Jika P x 3x 4 5x 3 14x 2 5x 16 dibagi dengan 3x 1 maka hasil bagi dan sisanya berturut turut adalah
Question
Basic Answer
Step 1: Polynomial Long Division Setup
We will perform polynomial long division to divide P(x) = 3x⁴ – 5x³ – 14x² + 5x + 16 by (3x + 1).
Step 2: Divide the leading terms
Divide the leading term of the dividend (3x⁴) by the leading term of the divisor (3x): 3x⁴ / 3x = x³. This is the first term of the quotient.
Step 3: Multiply and Subtract
Multiply the divisor (3x + 1) by x³: x³(3x + 1) = 3x⁴ + x³.
Subtract this result from the dividend: (3x⁴ – 5x³ – 14x² + 5x + 16) – (3x⁴ + x³) = -6x³ – 14x² + 5x + 16
Step 4: Repeat the process
Now, divide the leading term of the new dividend (-6x³) by the leading term of the divisor (3x): -6x³/3x = -2x². This is the next term of the quotient.
Multiply the divisor by -2x²: -2x²(3x + 1) = -6x³ – 2x².
Subtract: (-6x³ – 14x² + 5x + 16) – (-6x³ – 2x²) = -12x² + 5x + 16
Step 5: Repeat again
Divide -12x² by 3x: -12x²/3x = -4x. This is the next term of the quotient.
Multiply the divisor by -4x: -4x(3x + 1) = -12x² – 4x.
Subtract: (-12x² + 5x + 16) – (-12x² – 4x) = 9x + 16
Step 6: Final division
Divide 9x by 3x: 9x/3x = 3. This is the last term of the quotient.
Multiply the divisor by 3: 3(3x + 1) = 9x + 3.
Subtract: (9x + 16) – (9x + 3) = 13
Step 7: Result
The quotient is x³ – 2x² – 4x + 3 and the remainder is 13.
Final Answer
Hasil bagi: x³ – 2x² – 4x + 3, Sisa: 13
Posting Komentar