# x^5 3x^4+3x^3 x^2

Step 1.2.1

If a polynomial function has integer coefficients, then every rational zero will have the sườn where is a factor of the constant and is a factor of the leading coefficient.

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Step 1.2.2

Find every combination of . These are the possible roots of the polynomial function.

Step 1.2.3

Substitute and simplify the expression. In this case, the expression is equal lớn sánh is a root of the polynomial.

Step 1.2.3.1

Substitute into the polynomial.

Step 1.2.3.2

Step 1.2.3.3

Step 1.2.3.4

Step 1.2.3.5

Step 1.2.3.6

Step 1.2.3.7

Step 1.2.3.8

Step 1.2.4

Since is a known root, divide the polynomial by lớn find the quotient polynomial. This polynomial can then be used lớn find the remaining roots.

Step 1.2.5

Step 1.2.5.1

Set up the polynomials lớn be divided. If there is not a term for every exponent, insert one with a value of .

Step 1.2.5.2

Divide the highest order term in the dividend by the highest order term in divisor .

Step 1.2.5.3

Multiply the new quotient term by the divisor.

Step 1.2.5.4

The expression needs lớn be subtracted from the dividend, sánh change all the signs in

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Step 1.2.5.5

After changing the signs, add the last dividend from the multiplied polynomial lớn find the new dividend.

Step 1.2.5.6

Pull the next terms from the original dividend down into the current dividend.

Step 1.2.5.7

Divide the highest order term in the dividend by the highest order term in divisor .

Step 1.2.5.8

Multiply the new quotient term by the divisor.

Step 1.2.5.9

The expression needs lớn be subtracted from the dividend, sánh change all the signs in

Step 1.2.5.10

After changing the signs, add the last dividend from the multiplied polynomial lớn find the new dividend.

Step 1.2.5.11

Pull the next terms from the original dividend down into the current dividend.

Step 1.2.5.12

Divide the highest order term in the dividend by the highest order term in divisor .

Step 1.2.5.13

Multiply the new quotient term by the divisor.

Step 1.2.5.14

The expression needs lớn be subtracted from the dividend, sánh change all the signs in

Step 1.2.5.15

After changing the signs, add the last dividend from the multiplied polynomial lớn find the new dividend.

Step 1.2.5.16

Since the remander is , the final answer is the quotient.

Step 1.2.6

Write as a set of factors.