# If # g(x)=x^2+3x+1 # then show that #g(x+1)-g(x) = 2x+4#?

##### 2 Answers

Mar 13, 2017

**Verification,** refer to **The Explanation Section.**

#### Explanation:

Next,

**Verification.**

Mar 13, 2017

We have;

# g(x)=x^2+3x+1 #

And so:

# g(x+1) = (x+1)^2+3(x+1)+1 #

# " " = (x^2+2x+1)+(3x+3)+1 #

# " " = x^2+5x+5 #

Therefore:

# g(x+1) -g(x) = (x^2+5x+2) - (x^2+3x+1) #

# " " = x^2+5x+5 - x^2-3x-1 #

# " " = 2x+4 \ \ \ \ \ QED #