Expression in Factorized Form

Q. The factorization of the polynomial expression $m^2-25$ would be $(m+25)(m-25)$.

1. True
2. False

Q.

Factor by using the perfect-square trinomial: $64{\mathrm{x}}^2-144\mathrm{x}+81$

Q. Which of the following options would be equal to $4x+16y$?

1. $16(x+4y)$
2. $4(x+16y)$
3. $4(x+4y)$
4. $16(x+y)$

Q. What would be the irreducible factor form of $z^3-z$?

1. $z(z^2-1)$
2. $z^2(z-z^{-1})$
3. $z(z-1)(z+1)$
4. $z^3(1-z^{-2})$

Q. What is the prime factorization of $16x^2-64$?

1. $16(x^2-4)$
2. $16(x-2)(x+2)$
3. $4\times 4(x-2)(x+2)$
4. $2\times 2\times 2\times 2(x-2)(x+2)$

Q. Factorize $10a^{2}b-4ab+6a{b}^2$

1. $ab(5a-2+3b)$
2. $2ab(5a+2+3b)$
3. $2ab(5b-2+3a)$
4. $2ab(5a-2+3b)$

Q. Factorize the expression $pq-2q-5p+10$ and state the conditions on $p$, $q$ such that when numerical values are substituted for $p$ and $q$, the given expression is equal to $0$.

1. $(p-2)(q-5)$
   $0$ when $p=2$
2. $(p-2)(q-5)$
   $0$ when $q=5$
3. $(p-2)(q-5)$
   $0$ when $q=2$
4. $(p-2)(q-5)$
   $0$ when $p=5$

Q. Which of the following option is equivalent to the polynomial $-3t^2+11t^{10}-5t^4$?

1. $t^2(11t^8-5t^2-3)$
2. $11t^8-5t^2-3$
3. $t^4(11t^8-5t^2-3)$
4. None of the above

Q.

Match the two columns. Column-II gives factors for expression given in Column-I.

Column 1	Column 2
$9x^2+6xy+y^2$	$(2x+3y–4z)(2x+3y–4z)$
$4x^2+9y^2+16z^2+12xy–24yz–16xz$	$\left(x+\frac{y}{10}\right)\left(x-\frac{y}{10}\right)$
$27x^3+y^3+z^3–9xyz$	$(3x+y+z)(9x^2+y^2+z^2–3xy–yz–3zx)$
$x^2-\frac{y^2}{100}$	$(3x+y)(3x+y)$

Q. What is the standard simplest form of the polynomial: $-80s^3-2s^9+10s^5+100s$ ?

1. $s(-s^8+5s^4-40s^2+50)$
2. $2(-s^8+5s^4-40s^2+50)$
3. $2s(-s^8+5s^4-40s^2+50)$
4. $2s^2(-s^8+5s^4-40s^2+50)$

Q. Factorize: $4(a+b{)}^2-(a-b{)}^2$

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

Q. Select the pair which contains the same common factor.

1. $5x^5+10x^7+15x$
2. $3x^5+9x^7+6x$
3. $5x^5+25x^7+35x$
4. $18x^5+3x^7+9x$
5. $4x^5+16x^7+12x$
6. $72x^5+24x^7+4x$