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Adding Subtracting and Multiplying Polynomials

Adding Subtracting and Multiplying Polynomials 1.7 - Solution

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a
Remove the parentheses and add like terms.
(3x34x2)+(3x29)\left(3x^3-4x^2\right)+\left(3x^2-9\right)
3x34x2+3x293x^3-4x^2+3x^2-9
3x3x293x^3-x^2-9
The greatest exponent is 3,3, which means that it is a polynomial of degree 3.3.
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.
(5x4x)(5x42x+1)\left(5x^4-x\right)-\left(5x^4-2x+1\right)
5x4x5x4+2x15x^4-x-5x^4+2x-1
5x45x4x+2x15x^4-5x^4-x+2x-1
x1x-1
Since xx is the same thing as x1,x^1, the polynomial is of degree 1.1.
c
Since there is a negative sign in front of both parentheses the signs of all terms should be changed.
-(5x2x+4)(3x2+2x5)\text{-} \left(5x^2-x+4\right)-\left(3x^2+2x-5\right)
-5x2+x43x22x+5\text{-} 5x^2+x-4-3x^2-2x+5
-5x23x2+x2x4+5\text{-} 5x^2-3x^2+x-2x-4+5
-8x2x+1\text{-} 8x^2-x+1
The polynomial's degree is 2.2.