Divide the polynomials 4x4+4x−10
by 2x2−3
to determine the quotient and remainder.(1 point)
Responses
The quotient is 2x2−3
. The remainder is 4x+1
.
The quotient is 2 x squared minus 3. The remainder is 4 x plus 1.
The quotient is 2x2+3
. The remainder is 4x−1
.
The quotient is 2 x squared plus 3. The remainder is 4 x minus 1.
The quotient is 2x2−3
. The remainder is 4x−19
.
The quotient is 2 x squared minus 3. The remainder is 4 x minus 19.
The quotient is 2x2+3
. The remainder is 4x−19
.
The correct response is:
The quotient is 2x^2 + 3. The remainder is 4x - 19.
The quotient is 2x^2 - 3. The remainder is 4x + 1.
To divide the polynomials 4x^4+4x-10 by 2x^2-3, you can use polynomial long division. Here are the steps to find the quotient and remainder:
Step 1: Arrange the terms in descending order of powers. The dividend is 4x^4 + 4x - 10, and the divisor is 2x^2 - 3.
Step 2: Divide the leading term of the dividend (4x^4) by the leading term of the divisor (2x^2). The result is 2x^2.
Step 3: Multiply the quotient obtained in step 2 (2x^2) by the divisor (2x^2 - 3) to get 4x^4 - 6x^2.
Step 4: Subtract the result obtained in step 3 from the dividend. (4x^4 + 4x - 10) - (4x^4 - 6x^2) = 6x^2 + 4x - 10.
Step 5: Repeat steps 2-4 with the resulting polynomial from step 4 (6x^2 + 4x - 10) to find the next term in the quotient.
Step 6: Divide the leading term of the new polynomial obtained in step 5 (6x^2) by the leading term of the divisor (2x^2). The result is 3.
Step 7: Multiply the new quotient obtained in step 6 (3) by the divisor (2x^2 - 3) to get 6x^2 - 9.
Step 8: Subtract the result obtained in step 7 from the polynomial obtained in step 5 (6x^2 + 4x - 10). (6x^2 + 4x - 10) - (6x^2 - 9) = 4x - 1.
The quotient is 2x^2 + 3, and the remainder is 4x - 1.