Subtraction of Polynomials

Q.

Find the value of x³ - 8y³ - 36xy - 216, if x= 2y+6.

Q. If $x=\frac{2}{3}$ and $x=-3$ are roots of the quadratic equation $a{x}^2+7x+b=0,$ find the value of a and b.

Q. What must be subtracted from $(x^3-3x^2+5x-1)$ to get $(2x^3+x^2-4x+2)$ ?

1. $-x^3-4x^2+9x-9$

2. $-x^3-4x^2+9x-3$

3. $-x^3+4x^2+9x-3$

4. $-x^3-4x^2+6x-3$

Q.

Question 2
Determine the degree of each of the following polynomials.
(i) $2x-1$

(ii) $-10$

(iii) $x^3-9x+3x^5$

(iv) $y^3(1–y^4)$

Q.

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area: $25a^2-35a+12$
(ii) Area: $35y^2+13y-12$

Q.

Simplify: ${(3pq+3qr)}^2-18p{q}^{2}r$.

1. $9p^2$$q^2$ + $9q^2$$r^2$ - $18p{q}^2$r

2. $9p^2$$q^2$ + $9q^2$$r^2$ - $9p{q}^2$r

3. $9p^2$$q^2$ + $9q^2$$r^2$

4. $9p^2$$q^2$ + $9q^2$$r^2$ + $9p{q}^2$r

Q. Match the like terms.

1. $-7x$
2. $8x^2$
3. $-4x^4$
4. $\frac{3}{4}{x}^3$

Q. Subtract 7x - 3x² from 4x + 8x².

1. 3x
2. 11x² - 5x
3. 11x²
4. 11x² - 3x

Q. Simplify $(p^3-3p^{2}q)+(2p{q}^2+4q^3)-(3p^{2}q+p{q}^2)$

1. $p^3–5p^{2}q+4q^3$
2. $p^3-6p^{2}q+p{q}^2+4q^3$
3. $p^3+p{q}^2+4q^3$
4. $p^3-6p^{2}q+3p{q}^2+4q^3$

Q. Subtract the second polynomial from the first:
$\left(i\right)x^4+x^2+x-1;x^4-x^3-x^2+1$
$\left(ii\right)5x^2-2y+9;3x^2+5y-7$

Q.

By how much is $5a^2{b}^2-18a{b}^2-10a^{2}b$ greater than $-5a^2+6a^{2}b-7ab$?

1. $5a^2{b}^2-18a{b}^2-16a^{2}b+5a^2-7ab$

2. $5a^2{b}^2-18a{b}^2-16a^{2}b-5a^2+7ab$

3. $5a^2{b}^2+18a{b}^2+16a^{2}b-5a^2-7ab$

4. $5a^2{b}^2-18a{b}^2-16a^{2}b+5a^2+7ab$

Q.

The sum of $x^4-xy+2y^2$ and $-x^4+xy+2y^2$ is

1. Monomial and polynomial in $y$

2. Binomial and Polynomial

3. Trinomial and polynomial

4. Monomial and polynomial in $x$

Q.

Simplify: $39x–[23x–\{29x–(17x–3x)\left\}\right]$

1. $30x$

2. $31x$

3. $33x$

4. $29x$

Q. terms can be added or subtracted.

1. Like
2. Unlike
3. Similar

Q. Subtract $4x^3+8x^2$ from $-2x^3+3x^2$. .

1. $6x^3-5x^2$
2. $-6x^3-5x^2$
3. $-6x^3+5x^2$

Q. What should be subtracted from 2a + 6b $-$ 5 to get $-$ 3a + 2b + 3?

Q. Subtract the second expression from the first:

(i) $\frac{m}{3}+\frac{n}{2};\frac{m}{6}+\frac{n}{4}$

(ii) $0.07p^{2}q+3.6p{q}^2-p^2{q}^2-0.003p{q}^2+2p^{2}q-8.5p^2{q}^2$

Q. What should be added to 5x² + 2xy + y² to get 3x² + 4xy?

Q.

If $x^2$ + $y^2$ = 14 and xy = 3, find the value of $2{(x+y)}^2-5{(x-y)}^2$.

1. 0

2. 106

3. 52

4. 14

Q. Subtracting $7x-3x^2$ from $4x+8x^2$ we get

1. - 3x

2. 11x² − 5x

3. 11x²

4. 11x² − 3x

Q.

On simplification of $x-[x-\overline{y+x}-\{x-(x-\overline{y-x})\left\}\right]$, we get,

1. $2y-x$

2. $2y+x$

3. $2y$

4. $2x$

Q.

What value of $x$ makes the equation $4abc+\frac{1}{3}abc+x$+$\frac{2}{3}abc$=0 true ?

1. -6abc

2. -5abc

3. -8abc

4. -7abc

Q.

Add 5√2 + 3√3 and 2√2 - 5√3

1. 

2. 

3. 

4. 

Q.

State whether the following statement is True or False

The value of the polynomial $4x-7x^2+5x^3+4$ at $x=-1is-10$

1. True
2. False

Q.

The result obtained when we multiply $a^6-b^6$ with the product of $a^2+ab+b^2$ and $a-b$ is

1. $a^9-a^6{b}^3-a^3{b}^6+b^9$

2. $a^7-a^6{b}^3-a^3{b}^6+b^9$

3. $a^9-a^6{b}^4-a^3{b}^6+b^9$

4. $a^9-a^6{b}^3-a^3{b}^7+b^9$

Q. What polynomial added to $2x^2–3$ gives the result as $3x^2-4$?​

1. $x^2+1$
2. $x^2+1$
3. $5x^2-7$
4. $x^2-1$

Q.

What must be subtracted from $x^3-3x^2+5x-1$ to get $2x^3+x^2-4x+2$ ?

1. $-x^3+4x^2+9x-3$

2. $-x^3-4x^2+6x-3$

3. $-x^3-4x^2+9x-9$

4. $-x^3-4x^2+9x-3$

Q.

Identify the pairs of like terms among the following.

$3x^2$ and $-\frac{1}{4}{x}^2$

Q. Subtract the polynomial $z^2–2z+4$ from $3z^2-7$.​

1. $2z^2–2z–11$​
2. $2z^2+2z–3$​
3. $2z^2+2z–11$​
4. $4z^2+2z–11$​

Q. If $A=2y^2+3x-x^2,B=3x^2-y^2$ and $C=5x^2-3xy$ then find
$A+B+C$