Answer:
the factor of polynomial [tex]2x^{2}+5x+3[/tex] is [tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Step-by-step explanation:
We need to factor the polynomial [tex]2x^{2}+5x+3[/tex]
Break the expression into groups,
[tex]=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c[/tex]
[tex]x^2=xx[/tex]
then
[tex]2x^2+2x=2xx+2x[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}2x[/tex]
[tex]=2x\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
[tex]=2x\left(x+1\right)+3\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
[tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Hence, the factor of polynomial [tex]2x^{2}+5x+3[/tex] is [tex]=\left(x+1\right)\left(2x+3\right)[/tex]
