NCERT Solutions for Chapter: Factorisation, Exercise 1: Exercise

Factorise the following and find its irreducible form.

$15x^{2}y+6x^4{y}^2-9xy$

Satpal solved an algebraic equation as shown below.

Algebraic equation: $(s+4{)}^2=36+s^2$

Step 1:$s^2+16+8s=36+s^2$

Step 2: $8s=52$
Step 3: $\mathrm{s}=\frac{52}{8}=\frac{13}{2}$
Did Satpal solve the equation correctly? Explain your answer.

"When a monomial is divided by a monomial, the quotient is a monomial."
Siya disagrees with the statement as$x^2$  divided by $x^2$, is $1$. Is Siya correct? Justify your answer.

When $5\left(6t^2+12t\right)$ is divided by a polynomial gives $30t$ as the quotient. What would be the divisor of the polynomial?

$2x+5$ is divided by $5$, What is the quotient? 

Which of the following divides $25\left(x^{2}y+y^{2}x\right)$ completely? 

$\left(a^2-1\right)÷(a-1)=a+1$

What is the GCF of the expression below that could be used to rewrite the polynomial in factored form?

$4x^3+8x^2+20x$