Question

Find the factor of the polynomial given below.
$12x^2+16x+77$

Answer 1

Factor of polynomial -

$12x^2+16x+77$

$(\sqrt{12}x{)}^2+16x+77$

$(\sqrt{12}x{)}^2+16x+77+{\left(\frac{4}{\sqrt{3}}\right)}^2-{\left(\frac{4}{\sqrt{3}}\right)}^2$

$(\sqrt{12}x{)}^2+16x+{\left(\frac{4}{\sqrt{3}}\right)}^2+77-{\left(\frac{4}{\sqrt{3}}\right)}^2$

$={(\sqrt{12}x+\frac{4}{\sqrt{3}})}^2+77-\frac{16}{3}$

$={(\sqrt{12}x+\frac{4}{\sqrt{3}})}^2+\frac{215}{3}$

$=2\sqrt{12}b=16$

$b=\frac{8}{\sqrt{12}}=\frac{4}{\sqrt{3}}$