Answer:
a. (x+5)(x-5)
b. 3(x+1)(x-5)
c. (x^2+3)(x+2)
Step-by-step explanation:
a. x^2-25
The given expression can be factorized using the formula:
[tex]a^{2} -b^{2} =(a+b)(a-b)\\So,\\x^{2} -25\\=(x)^{2}-(5)^{2}\\=(x+5)(x-5)[/tex]
b. 3x^2-12x-15
We can see that 3 is common in all terms
=3(x^2-4x-5)
In order to make factors, the constant will be multiplied by the co-efficient of highest degree variable
So,
[tex]3[x^{2} -4x-5]\\=3[x^{2}-5x+x-5]\\=3[x(x-5)+1(x-5)]\\=3(x+1)(x-5)[/tex]
c. x^3+2x^2+3x+6
Combining the first and second pair of terms
[tex]x^{3}+2x^{2}+3x+6 \\=[x^{3}+2x^{2}]+[3x+6]\\Taking\ x^{2}\ common\ from\ first\ two\ terms\\=x^{2} (x+2)+3(x+2)\\=(x^{2}+3)(x+2)[/tex]
