Question

What is the coefficient of $x^2$ in the expansion of

$(3x^2-\frac{1}{5}x+1)(5x+\frac{1}{3})$

• A. $-4$
• B. $0$
• C. $2$
• D. $4$

Answer 1

The correct option is B $0$

$(3x^2-\frac{x}{5}+1)(5x+\frac{1}{3})$

$=3x^2(5x+\frac{1}{3})-\frac{x}{5}(5x+\frac{1}{3})+1(5x+\frac{1}{3})$

$=15x^3+x^2-x^2-\frac{x}{15}+5x+\frac{1}{3}$

$=15x^3-\frac{x}{15}+5x+\frac{1}{3}$

Since there is no $x^2$ term in the above expression, its coefficient is $0$.