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DIVIDING POLYNOMIALS

This guide teaches you how to divide a polynomial by a monomial and another polynomial using long division. The process involves taking each term of the polynomial, dividing it by the monomial, and factoring common expressions. You'll learn to simplify the answers and understand the roles of dividends, divisors, quotients, and remainders in polynomial division. With clear steps and examples, this resource is perfect for students looking to strengthen their algebra skills and tackle polynomial division confidently.

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DIVIDING POLYNOMIALS

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  1. DIVIDING POLYNOMIALS

  2. Dividing Polynomials The objective is to be able to divide a polynomial by a monomial.

  3. Step 1 Divide each term of the polynomial by the monomial. 2 x 6 3 - 3 x 3 x

  4. Step 2 Factor each expression. · · · 2 3 x x 3 - · · 3 x 3 x

  5. Step 3 Divide out the common factors in each expression. The numbers and variables which are crossed out divide out to 1.

  6. Step 4 Write in simplified form. 1 - 2 x x

  7. A A You Try It

  8. Dividing a Polynomial by a Polynomial The objective is to be able to divide a polynomial by a polynomial by using long division. Dividend – the number which is being divided. Divisor – The number that is being divided into the dividend. Quotient – The result obtained when numbers or expressions are divided. Remainder – The part that is left over when the divisor no longer goes into the dividend a whole number of times.

  9. Polynomial Long Division Step 1: Write it as you would a regular long division problem. The x+2 is the divisor and the x2+3x-1 is the dividend.

  10. 2 + + - x 2 x 3 x 1 Step 2 Divide x2 by x to get x. Place this on top. x Multiply x+2 by x to get x2 +2x. Subtract the x2+2x from the x2+3x-1. 2 + x 2 x - x 1

  11. x 2 + + - x 2 x 3 x 1 2 + x 2 x - x 1 Step 3 + 1 Divide the x by x to get 1. Multiply x+2 by 1 to get x+2. + x 2 Subtract x+2 from the x-1. - 3

  12. Step 4 Write your final answer. The x+1 is the quotient.

  13. A A You Try It

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