Polynomial Expressions

Q. Statement 1: The polynomial $x^5+2x^4+3x^3+x^2–7x+8$ when divided by x + 1, gives 14 as remainder.

Statement 2: The value of the polynomial $x^5+2x^4+3x^3+x^2–7x+8$ at x = -1 is 14.

1. Statement 1 is false but statement 2 is true.
2. Both the statements are true and statement 2 is the correct explanation of statement 1.
3. Both the statements are true and statement 2 is not the correct explanation of statement 1.
4. Statement 1 is true but statement 2 is false.
   

Q. Coefficient of ${}^{\prime }{b}^{\prime }$ in the expression $4b^2$ is ___.

1. 4
2. $b$
3. 2
4. $4b$

Q. Which of the following identity can be used to solve 1001 $\times$ 999?

1. ${(a+b)}^2$ = $a^2$ + $2ab$ + $b^2$
2. $(a+b)\times (a-b)=a^2$ - $b^2$
3. ${(a-b)}^2$ = $a^2$ -$2ab$ + $b^2$
4. $(x+y{)}^3$ = $x^3$ + 3$x^2$$y$ + 3$x$$y^2$ + $y^3$

Q.

$(x+y)(x-y)(x^2+y^2)$ = ___________.

1. $(x^3+y^3)$

2. $(x^3-y^3)$

3. $(x^4+y^4)$

4. $(x^4-y^4)$

Q.

Find the product of $(x+y-z+p)$ and $xyzp$.

1. $2xyzp-xy{z}^{2}p+xyz{p}^2$

2. $x^{2}yzp+x{y}^{2}zp-xy{z}^{2}p+xyz{p}^2$

3. $x^{2}yzp+x{y}^{2}zp+xy{z}^{2}p+xyz{p}^2$

4. $2xyzp+xy{z}^{2}p+xyz{p}^2$

Q.

Coefficient of $y$ in the term -$\frac{y}{9}$ is ______.

1. -1

2. -3

3. -$\frac{1}{9}$​

4. $\frac{1}{3}$​

Q.

Which of the following expressions are polynomials?
(i) $x^2+4$
(ii) $4-x^{-1}$
(iii) $2x^2-\frac{2}{x}$

1. i

2. ii, iii

3. iii

4. i, ii, iii

Q.

Which of the following is not true?

1. ${(a-b)}^2$ = $a^2$ - 2ab + $b^2$

2. $(x+a)(x+b)=x^2+(a+b)x+ab$

3. ${(a+b)}^2=b^2$ + 2ab + $a^2$

4. ${(a+b)}^2$ = $a^2$ - 2ab + $b^2$

Q.

Like terms are the terms that contain same variables, same exponents of variables and same coefficients.

1. True

2. False

Q.

-ba and ab are unlike terms.

1. True

2. False