#8x^3 +10x^2- px- 5# is divisible by #2x +1#. There is no remainder. How do you find the value of p?

1 Answer
Noah G
Dec 10, 2016

#p = 7#

Explanation:

The remainder theorem states that if a polynomial #f(x)# is divided by #x - a#, the remainder is given by evaluating #f(a)#.

Here, #a = -1/2#, since when we solve #2x+ 1 = 0#, we get #x = -1/2#.

So,

#8(-1/2)^3 + 10(-1/2)^2 - p(-1/2) - 5 = 0#

#8(-1/8) + 10(1/4) + 1/2p - 5 = 0#

#-1 + 5/2 + 1/2p - 5 = 0#

#1/2p = 5 - 5/2 + 1#

#1/2p = 7/2#

#p = (7/2)/(1/2)#

#p = 7#

Hopefully this helps!

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