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What is the factored form of the quadratic expression 2x2 - 5x - 3?
- a)(2x - 3)(x + 1)
- b)(2x + 1)(x - 3)
- c)(x - 1)(2x + 3)
- d)(x + 1)(2x - 3)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
What is the factored form of the quadratic expression 2x2 - 5x - 3?a)(...
We can use the factoring method called "ac method." Multiply 'a' (2) and 'c' (-3) to get -6.
Look for two numbers that multiply to -6 and add to -5.
These numbers are -6 and 1.
Rewrite the middle term (-5x) as -6x + x.
Then factor by grouping: 2x2 - 6x + x - 3 = 2x(x - 3) + (x - 3).
Factor out the common factor (x - 3) to get (2x - 3)(x + 1).
Look for two numbers that multiply to -6 and add to -5.
These numbers are -6 and 1.
Rewrite the middle term (-5x) as -6x + x.
Then factor by grouping: 2x2 - 6x + x - 3 = 2x(x - 3) + (x - 3).
Factor out the common factor (x - 3) to get (2x - 3)(x + 1).
Community Answer
What is the factored form of the quadratic expression 2x2 - 5x - 3?a)(...
Factored Form of the Quadratic Expression 2x^2 - 5x - 3
Step 1: Find Two Numbers that Multiply to -6 and Add to -5
- The leading coefficient is 2, the constant term is -3, and the middle term coefficient is -5.
- We need to find two numbers that multiply to (2)(-3) = -6 and add up to -5.
- The two numbers are -6 and 1 because (-6)(1) = -6 and -6 + 1 = -5.
Step 2: Rewrite the Middle Term Using the Two Numbers
- Rewrite the middle term -5x as -6x + 1x.
Step 3: Factor by Grouping
- Group the first two terms and the last two terms.
- Factor out the greatest common factor from each group.
- Factor out a 2x from the first group and a -1 from the second group.
Step 4: Factor Out the Common Binomial Factor
- Factor out the common binomial factor from the two grouped terms.
- The common binomial factor is (2x - 3).
Step 5: Write the Factored Form of the Quadratic Expression
- The factored form of the quadratic expression 2x^2 - 5x - 3 is (2x - 3)(x + 1).
Therefore, the correct answer is option B which is (2x - 3)(x + 1).
Step 1: Find Two Numbers that Multiply to -6 and Add to -5
- The leading coefficient is 2, the constant term is -3, and the middle term coefficient is -5.
- We need to find two numbers that multiply to (2)(-3) = -6 and add up to -5.
- The two numbers are -6 and 1 because (-6)(1) = -6 and -6 + 1 = -5.
Step 2: Rewrite the Middle Term Using the Two Numbers
- Rewrite the middle term -5x as -6x + 1x.
Step 3: Factor by Grouping
- Group the first two terms and the last two terms.
- Factor out the greatest common factor from each group.
- Factor out a 2x from the first group and a -1 from the second group.
Step 4: Factor Out the Common Binomial Factor
- Factor out the common binomial factor from the two grouped terms.
- The common binomial factor is (2x - 3).
Step 5: Write the Factored Form of the Quadratic Expression
- The factored form of the quadratic expression 2x^2 - 5x - 3 is (2x - 3)(x + 1).
Therefore, the correct answer is option B which is (2x - 3)(x + 1).
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What is the factored form of the quadratic expression 2x2 - 5x - 3?a)(2x - 3)(x + 1)b)(2x + 1)(x - 3)c)(x - 1)(2x + 3)d)(x + 1)(2x - 3)Correct answer is option 'B'. Can you explain this answer?
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