Final answer:
To subtract polynomials (19x^2+17x) - (-3x^2+3x), remove the parentheses and change the signs of the terms inside, resulting in 19x^2 + 17x + 3x^2 - 3x, and then combine like terms to get 22x^2 + 14x.
Step-by-step explanation:
To subtract polynomials, we combine like terms by subtracting the coefficients of terms with the same degree of x. In this case, the problem is to subtract the polynomial (-3x^2 + 3x) from the polynomial (19x^2 + 17x).
Performing the subtraction, we first remove the parentheses, which changes the signs of the terms in the second polynomial:
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- (19x^2 + 17x) - (-3x^2 + 3x)
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- 19x^2 + 17x + 3x^2 - 3x
Next, we combine like terms:
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- (19x^2 + 3x^2) + (17x - 3x)
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- 22x^2 + 14x
Thus, the result of subtracting the polynomial (-3x^2 + 3x) from (19x^2 + 17x) is 22x^2 + 14x.