Question

How do you identify the terms, like terms, coefficients and constant in each expression: $8 + 6t - 3t + t$?

Answer 1

Hint: In mathematics polynomial is the made by the terms and all the terms are separated by the sign of $ + $ and $ - $ in the polynomial terms we can say they are like the letters in the English word only the difference in the both is that terms are differ by the sign of $ + $ and $ - $.

Complete step by step Solution:
Given that –
Identify the terms in the given polynomial $8 + 6t - 3t + t$
Now we will first discuss all terms in polynomial which we have to find in the given polynomial $8 + 6t - 3t + t$
Terms – In the polynomial total number of terms are $4$ which are the $8,6t,3t$ and $t$, and they are separated by the sign of $ + $ and $ - $.
Like Terms – In the polynomial like terms are the terms which have the same order of the variable for example in the given polynomial we have three like terms which are $6t,3t$ and $t$ because they gave the same order variable $t$
Coefficients – Coefficients are the number which are written with variable as multiplication of the variable term for example in the given polynomial we three variable terms which are $6t,3t$ and $t$
So we can see that $6t$ in which $t$ is multiply by the $6$ so here the coefficient of $t$ is the $6$
Similarly, in $3t$ in which the coefficient is the $3$ and in the $t$here no number is number is multiply with the $t$, in these types of cases where only variable is written then always there the variable is the multiply by $1$ so the coefficient is always is $1$.
Constant – In the polynomial constant term are numbers which always have a static value that is the value of the constant is not changed or for identifying we can say that in the polynomial constant is a term which is written without the variable.
For example, in the given polynomial constant term is the $8$.

Note:
Polynomials are like the word of English because the polynomial is made by the terms and the terms are separated by the sign of $ + $ and $ - $ but in English word are made by the letters $a,b,c,...$ but always remember the difference between the variable and constant.