Question

Add \[3x + 11\] and \[7x - 5\].

Answer 1

Hint: We have to add \[3x + 11\] and \[7x - 5\]. This is a case of addition of two polynomials. Also, we can see that the nature of given polynomials is linear. So, this is a case of addition of linear polynomials. We will add them by adding the coefficients of terms with the same degree of the variable and coefficients of both the terms together.

Complete step-by-step answer:
We are given two polynomials which we have to add. Given polynomials are linear in nature.
Polynomial is an expression that contains variables and coefficients where variables are also called indeterminates.
This is a case of addition of like terms. Like terms can be defined as terms that contain the same variable raised to the same power. Only numerical coefficients are different. For example, \[x + 2x\] is an algebraic expression with like terms. When we have to simplify this algebraic expression, we can add the like terms. Thus, the simplification of \[x + 2x\] is \[3x\].
In a similar way, we can add \[3x + 11\] and \[7x - 5\].
Here, we can see that the first polynomial consists of two terms \[3x\] and \[11\] i.e., the coefficient is \[3\], the variable is \[x\] and \[11\] is a constant. Similarly, the second polynomial also consists of two terms \[7x\] and \[ - 5\] i.e., the coefficient is \[7\], variable is \[x\] and \[ - 5\] is a constant.
Now, for adding \[3x + 11\] and \[7x - 5\], we need to add the coefficients of the same variable with the same degree and both constants together.
Therefore, on adding we get
\[ \Rightarrow \left( {3x + 11} \right) + \left( {7x - 5} \right) = \left( {3x + 7x} \right) + \left( {11 - 5} \right)\]
On simplification we get
\[ \Rightarrow \left( {3x + 11} \right) + \left( {7x - 5} \right) = 10x + 6\]
Therefore, the addition of \[3x + 11\] and \[7x - 5\] is \[10x + 6\].
So, the correct answer is “\[10x + 6\]”.

Note: Here, we have to add two linear polynomials. So, we have used the concept of like terms. It is applicable for addition of any two or more polynomials if all the terms of the polynomial are of the same degree. One point to note is that the concept of like terms is also applicable in the case of subtraction.