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- Question 1, Exercise 5.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... tan. =====Question 1(i)===== Find the remainder by using 'Remainder Theorem': $2 x^{3}+3 x^{2}-4 x+1$ is divided by $x+2$. ** Solution. ** Given: $p(x)=2 x^{3}+3 x^{2}-4 x+1$\\ $x-c=x+2 \implies c=-2$. By Remainder Theorem, we have \begin{align*} \text{R
- Question 1 and 2, Exercise 5.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... mabad, Pakistan. =====Question 1===== Factorize by using factor theorem: $y^{3}-7 y-6$ ** Solution.... &=(-1)^{3}-7 (-1)-6 \\ &= -1+7-6 =0. \end{align*} By factor theorem, $y+1$ is factor of $f(y)$. Usin... align*} GOOD =====Question 2===== Factorize by using factor theorem: $2 x^{3}-x^{2}-2 x+1$ ** S
- Question 3 and 4, Exercise 5.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... mabad, Pakistan. =====Question 3===== Factorize by using factor theorem: $2 x^{3}+5 x^{2}-9 x-18$ *... - 18 \\ &= -16 + 20 + 18 - 18 = 0. \end{align*} By the factor theorem, \( x + 2 \) is a factor of \(... 2x - 3)(x + 3).$$ =====Question 4===== Factorize by using factor theorem: $3 x^{3}-5 x^{2}-36$ **Sol
- Question 5 and 6, Exercise 5.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... mabad, Pakistan. =====Question 5===== Factorize by using factor theorem: $t^{3}+t^{2}+3 t-5$ ** Sol... 1) - 5 \\ &= 1 + 1 + 3 - 5 \\ &= 0. \end{align*} By the factor theorem, \( t - 1 \) is a factor of \(... nd its other factors. **Solution.** It is given by the factor theorem, \( x - 2 \) is a factor of \(
- Question 1, Review Exercise
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... x+1)(x-2)$</collapse> ii. Divide $9 y^{2}+9 y-10$ by $3 y-2$, then remainder is:\\ * (a) $ 0$\\ ... </collapse> iv. If $3 x^{3}-2 x^{2}+5$ is divided by $x+1$, then $x+1$ will be its:\\ * (a) diviso... +3 p x^{2}-4 x$ has a remainder of 4 when divided by $x+2$, then $\mathbf{p}=$\\ * (a) $-2$
- Question 6 & 7, Review Exercise
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... emainder upon dividing $\left(x^{2}+8 x+k\right)$ by $(x-4)$ is zero. ** Solution. ** Let \( p(x) = ... given that the remainder upon dividing \( p(x) \) by \( (x - 4) \) is zero. \\ By the remainder theorem, the remainder is \( p(4) \). Since \( p(4) = 0 \
- Question 4 and 5, Exercise 5.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... $4 y^{3}-4 y^{2}+10+2 y$ is completely divisible by any of its factor such that the quotient is $4 y^... $ ' if $x^{3}+q x^{2}-7 x+6$ is exactly divisible by $(x+1)$. ** Solution. ** Let $p(x)=x^{3}+q x^{2}-7 x+6$ and $x-c=x+1$ $\implies c=-1$. By factor theorem $x+1$ is factor of $p(x)$ iff $p(-
- Question 3, Exercise 5.3
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ngth = $2x+2$ units \\ Volume = 144 cubic units. By given condition \begin{align*} & x(2x)(2x+2) = 1... height = 3 units Hence the dimension is 6 units by 8 units by 3 units. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf:sol:u
- Question 4, Exercise 5.3
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ight = $x-2$ units \\ Volume = 2475 cubic units. By given condition \begin{align*} & x(2x+3)(x-2) = ... = 11-2 = 9 units Hence the dimension is 11 units by 25 units by 9 units. GOOD ====Go to ==== <text align="left"><btn type="primary">[[math-11-nbf
- Question 2 and 3, Exercise 5.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... {3}-2 x^{2}-5 x+6$ and $x-c=x-3$ $\implies c=3$. By factor theorem $x-3$ is factor of $p(x)$ iff $p(3... {3}-2 x^{2}-5 x+1$ and $x-c=x-3$ $\implies c=3$. By factor theorem $x-3$ is factor of $p(x)$ iff $p(3
- Question 6 and 7, Exercise 5.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... nomial $2 x^{3}+3 x^{2}-3 x-m$ which when divided by $x-2$ gives the remainder of 16 . ** Solution. *... }+3 x^{2}-3 x-m$ and $x-c=x-2$ $\implies c=2$. \\ By the Remainder Theorem, we have \begin{align*} \te
- Question 8 and 9, Exercise 5.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... 0 \end{align} Hence 2 is zero of $p(x)$. \\ Then by using synthetic division: \begin{align} \begin{ar... =4$. (:!: statement corrected). ** Solution. ** By synthetic division \begin{align} \begin{array}{r|
- Question 7 and 8, Exercise 5.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ** Using synthetic division to divide \( f(x) \) by \( x - \frac{1}{2} \): \begin{align} \begin{arra... 0$. This given $-\frac{1}{2}$ is zeor of $h(x)$. By using synthetic division: \begin{align} \begin{ar
- Question 5, Exercise 5.3
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... cture}} The area of rectangle ACED is represented by $6 x^{2}+38 x+56$. Its width is represented by $2 x+8$. Point B is the midpoint of AC. ABFG is a squa
- Question 10, Exercise 5.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... tion. ** Suppose $p(x)=x^{3}+11 x^{2}+34 x+24$. By using synthetic division: \begin{align} \begin{ar