Box Method for Polynomial Division

Rachel introduces the box method for dividing polynomials, using the example of dividing 3x^3 - 5x + 7 by x - 2. She explains the setup, including placing the divisor in a box and arranging coefficients in descending order of exponents, filling in zeros for missing terms. The method involves multiplying and adding coefficients step-by-step to find the quotient and remainder. The final result is expressed as a polynomial with a remainder over the divisor.

What is the polynomial that we are dividing in the example?

• 3x^3 - 5x + 7

• 2x^2 + 4x - 6

• x^3 + 2x^2 - 5

• 5x^3 - 3x + 2

Which method is also known as the box method?

• Partial fraction decomposition

• Factorization

• Synthetic division

• Long division

What do you do with the number in the box in the box method?

• Multiply it with the coefficients

• Add it to the coefficients

• Subtract it from the coefficients

• Divide it by the coefficients

What should you do if an exponent is missing in the polynomial?

• Ignore it

• Add a zero in its place

• Use the next available exponent

• Repeat the previous exponent

What is the first step in the box method after setting up the box?

• Bring down the first coefficient

• Add the coefficients

• Multiply the coefficients

• Subtract the coefficients

What is the result of multiplying 2 by 3 in the box method example?

• 8

• 7

• 6

• 5

What is the next step after multiplying the number in the box with the first coefficient?

• Add it to the next coefficient

• Subtract it from the next coefficient

• Multiply it with the next coefficient

• Divide it by the next coefficient

What is the first coefficient brought down in the box method example?

• 7

• 3

• 5

• 2

What operation is performed after multiplying the box number with a coefficient?

• Subtraction

• Addition

• Exponentiation

• Division

What is the remainder in the box method example?

• 7

• 14

• 21

• 0