Question

Part A: Write the expression x2 + 5x + 6 as a product of two linear expressions. Show your work and justify each step. (5 points)

Part B: Rewrite x2 - 4x + 4 as a square of a linear expression. (3 points)

Part C: Do the expressions in parts A and B have a common factor? Justify your answer. (2 points)

Answer 1

help

Answer 2

what are the factors of 6 that add to 5

thats where to start

Answer 3

then you'll need the binomials..

(x + factor1)(x + factor 2)

Answer 4

part B is similar

find the factors of the constant 4, that add to -4... both factors are negative.

and you'll find the factors are identical so the factored form is

(x + factor)^2

Answer 5

Part C

look at both and decide if the is a common factor which would be in the form

(x + a)

Answer 6

The answer for Part A is (x+3)(x+2). We know that the first term for the two linear expressions has to be x since x*x=x^2. We can state (x+a)(x+b). The x-terms produced by this equation have to add up to 5x and the product of ab has to be 6. Thus a is 2 and b is 3, since ax+bx=3x+2x=5x. A and b when multiplied together equal 6. Thus the factors of x^2+5x+6 are x+3 and x+2.

Answer 7

Part b proceeds in the same manner and part c is just as campbell stated.

Answer 8

thank you