Question

From the sum of \[4+3x\] and \[5-4x+2{{x}^{2}}\], subtract the sum of \[3{{x}^{2}}-5x\] and \[-{{x}^{2}}+2x+5\]

Answer 1

Hint: Here in this question we are given four polynomial equations and we need to find the subtraction of addition of two of those equations. In addition to polynomials we can only add terms with the same power of variable with each other. It’s the same case with subtraction of polynomials, you can only subtract two terms with each other if the power of their variables is the same.


Complete step-by-step answer:
Now we are given four equations and we need to find the sum of first two equations which are
\[4+3x\] ---- equation I
\[5-4x+2{{x}^{2}}\] --- equation II
Now we need to find the sum of these equations,therefore we add both of them together and we add the coefficients of all the terms with the same power together, therefore keeping that in mind, we take,
\[(4+3x)+(5-4x+2{{x}^{2}})\]
Opening the brackets and grouping the terms with same power together
\[2{{x}^{2}}+(3x-4x)+(4+5)\]
Now adding the coefficients we get, and we let that be the third equation
\[2{{x}^{2}}-x+9\] --- equation III
Now we are given two other equations that we need to add with each other these equations are
\[3{{x}^{2}}-5x\] --- equation IIII
\[-{{x}^{2}}+2x+5\] --- equation V
Now we need to find the sum of these equations, therefore we add both of them together and we add the coefficients of all the terms with the same power together, therefore keeping that in mind, we take,
\[\left( 3{{x}^{2}}-5x \right)+\left( -{{x}^{2}}+2x+5 \right)\]
Opening the brackets and grouping the terms with same power together
\[\left( 3{{x}^{2}}-{{x}^{2}} \right)+\left( -5x+2x \right)+5\]
Now adding the coefficients we get, and we let that be the sixth equation
\[2{{x}^{2}}-3x+5\] --- equation VI
We now need to subtract equation VI from equation III, therefore
\[\left( 2{{x}^{2}}-x+9 \right)-\left( 2{{x}^{2}}-3x+5 \right)\]
Opening the brackets and grouping the terms with same power together,
\[\left( 2{{x}^{2}}-2{{x}^{2}} \right)+\left( -x+3x \right)+\left( 9-5 \right)\]
Now on subtracting all the coefficients with the same power we get
\[0+2x+4\]
Therefore we get the answer of this question which is
\[2x+4\]
So, the correct answer is “\[2x+4\]”.

Note: In questions like this always avoid making sign mistakes especially when subtracting two polynomials as it might give the wrong answer. To also explains polynomials in short, polynomial is an expression with coefficients and variable which is usually expressed in the form of \[P(x)=a{{x}^{n}}+b{{x}^{n-1}}+c{{x}^{n-2}}......\].