Question

p(x)=8×3-6x2-4x+3,g(x)=2x-1​

Answer 1

Question (Corrected): If p(x) = 8 × 3 - 6x² - 4x + 3, and g(x) = 2x - 1, the find the remainder after dividing p(x) with g(x). Or, check whether g(x) is the factor of p(x) or not.

p(x) = 8 × 3 - 6x² - 4x + 3

g(x) = 2x - 1

Zero of g(x):-

2x - 1 = 0

→ 2x = 1

→ x = ½

Thus,

p(x) = 8 × 3 - 6x² - 4x + 3

= 24 - 6x² - 4x + 3

= 27 - 6x² - 4x

Or,

p(½) = 27 - 6(½)² - 4(½)

= 27 - 6(¼) - 2

= 27 - 3/2 - 2

= 25 - 3/2

= (50 - 3)/2

[LCM - 2]

= 47/2

Or, p(x), when divided with g(x), leaves a remainder of 47/2. Or, simply g(x) is not a factor of p(x).

Hope it helps.