Priya has ₹ (x3 + x2 – 17x + 20). She wants to buy ice-cream cones each of cost ₹ (x – 3). After buying maximum number of ice-cream cones with her money, how much money is left with her?
Question
Priya has ₹ (x3 + x2 – 17x + 20). She wants to buy ice-cream cones each of cost ₹ (x – 3). After buying maximum number of ice-cream cones with her money, how much money is left with her?
Solution
To solve this problem, we need to perform polynomial division. We divide the polynomial (x^3 + x^2 - 17x + 20) by the polynomial (x - 3).
Step 1: Divide the first term of the dividend (x^3) by the first term of the divisor (x). This gives us x^2.
Step 2: Multiply the divisor (x - 3) by the result from step 1 (x^2) and subtract this from the original polynomial. This gives us a new polynomial:
x^3 + x^2 - 17x + 20 - (x^3 - 3x^2) = 4x^2 - 17x + 20
Step 3: Repeat the process with the new polynomial. Divide the first term of the new polynomial (4x^2) by the first term of the divisor (x). This gives us 4x.
Step 4: Multiply the divisor (x - 3) by the result from step 3 (4x) and subtract this from the new polynomial. This gives us a new polynomial:
4x^2 - 17x + 20 - (4x^2 - 12x) = 5x + 20
Step 5: Repeat the process with the new polynomial. Divide the first term of the new polynomial (5x) by the first term of the divisor (x). This gives us 5.
Step 6: Multiply the divisor (x - 3) by the result from step 5 (5) and subtract this from the new polynomial. This gives us a new polynomial:
5x + 20 - (5x - 15) = 35
So, the quotient is x^2 + 4x + 5 and the remainder is 35.
This means that Priya can buy (x^2 + 4x + 5) ice-cream cones and she will have ₹35 left.
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