Question

Divide polynomials using long division YN⁵ de. If the polynomial does not div (2b³+12b²-32b)-:(b-2)

Answer 1

To divide the polynomial (2b³+12b²-32b) by (b-2) using long division, arrange the terms in descending order, divide the first term by the first term of the divisor, multiply the divisor by the quotient, subtract the result from the original polynomial, and continue until no further division is possible. The quotient is 2b²+16b+32.

Step-by-step explanation:

To divide the polynomial (2b³+12b²-32b) by (b-2) using long division, follow these steps:

1. Arrange the polynomial in descending order of powers of b.
2. Divide the first term of the polynomial (2b³) by the first term of the divisor (b). The result is 2b².
3. Multiply the entire divisor (b-2) by the quotient obtained in step 2. The result is 2b³-4b².
4. Subtract the result obtained in step 3 from the original polynomial. The difference is 16b²-32b.
5. Repeat steps 2-4 using the new polynomial obtained in step 4.
6. Continue the process until you cannot divide any further. The final result is the quotient.

Therefore, the quotient when dividing (2b³+12b²-32b) by (b-2) is 2b²+16b+32.