Find the product
(x-2) (x*x+x+1)
Answers
Step-by-step explanation:
using the identity (a+b)(a-b) =a²- b² in all cases
[x+1/x][x-1/x][x²+1/x²][x⁴+1/x⁴]
= [x²- 1/x²][x²+1/x²][x⁴+1/x⁴]
=[(x²)²- (1/x²)²][x⁴+1/x⁴]
=[x⁴- 1/x⁴][x+1/x⁴]
=(x⁴)² - (1/x⁴)²
=x⁸-1/x⁸
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Step-by-step explanation:
GIVEN:-
(x+3) is a factor of the polynomial p(t)=at³ + t^²- 22t - 21
TO FIND:-
The value of "a".
CONCEPT USED:-
{\boxed{\rm{ Factor\:theorem}}}
Factortheorem
.
if (x - a) is a factor of p(x) then R = 0 and so on P(a) = 0.
Now,
\implies\rm{ f(t) = (x + 3) = 0}⟹f(t)=(x+3)=0
\implies\rm{ f(t) = x = -3}⟹f(t)=x=−3 .
Putting the value of "x" in (t)
\implies\rm{p(t) = at^3 + t^2 - 22t - 21}[tex] [tex]\implies\rm{ p(-3) = a(-3)^3+ (-3)^2 - 22(-3) - 21}⟹p(t)=at
3
+t
2
−22t−21[tex][tex]⟹p(−3)=a(−3)
3
+(−3)
2
−22(−3)−21
\implies\rm{ -27a + 9 + 66 - 21 = 0}⟹−27a+9+66−21=0
\implies\rm{ -27a + 54 = 0}⟹−27a+54=0
\implies\rm{ -27a = -54}⟹−27a=−54
\implies\rm{ a = \dfrac{54}{27}}⟹a=
27
54
\implies\rm{ a = 3}⟹a=3
Hence, The value of a is 3.