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Verify division algorithm i.e. Dividend = Divisor Quotient + Remainder, in each of the following. Also, write the quotient and remainder:

Dividend Divisor
(i) 14x2 + 13x - 15 7x - 4
(ii) 15z3 - 20z2 + 13z - 12 3z - 6
(iii) 6y5 - 28y3 + 3y2 + 30y - 9 2x2 - 6
(iv) 34x - 22x3 - 12x4 - 10x2 - 75 3x + 7
(v) 15y4 - 16y3 + 9y2 - \(\frac{10}{3}\)y + 6 3y - 2
(vi) 4y3 + 8y + 8y2 + 7 2y2 - y + 1
(vii) 6y4 + 4y4 + 4y3 + 7y2 + 27y + 6 2y3 + 1

 

1 Answer

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Best answer

(i)

Dividend = Divisor Quotient + Remainder

14x2 + 13x - 15 = (7x - 4) x (2x + 3) + (-3)

14x2 + 13x - 15 = 14x2 + 21x - 8x - 12 - 3

14x2 + 13x - 15 = 14x2 + 13x - 15

(ii)

Dividend = Divisor Quotient + Remainder

15z3 - 20z + 13z - 12 = (3z - 6) x (5z2\(\frac{10z}{3}\) + 11) + 54

15z3 - 20z + 13z - 12 = 15z3 + 10z2 + 33z - 30z2 - 20z + 54

15z3 - 20z + 13z - 12 = 15z3 - 20z2 + 13z - 12

(iii)

Dividend = Divisor Quotient + Remainder

6y5 - 28y3 + 3y2 + 30y - 9 = (2y2 - 6) x (3y3 - 5y + \(\frac{3}{2}\)) + 0

6y5 - 28y3 + 3y2 + 30y - 9 = 6y5 - 10y3 + 3y2 - 18y3 + 30y - 9

6y5 - 28y3 + 3y2 + 30y - 9 = 6y5 - 28y3 + 3y2 + 30y - 9

(iv)

Dividend = Divisor Quotient + Remainder

-12x4 - 22x - 10x2 + 34x - 75 = (3x + 7) x (-4x3 + 2x2 - 8x + 30) - 285

-12x4 - 22x - 10x2 + 34x - 75 = -12x4 + 6x3 - 24x2 - 28x3 + 14x2 + 90x - 56x + 210 - 285

-12x4 - 22x - 10x2 + 34x - 75 = -12x4 - 22x3 - 10x3 + 34x - 75

(v)

Dividend = Divisor Quotient + Remainder

15y4 - 16y3 + 9y2\(\frac{10y}{3}\) + 6 = (3y - 2) x (5y3 - 2y + \(\frac{5y}{3}\)) + 6

15y4 - 16y3 + 9y2\(\frac{10y}{3}\) + 6 = 15y4 - 6y3 + 5y2 - 10y3 + 4y2\(\frac{10y}{3}\) + 6

15y4 - 16y3 + 9y2\(\frac{10y}{3}\) + 6 = 15y4 - 16y3 + 9y2\(\frac{10y}{3}\) + 6

(vi)

Dividend = Divisor Quotient + Remainder

4y3 + 8y2 + 84y + 7 = (2y2 - y + 1) x (2y + 5) + 11y + 2

4y3 + 8y2 + 84y + 7 = 4y3 + 10y2 - 2y2 -5y + 2y  +5 + 11y + 2

4y3 + 8y2 + 84y + 7 = 4y3 + 8y2 + 8y + 7

(vii)

Dividend = Divisor Quotient + Remainder

6y5 - 4y4 + 4y3 + 7y2 + 27y + 6 = (2y3 + 1) x (3y2 + 2y + 2) + 4y2 + 25y + 4

6y5 - 4y4 + 4y3 + 7y2 + 27y + 6 = 6y5 + 4y4 + 4y3 + 3y2 + 2y + 2 + 4y2 + 25y + 4

6y5 - 4y4 + 4y3 + 7y2 + 27y + 6 = 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6

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