# Express as a polynomial. (3x^{3} + 4x^{2} - 7x -

Express as a polynomial. $\left(3{x}^{3}+4{x}^{2}-7x-1\right)+\left(9{x}^{3}-4{x}^{2}-6x\right)$
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poleglit3
Step 1
Given: $\left(3{x}^{3}+4{x}^{2}-7x-1\right)+\left(9{x}^{3}-4{x}^{2}-6x\right)$
We have to express the given expression as a polynomial.
Step 2
Explanation:
$\left(3{x}^{3}+4{x}^{2}-7x-1\right)+\left(9{x}^{3}-4{x}^{2}-6x\right)$
$=3{x}^{3}+9{x}^{3}+4{x}^{2}-4{x}^{2}-7x-6x-1$
$=12{x}^{3}-13x-1$

servidopolisxv
To obtain the sum of two polynomials in x, we may add the coefficients of like powers of x.
Therefore,
$\left(3{x}^{3}+4{x}^{2}-7x+1\right)+\left(9{x}^{3}-4{x}^{2}-6x\right)$
$=3{x}^{3}+4{x}^{2}-7x+1+9{x}^{3}-4{x}^{2}-6x$
[Removing the parenthesis]
$=\left(3+9\right){x}^{3}+\left(4-4\right){x}^{2}+\left(-7-6\right)x+1$
[Adding the coefficients of like powers of x]
$=12{x}^{3}-13x+1$ [Simplifying]
Hence, the required polynomial is
$12{x}^{3}-13x+1$