Algebraic Expressions Test

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Algebraic Expressions Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$-x^3\, +\, 4x^2\, -\, 9x\, +\, 3$$

B
$$x^3\, +\, 4x^2\, -\, 9x\, +\, 3$$

C
$$x^3\, -\, 4x^2\, +\, 9x\, -\, 3$$

D
$$-x^3\, -\, 4x^2\, +\, 9x\, -\, 3$$

Solution

Let the polynomial to be subtracted be $$p(x)$$.
$$\therefore x^3 - 3x^2 + 5x -1 - p(x) = 2x^3 + x^2 - 4x + 2$$
$$x^3-2x^3 - 3x^2 - x^2 +5x + 4x-1-2 = p(x)$$
$$\therefore p(x) = -x^3 - 4x^2 + 9x -3$$
Question 2
1 / -0

What must be added to $$x^3\, +\, 3x\, -\, 8$$ to get $$3x^3 \,+ \,x^2\, +\, 6$$?

A
$$2x^3\, +\, x^2\, - \,3x\, +\, 14$$

B
$$2x^2\, + \, x^2\, +\, 14$$

C
$$2x^3\, +\, x^2\, - \,6x\, -\,14$$

D
None of these

Solution

Let the polynomial to be added be $$p$$.
$$\therefore x^3 + 3x - 8 + p = 3x^3 + x^2 + 6$$
$$ \therefore p = 3x^3 + x^2 + 6 - x^3 - 3x + 8$$
$$\therefore p = 2x^3 + x^2- 3x + 14$$

Hence, Option A is correct.
Question 3
1 / -0

How many terms are there in the expression $$5x^3+3xy+y^2$$ ?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$5$$

Solution

There are 3 terms. The terms are $$5x^3, 3xy, y^2$$
Question 4
1 / -0

If we add two binomials $$4x^2+5y^2$$ and $$7x^2+y^2$$, what will be the result?

A
monomial

B
binomial

C
trinomial

D
cannot be determined

Solution

$$(4x^2+5y^2)+(7x^2+y^2)=11x^2+6y^2$$ is a binomial.
Question 5
1 / -0

What is the measure of the third side of a triangle given that its two sides are $$a^{2} - 2a + 1$$ and $$3a^{2} - 5a + 3$$ and has a perimeter $$6a^{2} - 4a + 9$$?

A
$$2a^{2} - 3a - 5$$

B
$$2a^{2} + 3a - 5$$

C
$$2a^{2} + 3a + 5$$

D
$$2a^{2} - 3a + 5$$

Solution

Let the third side of the triangle be $$x.$$

The perimeter of a triangle is equal to the sum of its sides so,
$$\begin{aligned}{}x + \left( {{a^2} - 2a + 1} \right) + \left( {3{a^2} - 5a + 3} \right) &= 6{a^2} - 4a + 9\\x + \left( {{a^2} + 3{a^2}} \right) + \left( { - 2a - 5a} \right) + \left( {1 + 3} \right)& = 6{a^2} - 4a + 9\\x + 4{a^2} - 7a + 4 &= 6{a^2} - 4a + 9\\x &= \left( {6{a^2} - 4{a^2}} \right) + \left( { - 4a + 7a} \right) + \left( {9 - 4} \right)\\& = 2{a^2} + 3a + 5\end{aligned}$$

Hence, option $$C$$ is correct.
Question 6
1 / -0

$$3x^{2} - 5x + 2$$
$$5x^{2} - 2x - 6$$
Which of the following is the sum of the two polynomials shown above?

A
$$8x^{2} - 7x - 4$$

B
$$8x^{2} + 7x - 4$$

C
$$8x^{4} - 7x^{2} - 4$$

D
$$8x^{4} + 7x^{2} - 4$$

Solution

Given polynomials are $$3x^2-5x+2$$ and $$5x^2-2x-6$$
The sum of the given polynomials is given by:
$$(3x^2-5x+2)+(5x^2-2x-6)$$
$$=(3x^2+5x^2)+(-5x-2x)+(2-6)$$
$$=(3+5)x^2 -(5+2)x -4$$
$$=8x^2-7x-4$$
Question 7
1 / -0

Simplify the polynomial and write it in standard form:
$$-3({x}^{3}-{x}^{2}-2x-5)-(4{x}^{3}-7x-1)$$

