Algebra RefresherDate: 12/31/97 at 11:49:42 From: Aileene Cottrell Subject: Need Help Immediately Dear Dr. Math: I am trying to get into an algebra class in college and am refreshing my memory of what I learned in high school. Currently, I am trying to figure out how to solve this equation: (x^3 + 3x^2 - 4x + 3) / (x+1). If you can walk me through this and give me a formula that I can always apply to get to the right answer, I'd really appreciate it. Thanks, Aileene Date: 12/31/97 at 12:11:47 From: Doctor Rob Subject: Re: Need Help Immediately First of all, this is not an equation. There is no "=" sign. If you mean to simplify this, it is already in simplest form. If you mean to divide, giving quotient and remainder, here is how to proceed, using long division: ----------------------- x + 1 ) x^3 + 3*x^2 - 4*x + 3 Divide the leading term "x" of the divisor into the leading term "x^3" of the dividend. The quotient is x^2. Put that above the 3*x^2 term of the dividend, and above the line. Multiply that x^2 times the divisor, putting the result below the dividend, and subtract. Bring down the next term from the dividend into the current remainder. Your work should look like this: x^2 ----------------------- x + 1 ) x^3 + 3*x^2 - 4*x + 3 x^3 + x^2 ------------- 2*x^2 - 4*x Now divide x into 2*x^2 to get the next term of the quotient. It is 2*x. Put it above the -4*x term of the dividend, and above the line. Multiply that 2*x times the divisor, putting the result below the current remainder, and subtract. Bring down the next term from the dividend into the current remainder. Now you should have: x^2 + 2*x ----------------------- x + 1 ) x^3 + 3*x^2 - 4*x + 3 x^3 + x^2 ------------- 2*x^2 - 4*x 2*x^2 + 2*x ------------- - 6*x + 3 Now divide x into -6*x to get the next term of the quotient. It is -6. Put it above the +3 term of the dividend, and above the line. Multiply that -6 times the divisor, putting the result below the current remainder, and subtract. Now you should have: x^2 + 2*x - 6 ----------------------- x + 1 ) x^3 + 3*x^2 - 4*x + 3 x^3 + x^2 ------------- 2*x^2 - 4*x 2*x^2 + 2*x ------------- - 6*x + 3 - 6*x - 6 ----------- 9 You are done, because 9 involves no x's at all, and the divisor x + 1 has x to the first power, so you cannot divide x + 1 into 9. The quotient is the top line, x^2 + 2*x - 6, and the remainder is the bottom line, 9. This means (x^3 + 3*x^2 - 4*x + 3)/(x + 1) is x^2 + 2*x - 6 with remainder 9, or, in other words, (x^3 + 3*x^2 - 4*x + 3)/(x + 1) = x^2 + 2*x - 6 + [9/(x+1)]. Notice that, reading down the columns, every term has the same exponent of x. This is the best way to arrange your work. Keeping your columns straight will help you keep from getting confused. I hope that this was what you wanted. If not, write back to us again. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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