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2. Polynomials
easy
Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $(x-1)(3 x-4)$
$(ii)$ $(2 x-5)\left(2 x^{2}-3 x+1\right)$
Option A
Option B
Option C
Option D
Solution
$(i)$ The given polynomial can be written as:
$(x-1)(3 x-4)=3 x^{2}-4 x-3 x+4$
$=3 x^{2}-7 x+4$
So, coefficient of $x^{2}$ in the given polynomial is $3 .$
$(ii)$ The given polynomial can be written as:
$(2 x-5)\left(2 x^{2}-3 x+1\right)=4 x^{3}-6 x^{2}+2 x-10 x^{2}+15 x-5$
$=4 x^{3}-16 x^{2}+17 x-5$
So, the coefficient of $x^{2}$ in the given polynomial is $-16 .$
Standard 9
Mathematics
