Question

How do you write $8{{x}^{2}}-4x+2{{x}^{2}}$ in standard form?

Answer 1

Hint: In the above question, we have been given a quadratic polynomial, which is $8{{x}^{2}}-4x+2{{x}^{2}}$, and are told to write it in the standard form. The standard form of a quadratic polynomial is written as $a{{x}^{2}}+bx+c$. Therefore we have to combine all the similar degree terms in the given quadratic polynomial and write them in the decreasing order of the powers for x. In the given quadratic polynomial $8{{x}^{2}}-4x+2{{x}^{2}}$ we can see that the terms $8{{x}^{2}}$ and $2{{x}^{2}}$ have the same degree. Therefore we have to combine them to get $8{{x}^{2}}+2{{x}^{2}}-4x$. Then on simplifying the obtained polynomial, we will finally get the standard form for the given quadratic polynomial.

Complete step by step answer:
Let us consider the polynomial given in the above question as
$\Rightarrow p\left( x \right)=8{{x}^{2}}-4x+2{{x}^{2}}$
According to the question we have to write the above polynomial in the standard form. We know that the standard form of a quadratic polynomial is given by $a{{x}^{2}}+bx+c$. Therefore, we arrange the first term and the third term together, since they have equal degrees, to get
$\begin{align}
  & \Rightarrow p\left( x \right)=8{{x}^{2}}+2{{x}^{2}}-4x \\
 & \Rightarrow p\left( x \right)=10{{x}^{2}}-4x \\
\end{align}$

Hence, we have finally expressed the given polynomial in the standard form as $10{{x}^{2}}-4x$.

Note: We must not forget the fact that the standard form of any polynomial is the arrangement of its terms in the decreasing order of the powers for the variable. We may think of taking $2x$ common from the obtained polynomial \[10{{x}^{2}}-4x\] to get \[2x\left( 5x-2 \right)\]. But since this is not the standard form for a polynomial, we must end our solution at \[10{{x}^{2}}-4x\].