In the exit slip, Brady factored the expressions wrong. He needed to factor x²-10x+25 and 16c2-9. This is his work.
12 - 10x + 25 = x²-10x+52 = x²-2(x)(5)+52 =(x+5)(x-5)
16c29
(4c)2 - (3)2
= (4c-3)2
Explain Brady's mistakes. Correct Brady's work to show the correct answer.
There are several mistakes in Brady's work:
1. In the first expression x²-10x+25, Brady factored it incorrectly by incorrectly adding 52 instead of subtracting 25. The correct factorization should be x²-10x+25 = (x-5)(x-5) = (x-5)².
2. In the second expression 16c²-9, Brady tried to factor it using the difference of squares formula, but made a mistake by not subtracting 9 from 16c². The correct factorization should be 16c²-9 = (4c+3)(4c-3).
Therefore, the correct factorizations are:
1. x²-10x+25 = (x-5)²
2. 16c²-9 = (4c+3)(4c-3)
Show your work
1. x²-10x+25
We want to factor the expression x²-10x+25.
To factor a trinomial of the form x²+bx+c, where b is the coefficient of the x term and c is the constant term, we look for two numbers that multiply to c and add up to b. In this case, c=25 and b=-10.
Since -5 and -5 multiply to 25 and add up to -10, we can factor x²-10x+25 as:
(x-5)(x-5) = (x-5)²
2. 16c²-9
We want to factor the expression 16c²-9.
This is a difference of squares, a²-b² = (a+b)(a-b). In this case, a=4c and b=3.
Therefore, we can factor 16c²-9 as:
16c²-9 = (4c+3)(4c-3)