A
$$-7{x}^{3}+3{x}^{2}+13x+16$$

B
$$7{x}^{3}+2{x}^{2}+11x+16$$

C
$$-6{x}^{3}+3{x}^{2}+12x+14$$

D
$$-4{x}^{3}+3{x}^{2}+11x+15$$

Solution

Solve the polynomial as follows:
$$-3(x^3-x^2-2x-5)-(4x^3-7x-1)$$
$$=-3x^3+3x^2+6x+15-4x^3+7x+1$$
$$=-7x^3+3x^2+13x+16$$
Question 8
1 / -0

The total terms in $$-x^3+4x^2+7x-2$$ is

A
2

B
3

C
4

D
5

Solution

We have a polynomial given by $$-x^3 + 4x^2 + 7x - 2$$
The total number of terms is given by 4, since we have 4 terms with either an addition or subtraction operated between them.
Those 4 terms are $$-x^3, 4x^2, 7x, -2$$
Question 9
1 / -0

Add $$(12x^2+4x+5y)$$ and $$(3x^2-2x+3y)$$.

A
$$2x^2-2x+8y$$

B
$$2x^2+15x+8y$$

C
$$15x^2-2x+8y$$

D
$$15x^2+2x+8y$$

Solution

Adding $$ (12x^2+4x+5y)+(3x^2-2x+3y)$$
$$\Rightarrow 12x^2+4x+5y+3x^2-2x+3y$$
$$\Rightarrow 15x^2+2x+8y$$
Question 10
1 / -0

$$x+y-\left( z-x-\left[ y+z-\left( x+y-\left\{ z+x-\left( y+z+x \right) \right\} \right) \right] \right) $$ is equal to

A
$$3x$$

B
$$2y$$

C
$$x$$

D
$$0$$

Solution

$$x+y-\left (z-x-\left [ y+z-(x+y-\left \{ z+x-(y+z+x) \right \}) \right ] \right )$$
$$=x+y-\left ( z-x-\left [ y+z-(x+y-\left \{ z+x-y-z-x \right \}) \right ] \right )$$
$$=x+y-\left (z-x-\left [ y+z-(x+y-z-x+y+z+x) \right ] \right )$$
$$=x+y-\left ( z-x-\left [ y+z-x-y+z+x-y-z-x \right ] \right )$$
$$=x+y-\left (z-x-y-z+x+y-z-x+y+z+x \right )$$
$$=x+y-z+x+y+z-x-y+z+x-y-z-x$$
$$=x$$

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Re-Attempt Weekly Quiz Competition

Algebraic Expressions Test - 16

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Algebraic Expressions Test - 16

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Question 1

$$-x^3\, +\, 4x^2\, -\, 9x\, +\, 3$$

$$x^3\, +\, 4x^2\, -\, 9x\, +\, 3$$

$$x^3\, -\, 4x^2\, +\, 9x\, -\, 3$$

$$-x^3\, -\, 4x^2\, +\, 9x\, -\, 3$$

Solution

Question 2

$$2x^3\, +\, x^2\, - \,3x\, +\, 14$$

$$2x^2\, + \, x^2\, +\, 14$$

$$2x^3\, +\, x^2\, - \,6x\, -\,14$$

None of these

Solution

Question 3

$$1$$

$$2$$

$$3$$

$$5$$

Solution

Question 4

monomial

binomial

trinomial

cannot be determined

Solution

Question 5

$$2a^{2} - 3a - 5$$

$$2a^{2} + 3a - 5$$

$$2a^{2} + 3a + 5$$

$$2a^{2} - 3a + 5$$

Solution

Question 6

$$8x^{2} - 7x - 4$$

$$8x^{2} + 7x - 4$$

$$8x^{4} - 7x^{2} - 4$$

$$8x^{4} + 7x^{2} - 4$$

Solution

Question 7

$$-7{x}^{3}+3{x}^{2}+13x+16$$

$$7{x}^{3}+2{x}^{2}+11x+16$$

$$-6{x}^{3}+3{x}^{2}+12x+14$$

$$-4{x}^{3}+3{x}^{2}+11x+15$$

Solution

Question 8

2

3

4

5

Solution

Question 9

$$2x^2-2x+8y$$

$$2x^2+15x+8y$$

$$15x^2-2x+8y$$

$$15x^2+2x+8y$$

Solution

Question 10

$$3x$$

$$2y$$

$$x$$

$$0$$

Solution

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