Question

Find the value of the given expression
$(4x^3+x^2+x)÷4x$

• A. $\frac{(4x^2+3x+4)}{4}$
• B. $\frac{(4x^2+x+1)}{4}$
• C. $\frac{(3x^2+2x+1)}{4}$
• D. $\frac{(4x^2+x+2)}{4}$

Answer 1

The correct option is B $\frac{(4x^2+x+1)}{4}$

Divide all the terms of the expression $(4x^3+x^2+x)$ separately by $4x$.

$\frac{4x^3}{4x}=x^2$;

$\frac{x^2}{4x}=\frac{x}{4}$;

$\frac{x}{4x}=\frac{1}{4}$.

Therefore, $\frac{(4x^3+x^2+x)}{4x}=x^2+\frac{x}{4}+\frac{1}{4}=\frac{(4x^2+x+1)}{4}$