we notice that 3 is a common factor of all the terms. We can factor out 3:
3(x^2 + 7x + 12)
Next, we can factor the quadratic expression x^2 + 7x + 12. We're looking for two numbers that multiply to get 12 and add up to 7. The numbers 3 and 4 fit these conditions, so we can factor the quadratic expression as:
(x + 3)(x + 4)
Putting it all together, we have:
3(x + 3)(x + 4)
Therefore, the correct answer is A) 3(x + 3)(x + 4).
To factor the expression 3x^2 + 21x + 36 completely, we can start by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 3. We can factor out 3 from each term:
3(x^2 + 7x + 12)
Next, we need to factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to give 12 and add up to 7. The numbers that fit these criteria are 3 and 4.
3(x + 3)(x + 4)
Therefore, the completely factored form of the expression 3x^2 + 21x + 36 is 3(x + 3)(x + 4).
So, the correct answer is A) 3(x + 3)(x + 4).