Question

Sari is factoring the polynomial 2x2 + 5x + 3. What is the missing number in her factorization?

Answer 1

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 $=\left(x+1\right)\left(2x+3\right)$