Question
Factorise the expressions and divide them as directed:
$\left(3 x^4-1875\right) \div\left(3 x^2-75\right)$
$\left(3 x^4-1875\right) \div\left(3 x^2-75\right)$
✓
Answer
$\left(3 x^4-1875\right) \div\left(3 x^2-75\right)$
We have,$=\frac{3\text{x}^4-1875}{3\text{x}^2-75}$
$=\frac{\text{x}^4-625}{\text{x}^2-25}$
$=\frac{(\text{x}^2)^2-(25)^2}{\text{x}^2-25}$
$=\frac{(\text{x}^2+25)(\text{x}^2-25)}{(\text{x}^2-25)}$
$=\text{x}^2+25$
We have,$=\frac{3\text{x}^4-1875}{3\text{x}^2-75}$
$=\frac{\text{x}^4-625}{\text{x}^2-25}$
$=\frac{(\text{x}^2)^2-(25)^2}{\text{x}^2-25}$
$=\frac{(\text{x}^2+25)(\text{x}^2-25)}{(\text{x}^2-25)}$
$=\text{x}^2+25$
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