Question

15x cube minus 20x square plus 13x minus 12 divided by 2x square minus 2x plus 2​

Answer 1

Answer:

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Step-by-step explanation:

Question

15x³ - 20x² + 13x - 12 ÷ x² - 2x + 2

Solution

Let quotient, q(x) = ax + b and remainder, r(x) = cx + d.

Using division algorithm, we have the following equation:

p(x) = g(x) × q(x) + r(x)

∴15x³ - 20x² + 13x - 12

= (x² - 2x + 2) (ax + b) + (cx + d)

= ax³ + bx² - 2ax² - 2bx + 2ax + 2b + cx + d

= ax³ + x²(b - 2a) + x(2a + c - 2b) + (2b + d)

Comparing the coefficient of same powers of x on both sides, we get

a = 15 [Comparing the coefficient of x³]

b - 2a = -20 [Comparing the coefficient of x²]

2a + c - 2b = 13 [Comparing the coefficient of x]

2b + d = -12 [Comparing the constant terms ]

Solving the above equation, we get the following values:

a = 15, b = 10, c = 3 and d = -32

Hence, quotient, q(x) = 15x + 10 and remainder, r(x) = 3x - 32.