Which of the following is the correct factorization of this trinomial?4x2 - 0x - 25A.(4x - 1)(x + 25)B.(4x - 5)(x + 5)C.(2x - 1)(2x + 25)D.(2x - 5)(2x + 5)SUBMITarrow_backPREVIOUS
Question
Which of the following is the correct factorization of this trinomial?4x2 - 0x - 25A.(4x - 1)(x + 25)B.(4x - 5)(x + 5)C.(2x - 1)(2x + 25)D.(2x - 5)(2x + 5)SUBMITarrow_backPREVIOUS
Solution
The correct factorization of the trinomial 4x^2 - 0x - 25 is (2x - 5)(2x + 5). So, the correct answer is D. (2x - 5)(2x + 5).
Here's the step-by-step process:
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The trinomial is in the form ax^2 + bx + c. In this case, a = 4, b = 0, and c = -25.
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We need to find two numbers that multiply to a*c (which is -100) and add up to b (which is 0). The numbers that satisfy this are -10 and 10.
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Rewrite the middle term (0x) of the trinomial as -10x + 10x.
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Factor by grouping: 4x^2 - 10x + 10x - 25 = 2x(2x - 5) + 5(2x - 5)
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Since the terms in the parentheses are the same, we can factor them out to get the final answer: (2x - 5)(2x + 5).
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