Question

How do you subtract \[7x-9\] from \[2{{x}^{2}}-11\]?

Answer 1

Hint: In order to find the solution to this question, we will start solving this question by converting the given statement to a mathematical expression, and then we will do the necessary calculations to get our required answer.

Complete step by step answer:
According to the question, we have been asked to find the value when \[7x-9\] is subtracted from \[2{{x}^{2}}-11\].
Now, to add or subtract two given polynomials, one should always combine the terms of the same degree. Like in order to add \[a{{x}^{2}}+bx+c\] and \[d{{x}^{2}}+ex+f\], we need to combine the terms \[(a+d){{x}^{2}}+(b+e)x+(c+f)\] which will be the desired polynomial by adding those two polynomials.
So, to subtract \[7x-9\] from\[2{{x}^{2}}-11\], we will first write both of our expressions in the form of standard quadratic equation, that is \[a{{x}^{2}}+bx+c\]. Therefore, we get \[7x-9=0{{x}^{2}}+7x-9\] and \[2{{x}^{2}}-11=2{{x}^{2}}+0x-11\].
Now, we have been asked to subtract \[7x-9\] from\[2{{x}^{2}}-11\], which means we have to subtract \[0{{x}^{2}}+7x-9\] from \[2{{x}^{2}}+0x-11\].
And we know that when we subtract \[a\] from \[b\], we mean to say \[b-a\]. Therefore, we can express the given statement as
\[\left( 2{{x}^{2}}+0x-11 \right)-\left( 0{{x}^{2}}+7x-9 \right)\]
Now, by using the properties of like terms, we can say that the coefficients of \[{{x}^{2}}\] will show algebraic sum and coefficients of \[x\] will show algebraic sum, and constants will show algebraic sum separately.
Therefore, we can write
\[\Rightarrow \left( 2-0 \right){{x}^{2}}+\left( 0-7 \right)x+\left( -11+9 \right)\]
Now, we will perform basic algebraic operations and make necessary calculations. Therefore, we get
\[\Rightarrow 2{{x}^{2}}+\left( -7 \right)x+\left( -2 \right)\]
And on further simplification, we get
\[\therefore 2{{x}^{2}}-7x-2\]
Thus, the required polynomial is \[2{{x}^{2}}-7x-2\].

Note:
One should always be careful about which polynomial should be subtracted from which one. That is when we subtract \[a\] from \[b\], we mean to say \[b-a\]. Sometimes, the sign change is done only for a few coefficients and not all, this leads to a wrong answer. Thus, one needs to be careful while writing these equations.