Question

(x-2) Is a factor of (x) =x+a x²-b x-8 when f(x) is divided by x+1 the remainder is -30.find the value of a and b

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Answer 1

Step-by-step explanation:

x - 2 = 0 => x = 2

therefore f(2) = 0 [ as x-2 is a factor ]

=> f(2) = a(2)² - b(2) - 8 = 0

=> 4a - 2b = 8..................1

similarly x + 1 = 0 => x = -1

therefore f(-1) = - 30 [ as it leaves a reminder of - 30 ]

f(-1) = a(-1)² - b(-1) - 8 = 30

=> a + b = 38..................2

solve equation 1 and 2

a + b = 38 × 2.................2

2a + 2b = 76

4a - 2b = 8

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6a + 0 = 84

therefore a = 84/6 => 14

14 + b = 38 => b = 38 - 14 => 24

hence a = 14 and b = 24

Answer 2

Answer:

f(x)=(x−a)q(x)+r(x)

where q(x) is the quotient when f(x) is divided by x−a and r(x)

The Remainder Theorem says that we can restate the polynomial in terms of the divisor, and then evaluate the polynomial

x=a

hence putting it we get

$$f(a)= 0 \times q(a) + r(a)$$

$$f(a) = r(a)$$

hence the remainder is f(a)

B