Solve 2x^2+y^2+2z^2+3xy+5xz+3yz

$$2 { x }^{ 2 } + { y }^{ 2 } +2 { z }^{ 2 } +3xy+5xz+3yz$$

Factor

$$\left(x+y+2z\right)\left(2x+y+z\right)$$

Solution Steps

Consider 2x^{2}+y^{2}+2z^{2}+3xy+5xz+3yz as a polynomial over variable x.

$$2x^{2}+\left(3y+5z\right)x+y^{2}+2z^{2}+3yz$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 2x^{2} and n divides the constant factor y^{2}+3yz+2z^{2}. One such factor is 2x+y+z. Factor the polynomial by dividing it by this factor.

$$\left(2x+y+z\right)\left(x+y+2z\right)$$

Evaluate

$$\left(x+y+2z\right)\left(2x+y+z\right)$$