(x³ - 7x² + 6x) ÷ (x - 6) = *
x³ - x²
x² - x
x - 1
x² - 6x
Answers
Answer:
=x+1
━━━━━━━━━━━━━━━━
Step-by-step explanation:
SOLUTION
TO DETERMINE
\displaystyle \sf{ \frac{ {x}^{3} + 7 {x}^{2} - x - 7 }{ {x}^{2} + 6x - 7 } }
x
2
+6x−7
x
3
+7x
2
−x−7
EVALUATION
Here the given expression is
\displaystyle \sf{ \frac{ {x}^{3} + 7 {x}^{2} - x - 7 }{ {x}^{2} + 6x - 7 } }
x
2
+6x−7
x
3
+7x
2
−x−7
Numerator
= \displaystyle \sf{ {x}^{3} + 7 {x}^{2} - x - 7 }=x
3
+7x
2
−x−7
For x = - 1 the value of the numerator is zero
∴ x + 1 is a factor of the numerator
\therefore \: \: \displaystyle \sf{ {x}^{3} + 7 {x}^{2} - x - 7 }∴x
3
+7x
2
−x−7
= \displaystyle \sf{ {x}^{3} + {x}^{2} + 6 {x}^{2} + 6x -7 x - 7 }=x
3
+x
2
+6x
2
+6x−7x−7
= \displaystyle \sf{ {x}^{2}(x + 1) + 6x(x + 1) - 7(x + 1) }=x
2
(x+1)+6x(x+1)−7(x+1)
\displaystyle \sf{ = (x + 1)({x}^{2} + 6x - 7) }=(x+1)(x
2
+6x−7)
Hence
\displaystyle \sf{ \frac{ {x}^{3} + 7 {x}^{2} - x - 7 }{ {x}^{2} + 6x - 7 } }
x
2
+6x−7
x
3
+7x
2
−x−7
= \displaystyle \sf{ \frac{ (x + 1)({x}^{2} + 6x - 7 ) }{ {x}^{2} + 6x - 7 } }=
x
2
+6x−7
(x+1)(x
2
+6x−7)
\sf{ = x + 1}=x+1
FINAL ANSWER
\boxed{ \: \: \displaystyle \sf{ \frac{ {x}^{3} + 7 {x}^{2} - x - 7 }{ {x}^{2} + 6x - 7 } = x + 1 } \: \: }
x
2
+6x−7
x
3
+7x
2
Step-by-step explanation:
x³-7x²+6x) ÷(x-6)
taking out x common from x³-7x+6x
x(x²-7x+6) ÷(x-6)
now factorizing
x{x²-(1+6)x +6} ÷ (x-6)
x(x²-x-6x +6) ÷(x-6)
x{x(x-1) -6(x-1)} ÷(x-6)
x(x-1) (x-6) /(x-6)
now we can see that x-6 can be cancel so we will cancel x-6
so now we will get
x(x-1)
the ans is x(x-1)