Question: 30x^3 + 18x^2 - 5x - 3
My Answer: 6x^2(5x+3)(-5x-3)
Is that right. If not can you please correct my answer and tell me what to do! Thanks :)
it's wrong
you have
6x²(5x+3)-(5x+3)
and you can facorize it
So what is the right answer?
(5x+3)(6x²-1)
or
(5x+3)(sqrt(6)x-1)(sqrt(6)x+1)
I believe mk-tintin intended to write:
(5x+3)(6x^2-1)
which can be further factored to obtain:
(5x+3)(sqrt(6)x-1)(sqrt(6)x+1)
To determine whether your answer is correct, we will need to factor the polynomial expression given: 30x^3 + 18x^2 - 5x - 3.
To factor a polynomial, the first step is to look for any common factors among the terms. In this case, we can see that there is no common factor other than 1.
The next step is to check if the polynomial can be factored using any special factoring techniques such as factoring by grouping, difference of squares, or perfect square trinomials. In this case, none of those techniques apply.
So, the next approach is to use the general factoring method for polynomials with four terms, which involves factoring by grouping or using trial and error.
To use factoring by grouping, we can group the terms in pairs and factor out a common factor from each pair. Let's group the terms as follows:
(30x^3 + 18x^2) + (-5x - 3)
Now, let's factor out the greatest common factor from each pair:
6x^2(5x + 3) - 1(5x + 3)
Notice that the terms inside the parentheses are the same, which indicates that we can further factor out a common binomial factor. Let's factor out (5x + 3):
(5x + 3)(6x^2 - 1)
So, the factored form of the given polynomial expression is (5x + 3)(6x^2 - 1).
Now, let's compare this with your answer to determine if it is correct:
Your answer: 6x^2(5x + 3)(-5x - 3)
It seems that you made a sign error. The correct factorization should be:
6x^2(5x + 3)(-5x + 3)
To correct your answer, simply change the sign of the last term in the parentheses to match the original expression.
Therefore, the correct factorization of the given polynomial expression is:
(5x + 3)(6x^2 - 1)