Adding and Subtracting Polynomials | MathHelp.com
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In this problem, we’re asked to add the given polynomials, then we’re asked to subtract the second polynomial from the first. In part a, to add the given polynomials, we simply add parentheses t^2 + 6t – 9 + parentheses t^2 + 7t - 3. Notice that I used parentheses around the polynomials. This is a good habit to get into, even though the parentheses will not affect the addition. Next, we simply add the like terms, t^2 + t^2 is 2t^2, 6t + 7t is 13t, and -9 - 3 is -12. So we have 2t^2 + 13t – 12. In part b, we’re asked to subtract the second polynomial from the first, so we have parentheses t^2 + 6t – 9 minus parentheses t^2 + 7t - 3. Notice that the second polynomial is subtracted from the first. And again, notice that we use parentheses around each polynomial. Now, it’s important to understand that the minus sign outside the second set of parentheses can be thought of as a negative 1, so we need to distribute the -1 through each of the terms in the second set of parentheses. So, after rewriting our first polynomial, t^2 + 6t – 9, we have -1 times t^2, or –t^2, -1 times positive 7t, which is -7t, and -1 times -3, which is positive 3. Now, we combine like terms. t^2 – t^2 cancels out, positive 6t minus 7t is -1t, or –t, and -9 + 3 is -6. So we have –t – 6. Makes sure to distribute the negative 1 through the parentheses when subtracting the second polynomial from the first.
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