Question

if the polynomial x ^4-2x^3+3x^2-px+8 is divided by (x-2),it leaves a remainder of 10. find the value of p.

Answer 1

$p(x) = x {}^{4} - 2x {}^{3} + 3x {}^{2} - px + 8 \\ g(x) = x - 2 \\ g(x) = 0 \\ x - 2 = 0 \\ x = 2 \\ by \: remainder \: theorem \: p(2) \: is \: the remainder$
When p(x) is divided by g(x), it leaves remainder 10.
So, p(2)=10
$2 {}^{4} - 2 \times 2 {}^{3} + 3 \times 2 {}^{2} - p \times 2 + 8 = 10 \\ 16 - 16 + 12 - 2p + 8 = 10 \\ 20 - 2p = 10 \\ 2p = 20 - 10 \\ p = \frac{10}{2} \\ p = 5$
Hope this will help you.
-------Mark as brainliest-------

Answer 2

x-2=0
Therefore the given factorial expression is 2.
So, putting 2 in this polynomial equation we get-
f (2)=>16-16+12-p*2+8=10
=>0-2p+20=10
=>-2p=10-20
=> p=(-10)/(-2)
Therefore p=5.
HOPE THIS HELPS. IF