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Using factorization, the expression 6x² + 14x + 4 = ?
- a)(6x + 2) (x + 2)
- b)(6x - 2) (x + 2)
- c)(6x + 2) (x - 2)
- d)(6x - 2) (x - 2)
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Using factorization, the expression 6x + 14x + 4 = ?a)(6x + 2) (x + 2)...
To factorize the expression 6x^2 + 14x + 4, we need to find two binomials that, when multiplied together, give us the original expression.
The first step is to look for common factors among the coefficients of the expression. In this case, we can see that all three coefficients (6, 14, and 4) are divisible by 2. So, we can factor out a 2 from the expression:
2(3x^2 + 7x + 2)
Next, we need to find two binomials that, when multiplied together, give us the expression inside the parentheses: 3x^2 + 7x + 2.
To do this, we need to find two numbers that multiply to give us the product of the leading coefficient (3) and the constant term (2), which is 6.
The numbers that satisfy this condition are 3 and 2. We can use these numbers to split the middle term (7x) into two terms: 3x and 2x.
So, the expression becomes:
2(3x^2 + 3x + 2x + 2)
Now, we can group the terms and factor out a common factor from each group:
2((3x^2 + 3x) + (2x + 2))
The common factor in the first group is 3x, and in the second group, it is 2:
2(3x(x + 1) + 2(x + 1))
Notice that we have now created a common binomial factor of (x + 1) in both terms. We can factor out this binomial:
2(x + 1)(3x + 2)
So, the fully factorized expression is:
2(x + 1)(3x + 2)
Therefore, the correct answer is option 'A': (6x + 2)(x + 2).
The first step is to look for common factors among the coefficients of the expression. In this case, we can see that all three coefficients (6, 14, and 4) are divisible by 2. So, we can factor out a 2 from the expression:
2(3x^2 + 7x + 2)
Next, we need to find two binomials that, when multiplied together, give us the expression inside the parentheses: 3x^2 + 7x + 2.
To do this, we need to find two numbers that multiply to give us the product of the leading coefficient (3) and the constant term (2), which is 6.
The numbers that satisfy this condition are 3 and 2. We can use these numbers to split the middle term (7x) into two terms: 3x and 2x.
So, the expression becomes:
2(3x^2 + 3x + 2x + 2)
Now, we can group the terms and factor out a common factor from each group:
2((3x^2 + 3x) + (2x + 2))
The common factor in the first group is 3x, and in the second group, it is 2:
2(3x(x + 1) + 2(x + 1))
Notice that we have now created a common binomial factor of (x + 1) in both terms. We can factor out this binomial:
2(x + 1)(3x + 2)
So, the fully factorized expression is:
2(x + 1)(3x + 2)
Therefore, the correct answer is option 'A': (6x + 2)(x + 2).
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Community Answer
Using factorization, the expression 6x + 14x + 4 = ?a)(6x + 2) (x + 2)...
6x^2+12x+2x+4
=6x(x+2) +2(x+2)
=(6x+2) (x+2)
a is the right answer
=6x(x+2) +2(x+2)
=(6x+2) (x+2)
a is the right answer
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Using factorization, the expression 6x + 14x + 4 = ?a)(6x + 2) (x + 2)b)(6x - 2) (x + 2)c)(6x + 2) (x - 2)d)(6x - 2) (x - 2)Correct answer is option 'A'. Can you explain this answer?
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