Visualisation of Addition of Polynomials

Q.

What is the difference between algebraic expression and polynomial

Q. Find all polynomials P(x) with real coefficients such that (x-8)P(2x)=8(x-1)P(x) .

Q.

Which of the following is a linear inequality with two variables?

1. 2x + 8y > 9

2. None of the above

3. 10x + 7 ≤ 2

4. 8x + 9y = 0

Q.

Do all polynomials have only one variable? What's the difference between algebraic expression and polynomials?

Q.

The product of two linear polynomials is x² – 7x + 12 .So, they are

1. x-6 and x+2

2. x-4 and x-3

3. x+4 and x+3

4. x+6 and x-2

Q.

Write three polynomials with variable y

Q.

Adding of the polynomials 4x and 4y can be visualized.

1. True

2. False

Q. Show that:
(i) $\frac{1}{1+x^{a-b}}+\frac{{\displaystyle 1}}{{\displaystyle 1+x^{b-a}}}=1$

(ii) ${\left[\left\{\frac{x^{a\left(a-b\right)}}{x^{a\left(a+b\right)}}\right\}÷\left\{\frac{x^{b\left(b-a\right)}}{x^{b\left(b+a\right)}}\right\}\right]}^{a+b}=1$

(iii) ${\left(x^{\frac{1}{a-b}}\right)}^{\frac{1}{a-c}}{\left(x^{\frac{1}{b-c}}\right)}^{\frac{1}{b-a}}{\left(x^{\frac{1}{c-a}}\right)}^{\frac{1}{c-b}}=1$

(iv) ${\left(\frac{x^{a^2+b^2}}{x^{ab}}\right)}^{a+b}{\left(\frac{x^{b^2+c^2}}{x^{bc}}\right)}^{b+c}{\left(\frac{x^{c^2+a^2}}{x^{ac}}\right)}^{a+c}=x^{2\left(a^3+b^3+c^3\right)}$

(v) ${\left(x^{a-b}\right)}^{a+b}{\left(x^{b-c}\right)}^{b+c}{\left(x^{c-a}\right)}^{c+a}=1$

(vi) ${\left\{{\left(x^{a-a^{-1}}\right)}^{\frac{1}{a-1}}\right\}}^{\frac{a}{a+1}}=x$

(vii) ${\left(\frac{a^{x+1}}{a^{y+1}}\right)}^{x+y}{\left(\frac{a^{y+2}}{a^{z+2}}\right)}^{y+z}{\left(\frac{a^{z+3}}{a^{x+3}}\right)}^{z+x}=1$

(viii) ${\left(\frac{3^a}{3^b}\right)}^{a+b}{\left(\frac{3^b}{3^c}\right)}^{b+c}{\left(\frac{3^c}{3^a}\right)}^{c+a}=1$

Q. Classify the following polynomials as polynomials in one-variable, two variables etc.:

(i) x² − xy + 7y²

(ii) x² − 2tx + 7t² − x + t

(iii) t³ − 3t² + 4t − 5

(iv) xy + yz + zx

Q.

Visualize addition of 30 and 24.

1. \N

Q.

Add the following algebraic expression:

$x^2-5x+1,2-5x+3x^2,-1+12x-2x^2$

Q.

Addition of the polynomials 6x and 6y can be visualized.

1. True

2. False

Q.

Ram was presented a riddle by his mathematics teacher to find the area of a rectangle whose length and breadth are definite but unknown. Can you find the answer to this riddle among the following options?

1. (L + B)(L + B)

2. L(L + B)

3. B(L + B)

4. L x B

Q.

Only subtraction of polynomials can be visualized geometrically.

1. True

2. False

Q.

Which of the following shows the visualization of the addition of 5x and 2 ?

1. 

2. 

3. 

4. 

Q. 79.do the following problem with the process of factarisation of polynomials (x-y)+ (y-x)2 is equal to 1)(y -x)2(1-y+x) 2)(x- y)2(1+y+x) 3)(x-y)2(1+y-x) 4)(y-x)2(1+y+x)

Q. Classify the following polynomials as polynomials in one-variable, two variables etc.:

(i) x² − xy + 7y²

(ii) x² − 2tx + 7t² − x + t

(iii) t³ − 3t² + 4t − 5

(iv) xy + yz + zx

Q.

Give possible expression for the length and breadth of the rectangle having 35y^2+13y-12 as its area.

Q.

Area of a face of a cuboid is of the form xy, where x and y are length and breadth respectively.

In the solution this statement is shown true.But area of one face of cuboid can also be breadth x height or length x height

Q.

Which of the following shows the visualization of the addition of 5x and 2?

1. \N

Q.

Only addition of polynomials can be visualized.

1. True

2. False

Q.

Which of the following shows the visualization of the addition of 3x and 9?

1. 

2. 

3. 

4. 

Q.

Visualize addition of 25 and 35.

1. 

2. 

3. 

4. 

Q.

Visualize addition of 30 and 24.

1. 

2. 

3. 

4. 

Q. Match the following according to the polynomial $-15x^4+0.5x^3-x^2+2x+8$.

1. 5
2. 1
3. 8
4. -5.5

Q.

visualize addition of 25 and 35.

1. \N

Q.

Give possible expressions for the length and breadth of the rectangle whose area is given as 16a²-32a+15 sq. units.