50.9k views
0 votes
(2x^3+x^2+25) divided by (2x+5),use long division to find the quotient

User Shona
by
8.2k points

1 Answer

5 votes

Step 1: Divide the leading term of the dividend by the leading term of the divisor.

2x^3 / 2x = x^2

Step 2: Multiply the divisor by the quotient obtained in Step 1.

(x^2)(2x + 5) = 2x^3 + 5x^2

Step 3: Subtract the result obtained in Step 2 from the dividend.

(2x^3 + x^2 + 0x + 25) - (2x^3 + 5x^2) = -4x^2 + 0x + 25

Step 4: Bring down the next term from the dividend.

-4x^2 + 0x + 25

Step 5: Divide the leading term of the new dividend by the leading term of the divisor.

-4x^2 / 2x = -2x

Step 6: Multiply the divisor by the quotient obtained in Step 5.

(-2x)(2x + 5) = -4x^2 - 10x

Step 7: Subtract the result obtained in Step 6 from the new dividend.

(-4x^2 + 0x + 25) - (-4x^2 - 10x) = 10x + 25

Step 8: Bring down the next term from the dividend.

10x + 25

Step 9: Divide the leading term of the new dividend by the leading term of the divisor.

10x / 2x = 5

Step 10: Multiply the divisor by the quotient obtained in Step 9.

(5)(2x + 5) = 10x + 25

Step 11: Subtract the result obtained in Step 10 from the new dividend.

(10x + 25) - (10x + 25) = 0

Step 12: Since the new dividend is zero, we stop the division.

Therefore, the quotient of (2x^3 + x^2 + 25) divided by (2x + 5) is x^2 - 2x + 5.

User DotNet NF
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories