I can't solve this problem:
4x^3 + 5x^2 - 12 + 27/(x + 3)
A. 4x^2 - 7x + 9
B. 4x^2 + 7x + 9
C. 4x^2 - 7x + 27
D. 4x^2 + 7x + 27
I can only get 4x^2 - 7x + 21 but obviously that isn't an answer..
You must mean:
(4x^3 + 5x^2 - 12x + 27)/(x + 3)
I did a synthetic division and got
4x^2 - 7x + 9 , which is A
since none of the answers had a remainder, you knew the division had to be exact, so it had to look like this
(4x^3 + 5x^2 - 12x + 27) = (x+3)(4x^2 .... +9)
so it had to be either A or B
How could it possible end it 21 ?
(x+3)(4x^2 ..... + 21) would be something like
(4x^3 ...... + 63) , which is not what you started with
"solve" involves at least one equation and one unknown.
I think you mean "simplify the expression".
Also, according to PEMDAS, you need parentheses when dividing a polynomial by a binomial, and the division is written on a single line (as you do when you enter it on your calculator).
I also assume the question is
(4x^3+5x^2-12x+27)/(x+3)
note -12x instead of -12.
So the problem is really:
"Simplify:
(4x^3 + 5x^2 - 12x + 27)/(x + 3)"
I would first see if (x+3) is a factor by substituting x=-3 into the numerator, which gives -108+45+36+27=0.
This means that (x+3) is a factor of the numerator. You will need to
1. do a synthetic division, or long division to obtain the answer, or
2. factor the numerator.
Hint for factorization:
4x^3 + 5x^2 - 12x + 27
= 4x^3+12x^2 -7x^2-12x+27
= 4x^3+12x^2 -7x^2-21x +9x+27
= 4x^2(x+3) -7x(x+3) +9(x+3)
To solve the problem, you need to simplify the given expression and then factor it if possible. Let's go through the steps together:
Start with the expression:
4x^3 + 5x^2 - 12 + 27/(x + 3)
Combine like terms:
4x^3 + 5x^2 + (27/(x + 3)) - 12
Now, let's focus on simplifying the rational expression 27/(x + 3). To do this, follow these steps:
1. Find the least common multiple (LCM) of the denominator (x + 3) and the numerator (27). In this case, the LCM is (x + 3).
2. Rewrite the numerator (27) so that its denominator becomes the same as the LCM (x + 3). Multiply the numerator/denominator by the same expression, which in this case is (x + 3). This gives us:
27 * (x + 3) / (x + 3)
The (x + 3) in the numerator and the denominator cancel out, leaving us with just 27:
27
3. Substitute 27 back into the original expression, which simplifies to:
4x^3 + 5x^2 + 27 - 12
Next, let's try to factor this polynomial expression:
4x^3 + 5x^2 + 15
To factor this, we look for common factors and try to use the techniques of factoring. In this case, we cannot easily factor this expression further.
So, the simplified expression is:
4x^3 + 5x^2 + 15
However, none of the answer choices provided match this expression. It seems like there might be an error in the problem or answer choices. Double-check the original problem statement or consult with your instructor to clarify the issue.