What minimum must be added to 2x^3 - 3x^2 + 6x + 7 so that the resulting polynomial will be divisible by x^2 - 4x + 8... | LA 4m | Maths | SuperPadhai

Polynomials > Question

LA4 marksYear: 2020HardCBSE Class 10

polynomialsdivision-algorithmremainder

Question

What minimum must be added to

2 x^{3} - 3 x^{2} + 6 x + 7

so that the resulting polynomial will be divisible by

x^{2} - 4 x + 8

?

Solution

1

Dividing

2 x^{3} - 3 x^{2} + 6 x + 7

by

x^{2} - 4 x + 8

:

2 x^{3} - 3 x^{2} + 6 x + 7 = (x^{2} - 4 x + 8) (2 x + 5) + (10 x - 33)

+3 marks

2

Remainder

= 10 x - 33

. We must add

(33 - 10 x)

to make the polynomial divisible.

+1 mark

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