Question

1. Divide each of the following polynomials by synthetic division method and also by
linear division method. Write the quotient and the remainder.
(i) (2m2 - 3m + 10) = (m - 5) (ii) (x4 + 2x3 + 3x2 + 4x + 5) - (x + 2)
(iii) (v3 - 216) - (y - 6)
(iv) (2x4 + 3x + 4x - 2x2 ) = (x + 3)
(v) (x4 - 3x2 - 8) + (x + 4) (vi) (13 - 3y2 + 5y - 1) = (y - 1)
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Answer 1

Answer:

(2m2 – 3m + 10) ÷ (m – 5)

Dividend = 2m2 – 3m + 10

∴ Coefficient form of dividend = (2, -3, 10)

Divisor = m – 5

∴ Opposite of -5 is 5.Coefficient form of quotient = (2, 7)

∴ Quotient = 2m + 7,

Remainder = 45

Linear division method:

2m2 – 3m + 10

To get the term 2m2, multiply (m – 5) by 2m and add 10m,

= 2m(m – 5) + 10m- 3m + 10

= 2m(m – 5) + 7m + 10

To get the term 7m, multiply (m – 5) by 7 and add 35

= 2m(m – 5) + 7(m- 5) + 35+ 10

= (m – 5) (2m + 7) + 45

∴ Quotient = 2m + 7,

Remainder = 45

Answer 2

Answer:

Step-by-step explanation:

(i) (2m2 - 3m + 10) = (m - 5)

= 45

(ii) (x4 + 2x3 + 3x2 + 4x + 5) - (x + 2)

= 1

(iii) (v3 - 216) - (y - 6)

= 210

(iv) (2x4 + 3x + 4x - 2x2 ) = (x + 3)

(v) (x4 - 3x2 - 8) + (x + 4)

(vi) (13 - 3y2 + 5y - 1) = (y - 1)