We need two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the factored form is (x + 6)(x - 2).
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Q2. What is the factored form of the expression x^2 - 5x + 6?
Solution:
To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factored form is (x - 2)(x - 3).
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Q3. Which of the following is the correct factorization of 2x^2 + 8x?
Solution:
First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).
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Q4. Factor the expression: x^2 + 3x - 10
Solution:
We need two numbers that multiply to -10 and add to 3. The numbers 5 and -2 work. Thus, the factorization is (x + 5)(x - 2).
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Q5. Factor the polynomial 3x^2 - 12.
Solution:
First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, factor x^2 - 4 as a difference of squares: 3(x - 2)(x + 2).
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Q6. Which of the following is the factored form of 2x^2 + 8x?
Solution:
First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).
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Q7. Factor the quadratic expression x^2 + 7x + 10.
Solution:
We need two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work. Thus, the factored form is (x + 5)(x + 2).
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Q8. Factor the expression 3x^2 - 12.
Solution:
First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 3(x - 2)(x + 2).
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Q9. What is the factored form of the expression x^2 - 6x + 9?
Solution:
This is a perfect square trinomial. The factored form is (x - 3)(x - 3) or (x - 3)^2.
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Q10. Factor the expression 4x^2 - 16.
Solution:
First, factor out the greatest common factor, which is 4. This gives us 4(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 4(x - 2)(x + 2).
