Polynomials

Q. The minimum value of the polynomial p(x) = 3x^2 - 5x + 2 is :

Q. When $x^3+2x^2-kx+4$ is divided by x -2, the remainder is k. The the value of k is ______.

1. -4
2. -$6\frac{2}{3}$
3. $6\frac{2}{3}$
4. 4

Q. Factorize a^4+b^4-a^2b^2

Q.

1. x² - px + q

2. x² + qx + p

3. px² + qx + 1

4. qx² + px + 1

Q.

Factorise: $ax+bx-ay-by$

Q. The value of {[4a^2-9b^2]^3+[9b^2-16c^2]^3+[16c^2-4a^2]^3}/[2a-3b]^3+[3b-4c]^3+[4c-2a]^3

Q. find the value of y y^{2/3 }- 2y^{1/3 }= 15

Q.

What must be subtracted from $3x^3-8x^2+4x-3$ so that the resulting expression is divisible by $x-2$?

1. 3

2. 4

3. -3

4. 3

Q. (4+x^2-4x)+25 = (4+x^2+4x)+81 can you please explain in detail please and don't show in short please

Q.

9x^2-9 (a+b)x +(2a^2×5ab+2b^2)=0

Q.

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^5-2x^3+x+\sqrt{3}$

(ii) $y^3+\sqrt{3}y$

(iii) $t^2-\frac{2}{5}t+\sqrt{5}$

Q. 64a^3 - 27b^3 - 144a^2b + 108ab^2

Q.

Factor Theorem is equivalent to Remainder Theorem when remainder is ____.

1. 0
2. 1
3. 2
4. 4

Q. What must be added to $f\left(x\right)=4x^4+2x^3-2x^2+x-1$ so that the resulting polynomial is divisible by $g\left(x\right)=x^2+2x-3$
[4 MARKS]

Q. Assertion :$x^3+x$ has only one real zero. Reason: A polynomial of nth degree must have n real zeroes.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. What must be added to $6x^4-x^3+3x^2+4x-2$, so that the result is exactly divisible by $3x^2-2x+4$? Also find the degree of the quotient.

1. $2x-2,2$
2. $2x+2,2$
3. None of these
4. $2x-3,2$

Q. State whether the following expression is a polynomial in one variable or not. Give reasons for your answer.

Q.

$(x-a)$ is a factor of the polynomial $p\left(x\right)$ then $p\left(a\right)=$

1. $2$

2. $-a$

3. $0$

4. $(x+a)$

Q.

Let $r_1$ and $r_2$ be the remainders when the polynomials $p\left(x\right)=x^3+x^2-5kx-7$ and $q\left(x\right)=x^3+k{x}^2-12x+6$ are divided by $x+1$ and $x-2$ respectively. If $2r_1-r_2=10$, the value of $k$ is

1. $\frac{7}{3}$

2. $\frac{3}{7}$

3. $\frac{5}{7}$

4. $\frac{7}{5}$

Q.

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $\frac{x^2}{2}-\frac{2}{x^2}$

(ii) $\sqrt[2]{22}{x}^2-8$

(iii) $\frac{1}{2x^2}$

Q. What must be subtracted from $8x^4+14x^3-2x^2+7x-8$ so that the resulting polynomial is exactly divisible by $4x^2+3x-2$ [4 MARKS]

Q. What is the degree of the expression (3x + 4)(2x + 3)?

1. 4
2. 1
3. 3
4. 2

Q. If $x^a+\frac{1}{x^b}$ is a polynomial and if it is given that a = b, then the value of $a$ is .

1. 0
2. 1
3. -1
4. 2

Q. 1^2 +5^2x+9^2x^2+13^2x^2+

Q. State whether the following expression is a polynomial in one variable or not. Give reasons for your answer.

Q. What is the degree of the expression (3x + 4)(2x + 3)?

1. 1
2. 2
3. 3
4. 4

Q.

Q5. At x=6, the value of the polynomial 2x-8 will be ______.

1. 2
2. 4

Q. If $x^2-18x+81$ is divided by x - 3, then the remainder is ________.

1. 144
2. 36
3. 12
4. 6

Q. Prove that (2a+3b-4c)^3-8a^3-27b^3+64c^3=6(2a+3b)(3b-4c)(a-2c)

Q. The equation of plane containing z-axis and passing through the point(1, 2, 3) is:

1. $2x=y$
2. $x=2y-z$
3. $9x=6y-7z=0$
4. $x+2y-z=0$