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kolezko [41]
3 years ago
11

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

Mathematics
1 answer:
babymother [125]3 years ago
3 0

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)

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