Answer:
Step 3 is not correct (should be [tex](x-4)^2[/tex], not [tex](x+4)^2[/tex]
Step-by-step explanation:
The expression that we have to simplify is:
[tex]5x^2-40x+15[/tex]
We proceed step-by-step, in order to find the mistake did by Cedric:
1) First, we factorize the 5 outside:
[tex]5(\frac{5x^2}{5}-\frac{40x}{5}+\frac{15}{5})=5(x^2-40x+3)[/tex] --> this step is correct
2) We add +16 and -16 inside the brackets:
[tex]5(x^2-8x+16-16+3)[/tex] --> this step is correct
3) We rewrite the term [tex](x^2-8x+16)[/tex] as the square of a bynomial, which is [tex](x-4)^2[/tex], so the expression becomes
[tex]5((x-4)^2-16+3)[/tex] --> we notice that this step is wrong: in fact, Cedric wrote [tex](x+4)^2[/tex], which is not correct.
4) Now we continue: we rewrite -16+3 as -13,
[tex]5((x-4)^2-13)[/tex]
5) Finally, we multiply the 5 by the terms in the bracket:
[tex]=5(x-4)^2-65[/tex]
