An NGO decided to distribute books and pencils to the students of a school running by some other NGO. For this, they collected some amount from different number of people. The total amount collected is represented by 4 x4(Power) + 2x3 (Power)– 8x2(Power) + 3x – 7. . The amount is equally divided between each of the students. The number of students, who received the amount is represented by x – 2 + 2x2(Power). After distribution, 5x- 11, amount is left with the NGO which they donated to school for their infrastructure. Find the amount received by each student from the NGO.
Answers
"To determine: The amount that was distributed by NGO for each student of the school
Given Data:
The total fund collected by NGO from different people p(x)\quad =\quad 4x^{ 4 }+2x^{ 3 }-8x^{ 2 }+3x-7p(x)=4x
4
+2x
3
−8x
2
+3x−7
Number of students, g(x)\quad =\quad x-2+2x^{ 2 }g(x)=x−2+2x
2
The amount left with the NGO after distribution is done r(x)\quad =\quad 5x-11r(x)=5x−11
Formulas to be used:
Division Algorithm: p(x)\quad =\quad g(x)\quad \times \quad q(x)\quad +\quad r(x)p(x)=g(x)×q(x)+r(x)
Calculation:
Step 1: Substituting the values of p(x), g(x), and r(x) in the division algorithm, we get
4x^{ 4 }+2x^{ 3 }-8x^{ 2 }+3x-7\quad =\quad \left( x-2+2x^{ 2 } \right) \quad \times \quad q(x)\quad +\quad 5x\quad -\quad 114x
4
+2x
3
−8x
2
+3x−7=(x−2+2x
2
)×q(x)+5x−11
q(x)\quad =\quad \frac { (4x^{ 4 }+2x^{ 3 }-8x^{ 2 }+3x-7)-(5x-11) }{ 2x^{ 2 }+x-2 } q(x)\quad =\quad \frac { 4x^{ 4 }+2x^{ 3 }-8x^{ 2 }-2x+4 }{ 2x^{ 2 }+x-2 }q(x)=
2x
2
+x−2
(4x
4
+2x
3
−8x
2
+3x−7)−(5x−11)
q(x)=
2x
2
+x−2
4x
4
+2x
3
−8x
2
−2x+4
Step 2: Using long division method, find q(x)
Thus, q(x)\quad =\quad 2x^{ 2 }-2q(x)=2x
2
−2
Amount received by each student =\quad 2x^{ 2 }-2=2x
2
−2 "
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Answer:
To determine: The amount that was distributed by NGO for each student of the school
Given Data:
The total fund collected by NGO from different people p(x)\quad =\quad 4x^{ 4 }+2x^{ 3 }-8x^{ 2 }+3x-7p(x)=4x
4
+2x
3
−8x
2
+3x−7
Number of students, g(x)\quad =\quad x-2+2x^{ 2 }g(x)=x−2+2x
2
The amount left with the NGO after distribution is done r(x)\quad =\quad 5x-11r(x)=5x−11
Formulas to be used:
Division Algorithm: p(x)\quad =\quad g(x)\quad \times \quad q(x)\quad +\quad r(x)p(x)=g(x)×q(x)+r(x)
Calculation:
Step 1: Substituting the values of p(x), g(x), and r(x) in the division algorithm, we get
4x^{ 4 }+2x^{ 3 }-8x^{ 2 }+3x-7\quad =\quad \left( x-2+2x^{ 2 } \right) \quad \times \quad q(x)\quad +\quad 5x\quad -\quad 114x
4
+2x
3
−8x
2
+3x−7=(x−2+2x
2
)×q(x)+5x−11
q(x)\quad =\quad \frac { (4x^{ 4 }+2x^{ 3 }-8x^{ 2 }+3x-7)-(5x-11) }{ 2x^{ 2 }+x-2 } q(x)\quad =\quad \frac { 4x^{ 4 }+2x^{ 3 }-8x^{ 2 }-2x+4 }{ 2x^{ 2 }+x-2 }q(x)=
2x
2
+x−2
(4x
4
+2x
3
−8x
2
+3x−7)−(5x−11)
q(x)=
2x
2
+x−2
4x
4
+2x
3
−8x
2
−2x+4
Step 2: Using long division method, find q(x)
$$\begin{lgathered}\begin{matrix} 2x^{ 2 }-2 \\ 2x^{ 2 }+x-2\overline { )4x^{ 4 }+2x^{ 3 }-8x^{ 2 }-2x+4 } \\ 4x^{ 4 }+2x^{ 3 }-4x^{ 2 } \end{matrix}\\ \qquad \qquad \overline { \qquad \qquad -4x^{ 2 }-2x+4 } \\ \qquad \qquad \qquad \qquad -4x^{ 2 }-2x+4\\ \overline { \qquad \qquad \qquad \qquad \qquad \qquad \qquad 0 }\end{lgathered}$$
Thus, $$q(x)\quad =\quad 2x^{ 2 }-2$$
Amount received by each student $$=\quad 2x^{ 2 }-2$$ "
Step-by-step explanation: