Question

Find the value of a if (x+3) is a factor of
p(x)=x³+ ax²+2(a-1)x+6
(a) 0
(b) 1
(c) 5
(d) 18​

Answer 1

${\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}}$

Question

⠀⠀⠀⠀• Find the value of a if (x+3) is a factor of

⠀⠀⠀⠀⠀p(x)=x³+ ax²+2(a-1)x+6

Answer

⠀⠀⠀⠀• a= 5

Given

⠀⠀⠀⠀• p(x) = x³+ax²+2(a-1)x+6

⠀⠀⠀⠀• g(x) = x+3

To Calculate

⠀⠀⠀⠀• Value of a

Step by step explanation

p(x) = x³+ax²+2(a-1)x+6

g(x) = x+3

➙ x+3=0

➙x=-3

Putting value of x in p(x)

• p(x) = x³+ax²+2(a-1)x+6=0

➙ (-3)³+a×(-3)²+2(a-1)(-3)+6=0

➙ -27+a×9+(2a-2)(-3)+6=0

➙ -27+9a+(-6a+6)+6=0

➙ -27+9a-6a+6+6=0

➙ -27+3a+12=0

➙ 3a-15=0

➙ 3a=15

➙a=15/3

${\boxed{\red{\tt{a=5}}}}$

${\huge{\underline{\underline{\sf{\blue{Hence :-}}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀${\boxed{\blue{\tt{a= 5 }}}}$

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