Jacob incorrectly factored 5x^2−11x+2 using the following steps.
Step 1: 5x^2−(10x+x)+2
Step 2: (5x^2−10x)+(x−2)
Step 3: 5x(x−2)+1(x−2)
Step 4: (5x+1)(x−2)
In which step did he first make an error?
A. In Step 1 because the expression inside the parentheses needs to have a sum of −11x, not 11x
B. In Step 2 because the sign on x should be negative and the sign on 2 should be positive.
C. In Step 3 because there is no need to multiply (x−2) by 1.
D. In Step 4 because (x−2) should be written first.
7 answers
B. In Step 2 because the sign on x should be negative and the sign on 2 should be positive.
The total area, in square inches, of a picture in a picture frame is calculated by the expression of 4x^2+16x+15, where x is the width of the picture frame. Which of the following are factors of 4x^2+16x+15?
select al that apply
A. (4x+3)
B. (x+5)
C. (x+1)
D. (4x+15)
E. (2x+5)
F. (2x+3)
G. (2x+15)
H. (4x+1)
select al that apply
A. (4x+3)
B. (x+5)
C. (x+1)
D. (4x+15)
E. (2x+5)
F. (2x+3)
G. (2x+15)
H. (4x+1)
To find factors of the expression 4x^2 + 16x + 15, we can factorize the expression.
The factors will be of the form (ax + b) * (cx + d), where a, b, c, and d are integers.
Factoring 4x^2 + 16x + 15:
4x^2 + 16x + 15 = (4x + 3)(x + 5)
Therefore, the correct factors of 4x^2 + 16x + 15 are:
A. (4x+3)
B. (x+5)
The factors will be of the form (ax + b) * (cx + d), where a, b, c, and d are integers.
Factoring 4x^2 + 16x + 15:
4x^2 + 16x + 15 = (4x + 3)(x + 5)
Therefore, the correct factors of 4x^2 + 16x + 15 are:
A. (4x+3)
B. (x+5)
Jess solved the quadratic equation x^2+2x=8 but made a mistake. Her work is shown below. Identify the step(s) in which a mistake was made.
Step 1: x^2+2x−8=0
Step 2: (x−4)(x+2)=0
Step 3: x−4=0 or x+2=0
Step 4: x=−4 or x=−2
A. Step 2 Only
B. Step 3 Only
C. Step 4 Only
D. Steps 2 and 3
E. Steps 2 and 4
Step 1: x^2+2x−8=0
Step 2: (x−4)(x+2)=0
Step 3: x−4=0 or x+2=0
Step 4: x=−4 or x=−2
A. Step 2 Only
B. Step 3 Only
C. Step 4 Only
D. Steps 2 and 3
E. Steps 2 and 4
The mistake made by Jess is in Step 2. The factored form should be (x-2)(x+4) instead of (x-4)(x+2).
Therefore, the step where the mistake was made is:
A. Step 2 Only.
Therefore, the step where the mistake was made is:
A. Step 2 Only.
what about step 3 only
Step 3 is actually correct. In solving a quadratic equation when it is factored into two linear factors equal to zero, setting each factor to zero to solve for x separately is the correct method.
So in this case, the mistake was made in Step 2 only.
So in this case, the mistake was made in Step 2 only.
3 answers