Through the addition and subtraction of the polynomial functions, g(x), f(x), and h(x), we have;
1. g(x) - k(x) = 6•x² - 3•x³ - 8•x + 8
2. h(x) + g(x) = 2•x² - x - 2
3. k(x) - g(x) = 3•x³ - 6•x² + 8•x - 8
4. h(x) - (g(x) + k(x)) = 2•x² - 3•x³ + 3
5. k(x)-g(x)+k(x)=6•x³- 10•x² + 13•x - 15
<h3>How can the expressions representing the polynomial functions be found?</h3>
The given functions are;
- g(x) = 2•x² - 3•x + 1
- h(x) = 2•x - 3
- k(x) = 3•x³ - 4•x² + 5•x - 7
Which gives;
1. g(x) - k(x) = 2•x² - 3•x + 1 - (3•x³ - 4•x² + 5•x - 7) = 6•x² - 3•x³ - 8•x + 8
- g(x) - k(x) = 6•x² - 3•x³ - 8•x + 8
2. h(x) + g(x) = 2•x - 3 + (2•x² - 3•x + 1) = 2•x² - x - 2
- h(x) + g(x) = 2•x² - x - 2
3. k(x) - g(x) = 3•x³ - 4•x² + 5•x - 7 - (2•x² - 3•x + 1) = 3•x³ - 6•x² + 8•x - 8
- k(x) - g(x) = 3•x³ - 6•x² + 8•x - 8
4. h(x) - (g(x) + k(x)) can be found as follows;
g(x) + k(x) = 2•x² - 3•x + 1 + 3•x³ - 4•x² + 5•x - 7 = 3•x³ - 2•x² + 2•x - 6
h(x) - (g(x) + k(x)) = 2•x - 3 - (3•x³ - 2•x² + 2•x - 6) = 2•x² - 3•x³ + 3
- h(x)- (g(x) + k(x)) = 2•x² - 3•x³ + 3
5. k(x) - g(x) + k(x) = 3•x³ - 4•x² + 5•x - 7 - (2•x² - 3•x + 1) + 3•x³ - 4•x² + 5•x - 7 = 6•x³ - 10•x² + 13•x - 15
- k(x)-g(x)+k(x)=6•x³-10•x²+13•x- 15
Learn more about polynomial functions here:
brainly.com/question/6948391
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