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