x4 (x2 + 5x - 14) - 16 (x2 + 5x - 14)
First recognize that x2 + 5x - 14 is a "common factor." So rewrite as:
(x2 + 5x - 14)(x4 - 16)
Both of these polynomial groupings may be factored further.
The first ( )'s is a trinomial that can be factored using FOIL:
I thought I'd throw in my two cents here too.
When I teach these type of problems (mixture story problems), I tell my students to look for two ideas: Quantity and Value. These two ideas will create two equations for the story.
Quantity - answers the question, "How many...
You can always distribute, Jamal, if formulas elude you...
First of all (6b + 2)^2 means (6b + 2)(6b + 2)
The acronym FOIL stands for First Outer Inner Last; this phrase helps students to keep track of what they're distributing.
F: 6b • 6b
O: 6b • 2
I: 2• 6b
L: 2 • 2
(2a + 4)^3 means (2a + 4)(2a + 4)(2a + 4)
Multiply the first two groupings together using FOIL:
(2a + 4)(2a + 4) = 4a^2 + 8a + 8a + 16
Combine like terms: 4a^2 + 16a + 16
Now take that answer and multiply by the third grouping using distributive property:
(4a^2 + 16a + 16)(2a...
Are you trying to write 2 to the 9th minus 8 to the 3rd?
If so, write it like this: 2^9 - 8^3 (this way we know what you're asking)
If this indeed is your question, use order of operations to help you calculate. Applying exponents comes before adding or subtracting.
So evaluate 2^...
If I'm reading your question correctly, you are asking to find the lcm of the expression:
2 + 5x .
x - 3 (x - 3)^2
Do you see how the factor (x - 3) is duplicated? I tell my students that...
To find perimeter of a triangle, we must have all three sides. We can assume the two triangles are right triangles since they make up a rectangle (window pane). Anytime we're working with right triangles, we may use the Pythagorean Theorem to help us find
a missing side.
a^3 b = 7 .
4 v c^2
Brian is right in his steps... just thought you would like to see what is happening with each of those steps:
The object is to get the variable, a, alone. So let's take care of the denominator first by multiplying both sides of the...
In my Algebra class we are doing something similar to this. Without the directions, it's hard to say if it's the same as our lesson.
Anyway, our book asks us to come up with possible number(s) to put in the blank so that you can factor the polynomial, 5x^2 + 11 x + blank. What...
This problem looks like a good candidate for using substitution to solve it.
y = -x + 8
y = x
We can substitute x (from the second equation) in place of y (in the first equation):
x = -x + 8
Now solve the new equation by getting the variable term on only...
Remember to "think opposite" when you solve equations like this. Use opposite operations in the reverse Order of Operations to get the variable term (the term with the letter) alone.
For example: 12x + 24 = 72
The variable term is on the left side. Check to see what's...
They work the same way as each other ...
You can express exponential equations using logarithms and vice versa:
logb(expression) = number ... means the same thing as bnumber = (expression).
What I tell my students is to remember to keep the bases the same, and the exponent of the...
Typically in literal equations, the student is asked to solve for one of the variables in the problem. For example, in your equation 7x + 2y = 5, you might have been asked to solve for y. This means you need to isolate the y by the same method you would
if you had all...
To solve equations like this type, make sure to follow three steps:
1) Simplify both sides of the equation
2) Make sure there is only a variable term (letters) on one side of the equation
3) Think "opposite" - that is, do opposite operations in the opposite order of...
I don't know if I would say one method is best over another, but I would say that I would prefer to use the Elimination Method on this system. The Elimination Method is when you add the equations vertically, and one of the variable terms conveniently "cancel
each other out."...
This type of story problem is called a "mixture" problem because you're mixing two things (plums and peaches). Whenever you have mixture problems, consider two ideas to create two equations:
The Quantity just states the relationship about the amounts of...
When solving equations, make sure you do the following:
1) Both sides of the equation need to be simplified
2) Arrange variable terms to only be on one side of the equation by doing the "opposite operation"
3) Solve what remains by doing "opposite operations" in the "reverse order of...
This polynomial has a GCF (Greatest Common Factor) of 2. The only thing you can do with this one is to rewrite it with a 2 in front of a grouping like this:
And then get the numbers inside the grouping by dividing each term of the original expression...
No, do not multiply the 10 times the terms in the grouping (parentheses). The 10 is not immediately in front of it, the negative sign is. You will be multiplying the terms in the grouping by -1 (the 1 is understood). So your new equation will look like
10 - 2x +...
When you are factoring polynomials of this type, think of all the possible factors of the last term (neg 48):
1 * -48
2 * -24
3 * -16
4 * -12
6 * - 8
8 * - 6
12 * -4
16 * -3
24 * -2
48 * -1
Of all these pairs, one of them fits into (x...