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
Molly can paint a house in 4 days.Tess could paint the same house in 6 days. How long would it take them to paint the house if they worked together
Let's go through each of the equations you have solved and check if they are correct.
1. Find the GCF:
To find the greatest common factor (GCF) of 16x^2z, 40xz^2, and 72z^3, you need to find the largest term that can divide all three expressions evenly. In this case, the GCF is obtained by multiplying the common factors with the smallest exponents:
GCF = 2z.
Your answer of 3^3z is incorrect because 3 is not a common factor among the given terms.
2. Factor out GCF:
To factor out the GCF from the expression a(a+1) - 3(a+1), you can apply the distributive property. Take (a+1) as a common factor:
(a+1)(a - 3).
Your answer of a+1 is correct.
3. Factor Polynomial:
For the polynomial 9a^2 - 64b^2, you can identify it as a difference of squares because it is in the form a^2 - b^2. You can factor it using the formula:
a^2 - b^2 = (a+b)(a-b).
Applying this formula, let a = 3a and b = 8b:
(3a+8b)(3a-8b).
Your answer of (3a+8b)(3a-8b) is correct.
4. Factor Polynomial:
For the expression 9w - w^3, you can first factor out the common factor w:
w(9 - w^2).
Your answer of w(3) is incorrect. Make sure you properly factor out the common factor before simplification.
Now, let's move on to the equations you need help with:
1. Factor Polynomials: x^3y + 2x^2y^2 + xy^3
To factor this polynomial, you can look for common terms among the three terms. In this case, the common term is xy. Factor it out:
xy(x^2 + 2xy + y^2).
2. Factor: x^3 + ax + 3a + 3x^2
To factor this expression, you need to look for common factors among the terms. Unfortunately, in this case, there isn't an obvious common factor. It appears that this expression may not factor further.
3. Factor: 18z + 45 + z^2
To factor this expression, you can rearrange the terms to group the like terms together:
z^2 + 18z + 45.
Now, you need to find two numbers that multiply to 45 and add up to 18. Those numbers are 15 and 3. With that, you can factor the expression as:
(z + 15)(z + 3).
I hope this helps you understand how to solve these equations. Let me know if you have any further questions!