To factor the given quadratic expression \(20x^2 + 22x - 12\), let's check for the correct factorization step by step.
Given: \(20x^2 + 22x - 12\)
Let's try factoring by grouping or using a method that fits.
### Step 1: Simplify by factoring out the greatest common factor (if any)
We notice there is no common factor among the coefficients 20, 22, and -12 other than 1, so we leave it as is.
### Step 2: Look for two numbers that multiply to \(a \times c\) and add to \(b\)
For the quadratic \(ax^2 + bx + c\):
- \(a = 20\)
- \(b = 22\)
- \(c = -12\)
We need numbers that multiply to \(20 \times -12 = -240\) and add to 22.
### Step 3: Find the right pair
After checking various pairs, we find that 30 and -8 work:
- \(30 \times (-8) = -240\)
- \(30 + (-8) = 22\)
### Step 4: Rewrite and factor by grouping
Now rewrite the middle term:
\[ 20x^2 + 30x - 8x - 12 \]
Group the terms:
\[ (20x^2 + 30x) + (-8x - 12) \]
Factor each group:
\[ 10x(2x + 3) - 4(2x + 3) \]
Factor out the common binomial \((2x + 3)\):
\[ (10x - 4)(2x + 3) \]
### Step 5: Simplify (if needed)
Notice that \(10x - 4\) can be further factored:
\[ (10x - 4) = 2(5x - 2) \]
So, the final factorization is:
\[ 2(5x - 2)(2x + 3) \]
### Conclusion
The correct factorization of \(20x^2 + 22x - 12\) is \(2(5x - 2)(2x + 3)\).
### Check the provided options:
A. \(2(5x + 4)(2x – 3)\)
B. \((10x – 2)(4x + 3)\)
C. \(2(5x – 2)(2x + 3)\)
D. \(2(5x + 2)(2x – 3)\)
The correct choice is:
**C. \(2(5x – 2)(2x + 3)\)**
5.
Factor the expression.
20x2 + 22x − 12
2(5x + 4)(2x – 3)
(10x – 2)(4x + 3)
2(5x – 2)(2x + 3)
2(5x + 2)(2x – 3)
1 answer
1 answer