If g(x)=2x2−3x+2, find g(4+c).

Answer 1

g(x)=2x² - 3x + 2

if x =4+c, we simply substitute (4+c) for x in the function, g(x).

g(4+c) = 2(4+c)²-3(4+c)+2

g(4+c) will, in this case, turn out to be a polynomial in c.

Looking at the first term of the right side of the equation, we have 2(4+c)².

We start by expanding (4+c)² either by simply multiplying (4+c) by (4+c) OR

using the binomial formula

(a+b)²=a²+2ab+b²

so

(4+c)²=4²+2*4*c+c²=16+8c+c²

and

2(4+c)²=2(16+8c+c²)=2*16+2*8c+2c²=32+16c+2c²

which we can rewrite as

2(4+c)²=2c²+16c+32

Looking at the second term, -3(4+c)

-3(4+c)=-12-3c

which we can rewrite as

-3(4+c)=-3c-12

Looking back to our original expression for g(4+c)

g(4+c) = 2(4+c)²-3(4+c)+2

we rewrite the terms in their expanded form.

g(4+c) = 2c²+16c+32 -3c-12 + 2

and we rewrite the equation further by consolidating the coefficients of c and c².

g(4+c) = 2c²+(16-3)c+(32-12 + 2)= 2c²+13c+22