How do you determine the like factors in a polynomial?

Question

When simplifying like terms, how do you determine the like terms?
Thanks for the help

Answer 1

The like terms are all of the numbers that look the same. 5x & 9x are like terms...5xy and 6y are not so you cant combine them. Hope this helps a little

Answer 2

In a polynomial, there are two main types of things

1.- The powers of a variable
2.- The constants multiplying each of this powers

If you have 'x' as a variable, a polynomial may be

5*x^5 - 2*x^5 - 3*x^3 + x + 1

Like terms are those who have the same power. In order to reduce them in a polynomial, just look at the same powers of the variable and sum algebraically their coefficients.

In the above example, there are two like terms, those with the 5th power, so you just have to do 5 - 2 (respective constants) to give

3*x^5 - 3*x^3 + x + 1

Talking about polynomials is important to know that the number of terms is finite and the powers of the variable are always non-negative. Recall that the constant that is not multiplying any power of the variable, actually is multiplying the 0th power (x^0 = 1).

Answer 3

Like terms in laymans terms are terms that look alike. Though if you've never seen many terms you probably wouldnt know what that means eh?

Basically like terms are terms (values and/or variables multiplying/dividing each other, no addition or subtraction) that have the exact same variable (all of that letter mush) component.

Ex:

3 and 5, 2x and 8x, and 7x^2y^6z^5 and 4x^2y^6z^5 are like terms.

3 and 5 have no variable component
2x and 8x have x as the variable
7x^2y^6z^5 and 4x^2y^6z^5 have x^2y^6z^5 as the variable

However!

3x and 5x^2, and 6y and 6x are not like terms

3x and 5x^2 has x and x^2 as variables; respectively
6y and 6x has y and x as variables; respectively

Answer 4

actual, in case you're able to do straightforward arithmetic on your head rather rapidly, attempting each and every mixture is oftentimes the quickest way, yet i ought to provide you some suggestion which will help to shrink the style of mixtures rapidly. The 5 can ingredient into in straightforward terms one mixture, (a million and 5), however the 12 can ingredient into 3, (a million and 12), (2 and six), and (3 and four). because of the fact the middle term is extremely intense, you could assume you would be using intense with intense and occasional with low (ex. a million,a million and 5,12). you could exceedingly actual see that mixture isn't precise, so then you certainly in straightforward terms have 2 mixtures to purpose somewhat of 6! wish that enables!

Answer 5

Like terms are those that alike except for the numerical coefficient. This means they have to contain all the litterals to the same powers.

x terms will combine with each other, but not with x².

x²y combines with x²y, but not with x²y².

Does that help?

Answer 6

All numbers are like terms

All terms having the same variable are like terms 3x^2, 7x^2 11 x^2 are all like terms.

2ab, 6ab, 8ab are like terms

16xyz, 17 xyz, 24 xyz are like terms

2a^2b^2c, 5a^2b^2c, 9a^2b^2c are like terms

xyz and wxyz are not like terms

Answer 7

same variable and same exponent.

that is what defines a like term

EX. 5X and 30x are like terms

5x and 30x^2 are not like terms