Introduction to factorization - class-X
introduction to factorization
Questions
Factorise ${\left( {3 - 4y - 7{y^2}} \right)^2} - {\left( {4y + 1} \right)^2}$
- $\left( {4 - 7{y^2}} \right)\left( {2 - 8y - 7{y^2}} \right)$
- $\left( {7{y^2} - 4} \right)\left( {2 - 8y - 7{y^2}} \right)$
- $\left( {4 - 7{y^2}} \right)\left( {7{y^2} + 8y - 2} \right)$
- $\left( {7{y^2} - 4} \right)\left( {7{y^2} - 8y - 2} \right)$
Factorise :
- $4(x+2)$
- $4(x+3)$
- $3(x+4)$
- none of these
- $y(y+100)$
- $y^2(y+100)$
- $y(y^2+100)$
- none of these
If (x+1) is a factor of $\displaystyle x^{3}+11x^{2}+15x+a$ then the value of 'a' is
- 2
- 3
- 5
- 4
Factorization is the ......... process of multiplication.
- equal
- same
- inverse
- common
________ is a method of writing numbers as the product of their factors or divisors.
- Polynomial
- Factorisation
- Division algorithm
- Quadratic equation
If the polynomial $f(x)$ is such that $f(-43) = 0$, which of the following is the factor of $f(x)$?
- $x - 43$
- $x$
- $x - 7$
- $x + 43$
The denominator of an algebraic fraction should not be
- $1$
- $0$
- $4$
- $7$
If the sum of two integers is $-2$ and their product is $-24$, the numbers are
- $6$ and $4$
- $-6$ and $4$
- $-6$ and $-4$
- $6$ and $-4$
The value of $k$ for which $x - 1$ is a factor of the polynomial $4 x ^ { 3 } + 3 x ^ { 2 } - 4 x + k$ is
- $3$
- $0$
- $1$
- $-3$
Factorise : $6xy^2 + 4x^2y$
- $2xy(3x+y)$
- $xy(3x+2y)$
- $2xy(2x+3y)$
- none of these
- $a(121c-16ab^{2})$
- $a(121c+16ab^{2})$
- $a(121c-16ac^{2})$
- none of these
Which of the following is an example of factorisation?
- $x^2+2x=x(x+2)$
- $x^2+2x=x(x+1)$
- $x^2+2x=x(x+3)$
- None of the above
Factorise : $5mn+15mnp$
- $5mn(1 + 3p)$
- $3mn(1 + 5p)$
- $5mn(1 - 3p)$
- none of these
Simplify: $\displaystyle \left( -80{ m }^{ 4 }npq \right) \div 10{ m }^{ 3 }{ pqn }^{ 2 }$
- $-8mn$
- $-8mnpq$
- $-8m$
- $\dfrac {-8m}{n}$
The factorisation of $ \left (21a^2+3a \right )$ is
- $3a(7a+1)$
- $7a(3a+1)$
- $3a(7a+3a)$
- $3a(a+7)$
Multiplying factors is an example of
- polynomial
- quadratic equation
- division algorithm
- factorisation
If $f(x)$ and $g(x)$ are two polynomials with integral coefficients which vanish at $x = \dfrac {1}{2}$, then what is the factor of HCF of $f(x)$ and $g(x)$?
- $x - 1$
- $x - 2$
- $2x - 1$
- $2x + 1$
If $\alpha$ and $\beta$ are the roots of $ax^2 + bx+c=0, a \neq 0$ then the wrong statement is
- $\alpha ^2+\beta ^2=\dfrac{b^2-2ac}{a^2}$
- $\alpha \beta =\frac{c}{a}$
- $\alpha +\beta =\frac{b}{a}$
- $\frac{1}{\alpha }+\frac{1}{\beta }=-\frac{b}{c}$
Consider the following statements :
1. $x - 2$ is a factor of $x^{3} - 3x^{2} + 4x - 4$
2. $x + 1$ is a factor of $2x^{3} + 4x + 6$
3. $x - 1$ is a factor of $x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$
Of these statements
- 1 and 2 are correct
- 1, 2 and 3 are correct
- 2 and 3 are correct
- 1 and 3 are correct
If $4x^{4} -12x^{3}+x^{^{2}}+3ax-b$ is divided by $x^{2}-1$ then a = _, and b=
- $5, 4$
- $4,9$
- $4,5$
- $1, -1$
$7+3x$ is a factor of $3x^3+7x$.
- True
- False
Divide : $\displaystyle \left( 51{ m }^{ 3 }{ p }^{ 2 }-34{ m }^{ 2 }{ p }^{ 3 } \right)$ by $17mp$
- $\displaystyle { m }^{ 2 }p$
- $\displaystyle m{ p }^{ 2 }$
- $\displaystyle 3{ m }^{ 2 }p-2m{ p }^{ 2 }$
- $\displaystyle mp$
If $\alpha$ and $\beta$ are the roots of $ax^2+bx+c=0$, then the quadratic equation whose roots are $\cfrac{1}{\alpha}$ and $\cfrac{1}{\beta}$ is
- $ax^2+bx+c=0$
- $bx^2+ax+c=0$
- $cx^2+bx+a=0$
- $cx^2+ax+c=0$