Question

4. Divide and check your answer by division algorithm:
(i) (x^2-10x+25)÷(x-5)
(ii) (x^2-9x+18)÷(x-6)



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Answer 1

Answer:

(i) (x²-10x+25) ÷ (x-5) = (x-5)

(ii) (x²-9x+18) ÷ (x-6) = (x-3)

Step-by-step explanation:

Here's the division algorithm

(i) (x-5) × (x-5) + 0 = (x²-10x+25)

=> x(x-5) -5(x-5) + 0= (x²-10x+25)

=> x² -5x -5x +25 + 0 = (x²-10x+25)

=> x² -10x +25 = x²-10x+25

LHS = RHS, Hence, Proved.

(ii) (x-6) × (x-3) +0 = (x²-9x+18)

=> x(x-3) -6(x-3) + 0 = (x²-9x+18)

=> x² -3x -6x -18 + 0 = (x²-9x+18)

=> x² -9x -18 = x²-9x+18

LHS = RHS, Hence, Proved.

I gave you 2 methods

And the verification

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