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# Adding Subtracting and Multiplying Polynomials

## Adding Subtracting and Multiplying Polynomials 1.7 - Solution

a
Remove the parentheses and add like terms.
$\left(3x^3-4x^2\right)+\left(3x^2-9\right)$
$3x^3-4x^2+3x^2-9$
$3x^3-x^2-9$
The greatest exponent is $3,$ which means that it is a polynomial of degree $3.$
b
When we remove the second parentheses, we need to change signs in front of every term inside of it, since there is a negative sign in front of the parentheses.
$\left(5x^4-x\right)-\left(5x^4-2x+1\right)$
$5x^4-x-5x^4+2x-1$
$5x^4-5x^4-x+2x-1$
$x-1$
Since $x$ is the same thing as $x^1,$ the polynomial is of degree $1.$
c
Since there is a negative sign in front of both parentheses the signs of all terms should be changed.
$\text{-} \left(5x^2-x+4\right)-\left(3x^2+2x-5\right)$
$\text{-} 5x^2+x-4-3x^2-2x+5$
$\text{-} 5x^2-3x^2+x-2x-4+5$
$\text{-} 8x^2-x+1$
The polynomial's degree is $2.$