Cubic Polynomial

Q. Question 17
Which of the following is a factor of $(x+y{)}^3–(x^3+y^3)$?

A) $x^2+y^2+2xy$
B) $x^2+y^2–xy$
C) $x{y}^2$
​​​​​​​D) $3xy$

Q. Question 4
Write the coefficient of $x^2$ in each of the following:

(i) $\frac{\pi }{6}x+x^2-1$

(ii) $3x-5$

(iii) $(x-1)(3x-4)$

(iv) $(2x-5)(2x^2–3x+1)$

Q. 3.Let ax^3+bx^2+ cx + d be a cubic polynomial. If its leading coefficient is unity such that p(2)=5, p(3)=4and its curve passes through the origin, then find the value of 3(b +c+ d)

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : The polynomial P(x) = x² – 34x + 289 has only one zero.
A : बहुपद P(x) = x² – 34x + 289 का केवल एक शून्यक है।

R : If (x – 5) is a factor of 2x² – 5x + 3k, then k equals $\left(\frac{-25}{3}\right).$
R : यदि 2x² – 5x + 3k का एक गुणनखण्ड (x – 5) है, तब k का मान $\left(\frac{-25}{3}\right)$ है।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q.

Which of the following is not a factor of $a{x}^2+b{y}^2+bxy+axy?$

1. x + y

2. ax + by

3. a + b

4. 1

Q. The sum of the three zeroes of the polynomial $p{x}^3+q{x}^2+rx+s$ is

1. $\frac{-q}{s}$
2. $\begin{array}{c}s\\ q\end{array}$
3. $-\begin{array}{c}q\\ p\end{array}$
4. $\begin{array}{c}q\\ s\end{array}$

Q. Identify the correct combination by matching the following polynomials with their respective maximum number of zeroes.

Q. if the zeros of the polynomial ax^2+bx+c be in ratio m:n then prove that b^2mn=(m^2+n^2)ac

Q. Find the coefficient of $xz$ in the expansion $(2x-y+4z{)}^2$.

1. $-2$
2. $-4$
3. $16$
4. $-16$