Question

Check whether q(x) is a multiple of R(x) or not if q (x) =2x3-11x2-4x 5;r(x)=2x 1

Answer 1

q (x) is a multiply of r (x)

Answer 2

q(x) is not a multiple of r(x) if q(x) = 2x³ - 11x²  - 4x  + 5 and r (x) = 2x + 1

Step-by-step explanation:

q(x) is a multiple of R(x) if q(x) has r(x) as one of the factor

q(x) = 2x³ - 11x²  - 4x  + 5

r (x) = 2x + 1

x = -1/2  

q(x) should be zero for x = -1/2 if  r(x) is one of the factor

q(-1/2) = 2(-1/2)³ - 11(-1/2)² - 4(-1/2) + 5

= -1/4 - 11/4  + 2  + 5

= -3 + 2 + 5

= 4  ≠ 0

Hence q(x) is not a multiple of r(x)

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