Question

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

2x2 + 5x + 3

Answer 1

the factor of polynomial
`2x^(2)+5x+3` is
`=\left(x+1\right)\left(2x+3\right)`

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)`