Question

find the value of a if (x-2) is a factor of x^3+2x^2-ax+10. hence check wheather (x+8) is also a factor

Answer 1

Given : (x-2) is a factor of x³+2x²-ax+10.

To Find : Value of  a

check whether (x+8) is also a factor

Solution:

if (x - a) is a factor of p(x)

then p(a) = 0

p(x) = x³+2x²-ax+10

x -2 is factor => p(2) = 0

=>  2³+2(2)²-a2+10 = 0

=> 8 + 8 - 2a + 10 = 0

=> 2a = 26

=> a = 13

Value of  a is 13

p(x) =  x³+2x²-13x+10

(x+8) is also a factor if p(-8) = 0

(-8)³ + 2(-8)² - 13(-8) + 10

= -512 + 128 + 104 + 10

= -270

≠ 0

Hence (x + 8) is not a factor

Additional Info

x³+2x²-13x+10 = (x - 2)(x² + 4x  - 5)  

= (x - 2)(x + 5)(x - 1)

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