Question

bell-ringer - 5 minutes - 10 points

1. select all of the following that are solutions to $5x + 3 > 2x - 9$.

0 -4 4
-5 -1 -8

step one: $-2(x - 3) \leq x - 3$
step two: $-2x + 6 \leq x - 3$
step three: $-3x + 6 \leq -3$
step four: $-3x \leq -9$
step five: $x \leq 3$

1. between which two consecutive steps was the work done incorrectly?

between steps $\square$ and $\square$.

after this lesson i will be able to:
● factor out the gcf from a polynomial expression.

recall
find the greatest common factor of the given terms.
a 60 and 24.
b $60x^3y^2$ and $24xy^4$.

example 2
factor the expression $8x^2+4x$.
factor the expression $3x(x - 4) + 7(x - 4)$.

lets practice

1. complete each factorization:

a) $y^2 + 5y = y(\\_\\_\\_ + \\_\\_\\_)$
b) $2t^2 + 2t = 2t(\\_\\_\\_ + \\_\\_\\_)$
c) $3y^2 + 6y = \\_\\_\\_(y + 2)$
d) $-m^2 + 19m = \\_\\_\\_(m - 19)$
e) $-y^2 - 2y = \\_\\_\\_(y + 2)$
f) $8v - v^2 = v(\\_\\_\\_ - \\_\\_\\_)$
va sol algebra 1 - 6.04 factor gcf

Explanation:

Question 27

Step1: Solve the inequality

$5x + 3 > 2x - 9$
Subtract $2x$ from both sides: $5x - 2x + 3 > -9$
Simplify: $3x + 3 > -9$
Subtract 3 from both sides: $3x > -9 - 3$
Simplify: $3x > -12$
Divide by 3: $x > -4$

Step2: Test given values

• $0 > -4$: True
• $-4 > -4$: False
• $4 > -4$: True
• $-5 > -4$: False
• $-1 > -4$: True
• $-8 > -4$: False

Step1: Analyze Step 1 to 2

$-2(x-3) = -2x + 6$, so Step 2 is correct.

Step2: Analyze Step 2 to 3

Subtract $x$ from both sides: $-2x - x + 6 \leq -3$
Simplify: $-3x + 6 \leq -3$, so Step 3 is correct.

Step3: Analyze Step 3 to 4

Subtract 6 from both sides: $-3x \leq -3 - 6$
Simplify: $-3x \leq -9$, so Step 4 is correct.

Step4: Analyze Step 4 to 5

Divide by $-3$ (reverse inequality): $x \geq 3$
But Step 5 says $x \leq 3$, which is wrong.

Part a: GCF of 60 and 24

List factors:

• 60: 1,2,3,4,5,6,10,12,15,20,30,60
• 24: 1,2,3,4,6,8,12,24

Largest common factor is 12.

Part b: GCF of $60x^3y^2$ and $24xy^4$

• Numerical part: GCF(60,24)=12
• $x$ terms: GCF($x^3,x$)=$x$
• $y$ terms: GCF($y^2,y^4$)=$y^2$

Multiply together: $12xy^2$

Answer:

0, 4, -1

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Question 28