Factor the polynomial
17xy^4+51x^2y^3
7xy(10y^4+44xy^2)
17xy^3 (y+3x)
17xy(1+ 1/3 xy^2)
xy(17+51y^2)
Can I have some help on solving this please?
Hey Lady Phantomhive,
Ok let's start from the basics. (i did this sort of thing yesterday and today so my brain is refreshed on it).
Do you know how to factor polynomials?
I don't think so, this is a pre-practice so its on things I havent gotten well acquainted on yet.
I am going to try to help you, but be warned I do sometimes (not often) need help on this subject.
We are going to figure out what numbers we need to make the numbers above.
We are trying to make that answer into a problem like
3(x-3)(x+8) <--(not your answer)
What are the GCF of 51 and 17. I think both numbers are prime numbers so we may have to use decimals in this problem (not often used ever in algebra)
The GCF is 17.
Ha, well your right. I forgot that 17 went into 51.
Anyway what number would it have to be for 17 to turn into 51 and also stay 17.
a(x+a)(x+a)
We are trying to figure out what numbers are to go where the A's go.
We just figured out the first a
17(x+a)(x+a)
Of course! Factoring a polynomial involves expressing it as a product of its factors. In this case, we have the polynomial 17xy^4 + 51x^2y^3.
Step 1: Look for the greatest common factor (GCF) among the terms. In this case, the GCF is 17xy^3. Divide each term by the GCF:
17xy^4 ÷ 17xy^3 = y
51x^2y^3 ÷ 17xy^3 = 3x
Step 2: Write the GCF outside of the parentheses and divide each term by the GCF to obtain the remaining factors:
17xy^4 + 51x^2y^3 = 17xy^3(y) + 17xy^3(3x)
Step 3: Combine the terms inside the parentheses:
17xy^3(y + 3x)
Therefore, the factored form of the given polynomial is 17xy^3(y + 3x).