Final answer:
The question involves dividing the polynomial 2x^3 + 4x^2 + 3x - 20 by the binomial (x + 3) using polynomial long division. Each step of this process reduces the polynomial until a remainder is achieved that cannot be divided by the binomial. The result is a quotient with or without a remainder, depending on the polynomial and the binomial.
Step-by-step explanation:
The student's question involves dividing a polynomial by a binomial. Specifically, the polynomial 2x3 + 4x2 + 3x - 20 is divided by the binomial (x + 3). To solve this, we will use the method of polynomial long division.
First, we divide the first term of the polynomial by the first term of the binomial, 2x3 divided by x, which gives us 2x2. Multiplying (x + 3) by 2x2 and subtracting from the polynomial gives us a new polynomial to work with. We continue this process until we have a remainder that is of a lower degree than the binomial we are dividing by.
The SEO keywords 'polynomial long division', 'binomial', and 'remainder' are important for understanding how to approach this type of division problem in algebra.
The given expression is a polynomial that is to be divided by a binomial. To divide 2x^3 + 4x^2 + 3x - 20 by (x + 3), we can use long division. Here are the steps:
- Set up the division, with the divisor (x + 3) outside and the dividend (2x^3 + 4x^2 + 3x - 20) inside.
- Start dividing by dividing the first term of the dividend, 2x^3, by the first term of the divisor, x. The quotient is 2x^2.
- Multiply the divisor (x + 3) by the quotient 2x^2, which gives us 2x^3 + 6x^2.
- Subtract this result from the dividend to get a new dividend: (2x^3 + 4x^2 + 3x - 20) - (2x^3 + 6x^2) = -2x^2 + 3x - 20.
- Continue the division process by repeating steps 2-4 with the new dividend -2x^2 + 3x - 20.
- Repeat the steps until we have no more terms left to divide. In this case, we will have a remainder of 16x - 20.
- Therefore, the quotient is 2x^2 + 2x - 6 and the remainder is 16x - 20.