Q. 1 E5.0( 3 Votes )

# Find the quotient and remainder using synthetic division.(8x4 – 2x2 + 6x + 5) ÷ (4x + 1)

Let p(x) = 8x4 2x2 + 6x – 5 be the dividend. Arranging p(x) according to the descending powers of x and insert zero for missing term.

p(x) = 8x4 + 0x3 2x2 + 6x – 5

Divisor, q(x) = 4x + 1

To find out Zero of the divisor –

q(x) = 0

4x + 1 = 0

x =

zero of divisor is .

And, p(x) = 8x4 + 0x3 2x2 + 6x – 5

Put zero for the first entry in the 2nd row.

p(x) = (Quotient)×q(x) + remainder.

So, 8x4 2x2 + 6x – 5 = (x + )( 8x3 – 2x2 x + ) + ()

= (4x + 1)(8x3 – 2x2 x + )

Thus, the Quotient = (8x3 – 2x2 x + )= (2x3 x2 x + ) and remainder is .

Hence, when p(x) is divided by (4x + 1) the quotient is (2x3 x2 x + ) and remainder is .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Relationship Between Coefficients and Zeros44 mins
Quiz on Important Algebra Questions26 mins
Quiz on Number of Solutions of an Equation24 mins
Interactive Quiz: Algebra Important Questions38 mins
Important Algebra Questions46 mins
Genius Quiz | NTSE Questions Algebra27 mins
Interactive Quiz: Nature of Roots51 mins
Know Some Interesting Proofs in Algebra42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses