Question

Please Help!!!!! I'll give medals!!!!!!



Part A: Write the expression x^2-18x+45 as a product of two linear expression. Show your work and justify each step.

Part B: Rewrite x^2-6x+9 as a square of a linear expression.

Part C: Do the expression in parts A and B have a common factor? Justify your answer.

Answer 1

Part A: You just need to solve the quadratic equation. By finding the two roots of your quadratic equation, you can then write x^2-18x+45 as a(x-root1)(x-root2)-0, where a(x-root) and (x-root2) are linear expressions (general form of a linear equation is constant*x + constant, the graph of which looks like a line)

*Note: "a" comes from the general for of the quadratic equation: a*x^2 + b*x +c =0, in this case a=1.

Part B: By solving that quadratic equation you will find out that both root1 and root2 are the same. Ergo, x^2-6*x+9 can be written as a(x-root1)^2, which is the square of a linear expression.

Part C: If you mean to say whether or not those equations have the same roots, the answer is yes, they do have a common root - which you will notice after solving both equations. Because they share a root, (x-root) will be the common factor of those equations.