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- Question 3 and 4, Exercise 5.2
- ====== Question 3 and 4, Exercise 5.2 ====== Solutions of Question 3 and 4 of Exercise 5.2 of Unit 05: Polyn... sing factor theorem: 2x3+5x2−9x−18 ** Solution. ** Suppose \( f(x) = 2x^{3} + 5x^{2} - 9x - 18 ... )] \\ &= (x + 2)(2x - 3)(x + 3). \end{align*} The solution set is f(x)=(x+2)(2x−3)(x+3). =====Que... by using factor theorem: 3x3−5x2−36 **Solution.** Suppose f(x)=3x3−5x2−36. \
- Question 1, Exercise 5.1
- ====== Question 1, Exercise 5.1 ====== Solutions of Question 1 of Exercise 5.1 of Unit 05: Polynomials. This... 2x3+3x2−4x+1 is divided by x+2. ** Solution. ** Given: p(x)=2x3+3x2−4x+1\\ x−c=x...4+2x3−x2+2x+3 is divided by x−2. ** Solution. ** Given: \( p(x) = x^{4} + 2x^{3} - x^{2} + 2x
- Question 2 and 3, Exercise 5.1
- ====== Question 2 and 3, Exercise 5.1 ====== Solutions of Question 2 and 3 of Exercise 5.1 of Unit 05: Polyn... t x−3 is a factor of x3−2x2−5x+6. ** Solution. ** Let p(x)=x3−2x2−5x+6 and x−c=x−3... is a factor of x3−2x2−5x+1 or not. ** Solution. ** Let p(x)=x3−2x2−5x+1 and x−c=x−3
- Question 4 and 5, Exercise 5.1
- ====== Question 4 and 5, Exercise 5.1 ====== Solutions of Question 4 and 5 of Exercise 5.1 of Unit 05: Polyn... is 4y2−8y+10, then find other factor. ** Solution. ** =====Question 5===== Find the value of... x^{2}-7 x+6isexactlydivisibleby(x+1)$. ** Solution. ** Let p(x)=x3+qx2−7x+6 and x−c=x+1
- Question 6 and 7, Exercise 5.1
- ====== Question 6 and 7, Exercise 5.1 ====== Solutions of Question 6 and 7 of Exercise 5.1 of Unit 05: Polyn... divided by x−2 gives the remainder of 16 . ** Solution. ** Let p(x)=2x3+3x2−3x−m and x−c=x−...ther1and−2arethezerosofx^{3}-7 x+6$. ** Solution. ** Suppose p(x)=x3−7x+6.\\ 1 will be zero o
- Question 8 and 9, Exercise 5.1
- ====== Question 8 and 9, Exercise 5.1 ====== Solutions of Question 8 and 9 of Exercise 5.1 of Unit 05: Polyn... s of the polynomial 2x3+3x2−11x−6. ** Solution. ** Suppose p(x)=2x3+3x2−11x−6. \\ Since \be... )+r,wherea=4$. (:!: statement corrected). ** Solution. ** By synthetic division \begin{align} \begin{a
- Question 1 and 2, Exercise 5.2
- ====== Question 1 and 2, Exercise 5.2 ====== Solutions of Question 1 and 2 of Exercise 5.2 of Unit 05: Polyn... torize by using factor theorem: y3−7y−6 ** Solution. ** Suppose f(y)=y3−7y−6. \begin{align*} ... y using factor theorem: 2x3−x2−2x+1 ** Solution. ** \begin{align*} f(x) &= 2x^{3} - x^{2} - 2x +
- Question 5 and 6, Exercise 5.2
- ;====== Question 5 and 6, Exercise 5.2 ====== Solutions of Question 5 and 6 of Exercise 5.2 of Unit 05: Poly... by using factor theorem: t3+t2+3t−5 ** Solution. ** Suppose f(t)=t3+t2+3t−5.... {3}-15 x^{2}+16 x+12$, find its other factors. **Solution.** It is given by the factor theorem, \( x - 2 \
- Question 7 and 8, Exercise 5.2
- ====== Question 7 and 8, Exercise 5.2 ====== Solutions of Question 7 and 8 of Exercise 5.2 of Unit 05: Polyn... 10if′\dfrac{1}{2}$ ' is one of its zero. ** Solution. ** Using synthetic division to divide \( f(x) \... frac{-1}{2}\right)=0,thenfactorizeh(x)$. ** Solution. ** Given: h(x)=4x3+4x2+73x+36 and $h
- Question 2 & 3, Review Exercise
- ====== Question 2 & 3, Review Exercise ====== Solutions of Question 2 & 3 of Review Exercise of Unit 05: Pol... (64y3−8)÷(4y−2) ** Solution. ** \begin{align*} \frac{(64 y^{3}-8)}{(4 y-2)}&... 3===== (125y3−8)÷(5y−2) ** Solution. ** \begin{align*} \frac{(125 y^{3}-8)}{(5 y-2)}
- Question 4 & 5, Review Exercise
- ====== Question 4 & 5, Review Exercise ====== Solutions of Question 4 & 5 of Review Exercise of Unit 05: Pol... s 3y−2 a factor of 6y3−y2−5y+2 ? ** Solution. ** Given \begin{align*}3y-2&=0\\ 3y&=2\\ y&=\fr... are 4,35,−2, find the polynomial. ** Solution. ** Let the required polynomial be f(x). G
- Question 6 & 7, Review Exercise
- ====== Question 6 & 7, Review Exercise ====== Solutions of Question 6 & 7 of Review Exercise of Unit 05: Pol... \left(x^{2}+8 x+k\right)by(x-4)$ is zero. ** Solution. ** Let p(x)=x2+8x+k. We are give... -x+32-\frac{121}{x+4}$. What is the dividend? ** Solution. ** :!: The question doesn't seem to solvable.
- Question 10, Exercise 5.1
- ====== Question 10, Exercise 5.1 ====== Solutions of Question 10 of Exercise 5.1 of Unit 05: Polynomials. Th... is (x+1) feet. Find the area of its floor. ** Solution. ** Suppose p(x)=x3+11x2+34x+24. By u
- Question 1, Exercise 5.3
- ====== Question 1, Exercise 5.3 ====== Solutions of Question 1 of Exercise 5.3 of Unit 05: Polynomials. This... he dimensions of the bottle. (:!: Correction) ** Solution. ** Consider length of bottle = x cm\\ Width o
- Question 2, Exercise 5.3
- ====== Question 2, Exercise 5.3 ====== Solutions of Question 2 of Exercise 5.3 of Unit 05: Polynomials. This... uring the twelfth game of the cricket season. ** Solution. ** Given: t(x)=x3−12x2+48x+74. When