Question

Given the function p(c)=c² +c: a. Evaluate p(-3). b. Solve p(c) = 2.

Answer 1

Step-by-step explanation:

a.

this is totally easy.

we need to put the given value for c (-3) into all the places of c in the functional expression and then calculate.

p(-3) = (-3)² + -3 = 9 - 3 = 6

b.

this is a bit trickier.

p(c) = 2

so,

c² + c = 2

c² + c - 2 = 0

remember, how 2 sums are multiplied with each other :

(a + b)(c + d) = ac + ad + bc + bd

to make it clearer, the functional expression suggests that a = c.

so,

(c + b)(c + d) = c² + cd + bc + bd = c² + c(d + b) + bd

when we compare this to our equation c² + c - 2 = 0, that means

d + b = 1

-2 = bd

when we think about integer numbers, what comes to mind ?

d = 2

b = -1

or vice versa. but the sequence does not matter, because we bring them together in an addition and in a multiplication, where the commutative principle is active (the sequence does not matter).

so,

c² + c - 2 = (c + 2)(c - 1)

and that must be 0.

so,

(c + 2)(c - 1) = 0

when is a product 0 ? when at least one of the factors is 0.

therefore, either

c + 2 = 0

c = -2

or

c - 1 = 0

c = 1

the solution is

c = -2

or

c = 1

Answer 2

Answer: a. p(-3) = 6 b. c = -2 , c = 1

Step-by-step explanation:

a. Evaluate p(-3):

Step 1: Plug in -3 into c

p(-3) = (-3)^2-3

Step 2: Use PEMDAS

p(-3) = 9-3

Step 3: Subtract

p(-3) = 6

b. Solve p(c) = 2:

Step 1: Set the equation equal to 2

2 = c^2+c

Step 2: Bring the 2 to the right

c^2+c-2 = 0

Step 3: Factor

(c+2)(c-1) = 0

Step 4: Use the Zero Product Property

c = -2 , c = 1