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Q: What does the factor x of the first term of the expression represent?
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How do you factor out the GCF of an expression if the first term is negative?

i have to finish my algebra 1 homework and i have no idea what the answer is.... help!

How do you common factor an expression?

Find a number that evenly divides each term of the expression.

What is the numerical factor of a variable term of an algebraic expression?


Differences of a term and a factor?

In a function, a term is something that appears as part of the expression. A factor is something that goes into the expression WITHOUT REMAINDER. So if you consider y = x2 + 2x + 1 then 2x is a term in the expression, and, since y = (x + 1)2 = (x + 1)*(x + 1) then (x + 1) is a factor. A term need not be a factor and a factor need not appear as a term - as illustrated by this example. In the context of integers, a term would be similar to one of the digits [think of a decimal polynomial], whereas a factor would be a factor in the normal sense.

What is the number or constant factor in a variable term in an expression?

This is known as a coefficient.

What is the difference between factors and terms?

Terms are those parts of the expression between addition signs and subtraction signs. Consider this expression:x + y - zThis expression has three terms: the variables x, y, and z. We say that the first term is x, that the second term is y, and so on.Here is another expression:7 - f(x) + aThis expression also has three terms: the number 7, the function f(x), and the variable a.The first term is the number 7, the second term is the function f(x), and the third term is the variable a.Now, consider this expression:xy + 2Here, the first term is this:xyNotice that this term is made up of two parts, the variable x and the variable y.Factors are the separate parts of a multiplication. Consider this expression:xyThe above, of course, is a multiplication of x times y. The factors in this multiplication are x and y.In the following expression the factors are 8, p, and q:8pqNow, back to this expression:xy + 2Here the first term is xy, and that first term is made up of two factors, x and y.So, terms are groups of factors.The second term in this expression is the number 2. This term is made up of one factor, 2.Consider this expression:cd2This expression has one term which is made up of two factors. The first factor is c. The second factor is d2.In other words, powers are considered single factors. The factor d2 is not considered two factors even though it is equal to d times d.What about division? Well, it can defined in terms of multiplication, as in:So, one could say that the factors of a/b are a and 1/b.Also, we could work things this way:And clearly see that the factors of a/b are a and b-1.So, terms are inside of factors, but the factors themselves can be made up of terms which can have factors inside of them, and so it. It can get quite complicated! Consider this:(a + b + c)(d - ef)From the outer most viewpoint, this is an expression with one term, the entire expression.From this outer most viewpoint the first and only term in this expression is made up of two factors. The first factor is:(a + b + c)The second factor of this first and only term is:(d - ef)Now, let's look at that first factor of the first term. Again it is:(a + b + c)Or simply:a + b + cThis factor is itself made up of three terms: a, b, and c. Each of these terms has but one factor since each is but one variable.Let's also look at the second factor of the first term. Again it is:(d - ef)Or simply:d - efThis factor is made up of two terms, d and ef.The first term here, d, is made up of one factor, the single variable d.The second term here is made up of two factors, e and f.So, considering the original expression:(a + b + c)(d - ef)One could correctly say that the second term of the second factor is ef.Taking it just a bit further, the second factor of the second term of the second factor of the original expression is f.And so on...Custom SearchWhen discussion expression evaluation it is handy to understand what is meant in mathematics by the words 'term' and 'factor'.We have looked at expressions and discussed them from the viewpoint of operators and operands. Now, we will look at an expression from the viewpoint of terms and factors. From this viewpoint we are less concerned with the interactions among the parts of the expression, but more concerned with how to generally name the parts of an expression.

How do you factor a 4-term expression that doesn't have a common factor?

If it does not have a common factor, you cannot factorise it!

What are the rules in finding the special product?

Multiply the first term of the first factor to the first term of the second factor

What is each factor in a term called?

Make note that a term doesn't have to be a number. It can be the expression, like (3x - 6). In order to consider a term of the factorization of the term to be the factor, it must be prime. Therefore, we call each factor in a term "prime factor". Here is the example: 2x + 6 has a factor of 2. Then, we can factor out 2x + 6 to get 2(x + 3)

What are the special product?

multiply the first factor to the first term of the second factor

When factorising find the common factor?

To find the common factor when factorising, look for any common factors that can be divided evenly from all the terms in the expression. Divide each term by this common factor, and then factorise the resulting expression further if possible. This will help simplify the expression and make it easier to work with.

What are the finding special products?

multiply the first factor to the first term of the second factor