Question

p(x) = x cube - 3x square - 5x + 8 and g(x) = x - 3

Answer 1

Seems like we've to find the remainder

Given,

p(x) = x³ - 3x² - 5x + 8
g(x) = x - 3

We know,
x - 3 = 0
=> x = 3

:. p(3) = (3)³ - 3(3)² - 5(3) + 8
= 27 - 27 - 15 + 8
= -7


Thus,
The remainder is -7

P.S - We can also make out that g(x) is not one of the factor of p(x).

Answer 2

Hey there!

$p(x) = x {}^{3} - 3x {}^{2} - 5x + 8$

$g(x) = x - 3$

$x - 3 = 0$

$x = 3$

∴ p(3) = 0

$(3) {}^{3} - 3 \times (3) {}^{2} - 5 \times 3 + 8$

$(3) {}^{3} - 3 {}^{3} - 7$

= -7

Hence, -7 is the remainder

Hope it helps!