Solve 25x^2+10x+5/sqrt{5}

$$\frac { 25 x ^ { 2 } + 10 x + 5 } { \sqrt { 5 } }$$

Factor

$$\sqrt{5}\left(5x^{2}+2x+1\right)$$

Solution Steps

Rationalize the denominator of \frac{25x^{2}+10x+5}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$factor(\frac{\left(25x^{2}+10x+5\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}})$$

The square of \sqrt{5} is 5.

$$factor(\frac{\left(25x^{2}+10x+5\right)\sqrt{5}}{5})$$

Use the distributive property to multiply 25x^{2}+10x+5 by \sqrt{5}.

$$factor(\frac{25x^{2}\sqrt{5}+10x\sqrt{5}+5\sqrt{5}}{5})$$

Divide each term of 25x^{2}\sqrt{5}+10x\sqrt{5}+5\sqrt{5} by 5 to get x^{2}\times 5^{\frac{3}{2}}+2\sqrt{5}x+\sqrt{5}.

$$factor(x^{2}\times 5^{\frac{3}{2}}+2\sqrt{5}x+\sqrt{5})$$

Factor out \sqrt{5}. Polynomial 5x^{2}+2x+1 is not factored since it does not have any rational roots.

$$\sqrt{5}\left(5x^{2}+2x+1\right)$$

Evaluate

$$\sqrt{5}\left(5x^{2}+2x+1\right)$$