# Find the sum of the polynomials: 8x^{3}-2x^{2}+6x-2 and 3x^{4}-2x^{3}+x^{2}+x

Find the sum of the polynomials:
$8{x}^{3}-2{x}^{2}+6x-2$ and $3{x}^{4}-2{x}^{3}+{x}^{2}+x$
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Step 1
To find the sum of polynomials: $8{x}^{3}-2{x}^{2}+6x-2$ and $3{x}^{4}-2{x}^{3}+{x}^{2}+x$
Solution:
$\left(8{x}^{3}-2{x}^{2}+6x-2\right)+\left(3{x}^{4}-2{x}^{3}+{x}^{2}+x\right)$
On simplifying further we get:
$\left(8{x}^{3}-2{x}^{2}+6x-2\right)+\left(3{x}^{4}-2{x}^{3}+{x}^{2}+x\right)=3{x}^{4}+8{x}^{3}-2{x}^{3}-2{x}^{2}+{x}^{2}+6x+x-2$
$⇒\left(8{x}^{3}-2{x}^{2}+6x-2\right)+\left(3{x}^{4}-2{x}^{3}+{x}^{2}+x\right)=3{x}^{4}+\left(8{x}^{3}-2{x}^{3}\right)-\left(2{x}^{2}-{x}^{2}\right)+\left(6x+x\right)-2$
$⇒\left(8{x}^{3}-2{x}^{2}+6x-2\right)+\left(3{x}^{4}-2{x}^{3}+{x}^{2}+x\right)=3{x}^{4}+6{x}^{3}-{x}^{2}+7x-2$
Step 2
Result:
Required expression is:
$3{x}^{4}+6{x}^{3}-{x}^{2}+7x-2$
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