GCD of Polynomials

Q.

A rectangular Courtyard is $18m72cm$ long and $13m20cm$ broad it is to be paved with square tiles of the same size and the least possible number of such tiles?

Q. Question 6
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is the HCF (525, 3000)? Justify your answer.

Q. Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

1. 63
2. 58
3. 82
4. 49

Q. Question 12
On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?

Q. Find HCF of 196 and 38220 by Euclid's division lemma method

Q.

Using Euclid’s division algorithm, find the HCF of

405 and 2520

Q.

Find HCF and LCM of $90$ and $144$ by the prime factorization method.

Q.

Using prime factorization, find the $HCF$and $LCM$of $36$, $84$.

Q.

Justify the statement all polynomials are algebric expressions but all algebric expressions are not polynomials. Give examples

Q.

Using Euclid's division, find the HCF of 56, 96 and 404

Q.

If $A$ is a $2\times 2$ matrix with non - zero entries let $A^2=I$, where $I$ is $2\times 2$ identity matrix.

Define $tr\left(A\right)=$ Sum of diagonal element of $A$ and $\left|A\right|=$ Determinant of matrix $A$.

Statement I $tr\left(A\right)=0$.

Statement II $\left|A\right|=i$

1. Statement I is correct, Statement II is correct; Statement II is the correct explanation for Statement I

2. Statement I is correct, statement II is correct, Statement II is not the correct explanation for Statement I

3. Statement I is correct, Statement II is incorrect

4. Statement I is incorrect, Statement II is correct

Q.

Why 6/15 has a terminating expansion and 64/455 has a non terminating expansion

Q.

Find the HCF of $144$ and $198$

Q.

Question 24
Factorise
(i) $2x^3–3x^2–17x+30$

(ii) $x^3–6x^2+11x–6$

(iii) $x^3+x^2-4x-4$

(iv) $3x^3–x^2-3x+1$

Q. Using Euclid’s division algorithm, find the HCF of 70 and 30.

Q. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

129÷2²5⁷7⁵

Q.

Find the HCF of $170$ and $238$ using prime factorization of $170$ and $238$

Q.

Write the condition for a rational number which can have a terminating decimal expansion.

Q.

Question 2 (iii)
Find the LCM and HCF of 336, 54 and verify that LCM $\times$ HCF = product of the two numbers.

Q.

Factorise the following expression: $a{m}^2+b{m}^2+b{n}^2+a{n}^2$

Q. Find the GCD of $(a^3-4a^2+7a-6)$ and $(a^3-5a^2+10a-8)$ by using the division method.

1. $(a-2)$
2. $3(a-2)$
3. $4(a-2)$
4. $(a+2)$

Q. How many polynomials having zeroes as-7 and 2 ?

Q.

Find the HCF and LCM of $117$and$221.$

Q. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk, so that each can cover the same distance in complete steps?

1. 2500 cm
2. 2550 cm
3. 2520 cm
4. 2505 cm

Q.

What type of decimal expansion does 29_{^{÷ 2^2×5×7 have?}}

Q.

If p(x) = g(x) × q(x) + r(x), p(x) and g(x) are any two polynomials with g(x) $\ne$ 0, then we can find polynomials q(x) and r(x) by division algorithm.We should stop the division process when

1. r(x) = 0

2. degree of r(x) < degree of g(x)

3. Either A or B

4. None of these

Q. Question 16
The factorization of $4x^2+8x+3$ is

A) $(x+1)(x+3)$
B) $(2x+1)(2x+3)$
C) $(2x+2)(2x+5)$
​​​​​​​D) $(2x-1)(2x-3)$

Q.

The sum of two numbers is $55$ and the HCF and LCM of these two numbers are $5$ and $120$ respectively. Find the sum of reciprocals of these numbers.

Q.

Using prime factorization method, find the HCF of $40,48$ and $72$

Q.

How do you factor $64x^3+27$?