Using the remainder theorem, determine whether (x-4) and (x-1) are factors of the expression x^{3}+3x^{2}-22x-24. Hence, by use of long division, find all remaining factors of the expression.

Sinead Mcgee 2021-07-30 Answered
a) Using the remainder theorem, determine whether (x4) and (x1) are factors of the expression x3+3x222x24.
b) Hence, by use of long division, find all remaining factors of the expression.
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Expert Answer

Dora
Answered 2021-07-31 Author has 98 answers

Step 1
Given: x3+3x222x24
a) (x4) Factor x4=0
x4
(4)3+3(4)222(4)24
=64+488824
=112112=0
(x1) Factor x1=0
x=1
(1)3+3(1)222(1)24
=1+32224
=446
=40(not a factor)
Step 2
b) (x4) Factor of x3+3x222n24
x=4
41322240428241760
x2+7x+6
=x2+6x+x+6
=x(x+6)+1(x+6)
=(x+6)(x+1)
(x+6)(x+1) are the remaining factors.

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