Question

Assignment –Ch2
1. Which of the following are polynomials in one variable and which are not? Give reason.
a) 3x2+4x+5 b) 4√y+√2 y c) x15+y10+z9.
2. Verify that 2 and -3 are zeroes of the polynomial p(x)=(x-2)(x+3).
3. If p(t)=t3+2t2+t , find p(3) , p(-3) and p(4).
4. By actual division , find the quotient and remainder when the first polynomial is divided by the second polynomial
X4+1; x-1.
5. Find the value of k if the polynomial p(x)=3x3+kx2+5x-16 is divided by x-2 leaves a remainder -8.
6. The polynomial ax3+3x2-3 and 2x3-5x+a when divided by x-4 leave the same remainder in each case. Find the value of a.
7. If x+2a is a factor of x5-4a2x3+2x+2a+3 , find a.
8. Without actual division , prove that 2x4-8x3+3x2+12x-9 is exactly divisible by x2-4x+3.
9. Evaluate using identities : a) (2x+3y)^3 b) (3y^2-z)^3 c) 4x2-9y2 d) 1043 e) 9993.
10. If 3x+2y=12 and xy=6, find the value of 9x2+4y2 and 27x3+8y3.
11. Write the expanded form of (-2x+3y+4z)^2.
12. If x+1/x = 7 , find the value of a) x^2+1/x^2 b) x^3+1/x^3 c) x^4+1/x^4 .
13. If x+y=10 and xy=25 , find the value of x^3+y^3.
14. Find the value of a and b so that the polynomial x^3-ax^2-13x+b has (x-1) and (x+3) as a factor.
15. Factorize: a) p 3-125q3+1+15pq b) x6+5x3+6 c) 25x2+4y2+9z2-20xy-12yz+30xz d) 16a4-54a.
16. If both (x-2) and (x-1/2) are factors of px^2+5x+r then show that p=r.
17. Find the value of x3-8y3-36xy-216 , when x=2y+6.
18. Simplify : (a+2b-3c)^2-(a-2b+3c)^2.
19. If x^4+1/x^4 =527, find the value of x+1/x.
20. Find the remainder when p(x)=x3-6x2+2x-4 is divided by 1-3x. Verify the same by long division.

Answer 1

Required Answer : -

Given ,

If 3 is subtracted from the numerator of a fraction, the fraction is reduced to ⅔

Solution

3x - 2 y = 9 (i)

6x - 5y = 30 (ii)

let's solve the this problem with first equation = 3x - 2 y = 9 (i)

$3 \times - 2(15) = 153×−2(15)=1 \\ \\ </p><p></p><p> \\ 3 \times - 30 = 93×−30=9</p><p></p><p> \\ \\ 3 \times = 9 + 303×=9+30</p><p></p><p> \\ \\ \\ 3 \times = 393×=39$

x = 13x=13

➠ hence , the numerator is 13 fraction

$= \frac{13}{15}$

Answer 2

Answer:ans- 3/2Step-by-step explanation:7) Let p(x)=x 5 −4a 2x3 +2x+2a+3 and g(x)=x+2aNow. g(x)=x+2ax+2a=0x=−2aNow, if g(x) is a factor of p(x), then p(−2a) must be 0Thus, p(−2a)=0 =>(−2a) 5 −4a 2 (−2a) 3 +2(−2a)+2a+3=0 =>−32a 5+32a 5 −4a+2a+3=0 =>−2a+3=0 =>a= 3/2

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