How do you divide (4x^3 + 3x^2 - 3x + 14)/ (x + 2)?

1 Answer
Sep 6, 2016

Use polynomial long division, or synthetic division.

Explanation:

Set up the problem like traditional long division. Divide the first term of the dividend by the first term of the divisor. 4x^3 divided by x, gives 4x^2. Place 4x^2 over the squared term of the dividend. Then multiply 4x^2 by the divisor. Place the result, 4x^3 +8x^2, under the dividend, lining up the cubed and squared terms.

Next. subtract 4x^3 +8x^2 from the dividend. Be careful to subtract the 8x^2 term from 3x^2. Draw a line underneath, and write the result, -5x^2. Then "pull down" the next term from the dividend, giving you -5x^2 -3x under the line.

Divide the first term of the "new dividend" (-5x^2-3x) by the first term of the divisor (x-2). (-5x^2)/x =-5x. Place this result over the "x term" of the dividend. Multiply this result by the divisor and write it underneath. So -5x * (x-2) = -5x^2-10x, and -5x^2-10x is the next line of the problem. Subtract from the line above. Be careful. You are subtracting -3x -(-10x).

Draw a line again, and write the answer, 7x underneath. Pull down the last term, 14. Divide 7x by x and write the answer 7 over the constant term of the dividend. Multiply and subtract like in the previous steps. You should get zero.

See the picture. Lots of words for a simple problem illustrated below.
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