Factor x^2+3x+9/4

$x^{2} + 3 x + \frac{9}{4}$

Step 1

Rewrite $9$ as $3^{2}$ .

$x^{2} + 3 x + \frac{3^{2}}{4}$

Step 2

Rewrite $4$ as $2^{2}$ .

$x^{2} + 3 x + \frac{3^{2}}{2^{2}}$

Step 3

Rewrite $\frac{3^{2}}{2^{2}}$ as ${(\frac{3}{2})}^{2}$ .

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

Step 4

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$3 x = 2 \cdot x \cdot \frac{3}{2}$

Step 5

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot \frac{3}{2} + {(\frac{3}{2})}^{2}$

Step 6

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = \frac{3}{2}$ .

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