Question

I am 8th class .this is maths A, polynomials chapter please tell​

Answer 1

Required Solution:

Find the remainder :-

• $\sf{ \dfrac{ {x}^{4} + {4x}^{3} - {5x}^{2} - 6x + 7 }{x - 3} = \pmb \sf \red{133_{(Remainder)}}}$

• $\sf{ \dfrac{ {x}^{4} + {4x}^{3} - {5x}^{2} - 6x + 7 }{x+ 3} = \pmb \sf \red{-47_{(Remainder)}}}$

• $\sf{ \dfrac{ {x}^{4} + {4x}^{3} - {5x}^{2} - 6x + 7 }{x - 2} = \pmb \sf \red{23_{(Remainder)}}}$

• $\sf{ \dfrac{ {x}^{4} + {4x}^{3} - {5x}^{2} - 6x + 7 }{x + 2} = \pmb \sf \red{-17_{(Remainder)}}}$

• $\sf{ \dfrac{ {x}^{4} + {4x}^{3} - {5x}^{2} - 6x + 7 }{x - 1} = \pmb \sf \red{1_{(Remainder)}}}$

• $\sf{ \dfrac{ {x}^{4} + {4x}^{3} - {5x}^{2} - 6x + 7 }{x + 1} = \pmb \sf \red{5_{(Remainder)}}}$

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A little further...!

• A polynomial is an algebraic expression involving one or two or more variables.

• A polynomial contains only non-negative integral exponents.

• There are three types of polynomials on the basis of number of the terms:

1. Monomial (contains 1 term)
2. Binomial (contains 2 terms)
3. Trinomial (contains 3 terms)
4. Quadrinomial (contains 4 terms)

• To verify the solutions of the division of a polynomial by a polynomial , we can use the division algorithm, i.e

✰ Dividend = Divisor × Quotient + Remainder