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Using factorization, the expression 4x² + 14x + 10 = ?
- a)(2x + 2) (2x + 5)
- b)(2x - 2)(2x - 5)
- c)(x + 2)
- d)(x - 5)
Correct answer is option 'A'. Can you explain this answer?
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Using factorization, the expression 4x + 14x + 10 = ?a)(2x + 2) (2x + ...
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Using factorization, the expression 4x + 14x + 10 = ?a)(2x + 2) (2x + ...
Factorizing 4x^2 + 14x + 10
To factorize the expression 4x^2 + 14x + 10, we need to find two binomials that when multiplied together, will give us the original expression.
Step 1: Look for the common factors
In this case, there are no common factors among the coefficients.
Step 2: Multiply the coefficient of x^2 and the constant term
The coefficient of x^2 is 4 and the constant term is 10. Multiplying them together, we get 4 * 10 = 40.
Step 3: Find two numbers that multiply to give the product obtained in step 2 and add up to the coefficient of x
In this case, we need to find two numbers that multiply to give 40 and add up to 14 (the coefficient of x). The numbers that satisfy this condition are 4 and 10.
Step 4: Rewrite the expression using the two numbers obtained in step 3
We can rewrite the expression 4x^2 + 14x + 10 as:
4x^2 + 4x + 10x + 10
Step 5: Group the terms and factor by grouping
Now, we group the terms:
(4x^2 + 4x) + (10x + 10)
Next, we factor out the common terms from each group:
4x(x + 1) + 10(x + 1)
Step 6: Factor out the common binomial
We notice that we have a common binomial (x + 1) in both terms. So, we can factor it out:
(x + 1)(4x + 10)
Step 7: Simplify the expression
To simplify the expression, we can further factor out the common factor of 2 from each term:
(x + 1)(2x + 5)
Therefore, the factorization of 4x^2 + 14x + 10 is (x + 1)(2x + 5).
Comparing the factorization with the given options, we can see that the correct answer is option A: (2x + 2)(2x + 5).
To factorize the expression 4x^2 + 14x + 10, we need to find two binomials that when multiplied together, will give us the original expression.
Step 1: Look for the common factors
In this case, there are no common factors among the coefficients.
Step 2: Multiply the coefficient of x^2 and the constant term
The coefficient of x^2 is 4 and the constant term is 10. Multiplying them together, we get 4 * 10 = 40.
Step 3: Find two numbers that multiply to give the product obtained in step 2 and add up to the coefficient of x
In this case, we need to find two numbers that multiply to give 40 and add up to 14 (the coefficient of x). The numbers that satisfy this condition are 4 and 10.
Step 4: Rewrite the expression using the two numbers obtained in step 3
We can rewrite the expression 4x^2 + 14x + 10 as:
4x^2 + 4x + 10x + 10
Step 5: Group the terms and factor by grouping
Now, we group the terms:
(4x^2 + 4x) + (10x + 10)
Next, we factor out the common terms from each group:
4x(x + 1) + 10(x + 1)
Step 6: Factor out the common binomial
We notice that we have a common binomial (x + 1) in both terms. So, we can factor it out:
(x + 1)(4x + 10)
Step 7: Simplify the expression
To simplify the expression, we can further factor out the common factor of 2 from each term:
(x + 1)(2x + 5)
Therefore, the factorization of 4x^2 + 14x + 10 is (x + 1)(2x + 5).
Comparing the factorization with the given options, we can see that the correct answer is option A: (2x + 2)(2x + 5).
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Using factorization, the expression 4x + 14x + 10 = ?a)(2x + 2) (2x + 5)b)(2x - 2)(2x - 5)c)(x + 2)d)(x -5)Correct answer is option 'A'. Can you explain this answer?
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