The first three equations I have solved, I would just appreciate someone checking them over to make sure I'm doing them right.
Find the GCF:
16x^2z ,40xz^2 , 72z^3
= 3^3z
Factor our GCF:
a(a+1) - 3(a+1)
= a+1
Factor Polynomial:
9a^2 - 64b^2
= (3a+8b)(3a-8b)
9w - w^3
= w(3) (?really unsure if correct?)
I'm not sure how to do the following, or where to even begin. Some help getting started would be very appreciated! :)
Factor Polynomials:
x^3y + 2x^2y^2 + xy^3
x^3 + ax + 3a + 3x^2
Factor:
18z + 45 +z^2
16x^2z ,40xz^2 , 72z^3
the GCF I see is 4xz, I can't see how you got your answer.
a(a+1) - 3(a+1)
= (a+1)(a-3) fully factored
9a^2 - 64b^2
= (3a+8b)(3a-8b) that is ok
9w - w^3 , I see a common factor of 3w
= 3w(3 - w^2)
x^3y + 2x^2y^2 + xy^3 first go for a common factor
= xy(x^2 + 2xy + y^2)
= xy(x+y)(x+y)
= xy(x+y)^2
x^3 + ax + 3a + 3x^2
this is a "grouping" type of factoring
= x^3 + 3x^2 + ax + 3a
= x^2(x+3) + a(x+3)
= (x+3)(a+3)
18z + 45 +z^2
= z^2 + 18z + 45
= (z+15)(z+3)
in the first one: 16x^2z ,40xz^2 , 72z^3
the only question I have is, how can it be 4xz when they don't all have the variable 'x'? the way I factored it was like this:
16x^2z
16 = 8 & 2 x^2z
4&2 (x)(x)(z)
2&2
= 2^4
40xz^2
40 = 10 & 4 xz^2
5&2 2&2 (x)(z)(z)
= 5(2^3)
72z^3
72 = 36 & 2 z^3
18&2 (z)(z)(z)
9&2
3&3
= 3^2(2^3)
with the answer being 2^3z, which is what they all have in common
3w-3
Factor 9z + 18 using the GCF.(1 point)
Let's check the first three equations you solved to make sure they are correct:
Find the GCF:
To find the greatest common factor (GCF) of the given terms: 16x^2z, 40xz^2, and 72z^3, we need to look for the highest power of each variable that appears in all the terms.
Factors of 16x^2z: 2^4, x^2, z^1
Factors of 40xz^2: 2^3, 5^1, x^1, z^2
Factors of 72z^3: 2^3, 3^2, z^3
The highest power of 2 that appears in all the terms is 2^3 (since 2^3 is common to all three terms). The highest power of x is x^1 (since it appears in the first and second terms). The highest power of z is z^1 (since it appears in the first and third terms).
Therefore, the GCF is 2^3 * x^1 * z^1 = 8xz.
So, the answer should be 8xz instead of 3^3z.
Factor out GCF:
You correctly factored out the greatest common factor (GCF) of a(a+1) - 3(a+1) as (a+1). Well done!
Factor Polynomial:
You correctly factored the polynomial 9a^2 - 64b^2 as (3a+8b)(3a-8b). Great job!
Now, let's move on to the ones you're unsure about and guide you on how to solve them:
Factor Polynomials:
To factor the polynomial x^3y + 2x^2y^2 + xy^3, we look for any common factors between the terms. In this case, we can factor out the common factor "xy" from all the terms:
xy(x^2 + 2xy + y^2)
The expression x^2 + 2xy + y^2 can be further factored as a perfect square:
xy(x + y)^2
So, the fully factored expression is xy(x + y)^2.
Factor:
To factor the expression x^3 + ax + 3a + 3x^2, we typically try to group terms and look for common factors. However, in this case, it seems that there is no clear grouping or common factor that can be factored out. It is possible that this expression cannot be factored further using simple algebraic techniques. Therefore, the expression x^3 + ax + 3a + 3x^2 may not be factorable.
Factor:
To factor the expression 18z + 45 + z^2, we first need to rearrange the terms to make it easier to work with:
z^2 + 18z + 45
This expression can be factored by finding two numbers whose product is 45 and whose sum is 18. In this case, the numbers are 9 and 5. We can rewrite the expression as:
(z + 9)(z + 5)
So, the fully factored expression is (z + 9)(z + 5).
I hope this explanation helps! If you have any more questions or need further assistance, feel free to ask.