Question

Divide the first polynomial by the Second polynomial and find the remiander using factor thoerem i) (x2 - 7x + 9) : (x + 1​

Answer 1

. p(x) = x2 – 7x + 9  Divisor = x + 1  ∴ take x = – 1  ∴ By remainder theorem,  ∴ Remainder =p(-1)  p(x) = x2 – 7x + 9  ∴ p(-1) = (- 1)2 – 7(- 1) + 9  = 1 + 7 + 9  ∴ Remainder = 17 ii. p(x) = 2x3 – 2x2 + ax – a  Divisor = x – a  ∴ take x = a  By remainder theorem,  Remainder = p(a)  p(x) = 2x3 – 2x2 + ax – a  ∴ p(a) = 2a3 – 2a2 + a(a) – a  = 2a3 – 2a2 + a2 – a  ∴ Remainder = 2a3 – a2 – a  iii. p(m) = 54m3 + 18m2 – 27m + 5  Divisor = m – 3  ∴ take m = 3  ∴ By remainder theorem,  Remainder = p(3)  p(m) = 54m3 + 18m2 – 27m + 5  ∴ p(3) = 54(3)3 +18(3)2 – 27(3) + 5  = 54(27) + 18(9) – 81 + 5  = 1458 + 162 – 81 + 5 ∴ Remainder = 1544

Answer 2

Question:-

Divide the first polynomial by the Second polynomial and find the remiander using factor thoerem i) (x2 - 7x + 9) : (x + 1).

Correct answer:-

i. p(x) = x2 – 7x + 9

Divisor = x + 1

∴ take x = – 1

∴ By remainder theorem,

∴ Remainder = p(-1) p(x)

= x2 – 7x + 9 ∴ p(-1)

= (- 1)2 – 7(- 1) + 9

= 1 + 7 + 9

∴ Remainder = 17 [Ans].

Thnkuuu...!!! :)

hope it helps...!!! ♡

#ItzzMichhAditi ♡