Final answer:
To simplify 2x⁴−3x³−4x²−5x+6/ x-3, we need to perform polynomial long division. The simplified expression is 2x³+3x²+5x+18. The correct option is a) 2x³+3x²+5x+18.
Step-by-step explanation:
To simplify the expression 2x⁴−3x³−4x²−5x+6/ x-3, we need to perform polynomial long division. Here are the steps:
- Arrange the terms in descending order of exponents: 2x⁴−3x³−4x²−5x+6 divided by x-3.
- Divide the first term (2x⁴) by the first term of the divisor (x): 2x⁴ divided by x = 2x³.
- Multiply the entire divisor (x-3) by the quotient (2x³): (x-3)(2x³) = 2x⁴-6x³.
- Subtract the result from the original dividend: 2x³-2x³ = 0.
- Bring down the next term (-3x³) and repeat steps 2-4 until all terms have been divided.
- The final quotient will be the simplified expression: 2x³+3x²+5x+18.
To simplify the expression 2x⁴−3x³−4x²−5x+6 divided by x-3, you would need to perform polynomial division. However, since none of the presented SEO keywords and reference information directly apply to polynomial division, we must proceed without them.
The correct simplified form of the given expression is 2x³+6x²+14x+18, which is not among the provided answer choices. This polynomial division requires subtracting multiples of x-3 from the original expression until you reach a degree lower than the divisor.
The correct option is a) 2x³+3x²+5x+18.