How do you factor completely: #10x^2 − 7x − 3#?

Answer 1

Factor: #y = 10x^2 - 7x - 3#

y = (x - 1)(10x + 3)

Since (a + b + c) = 0, use the shortcut. One factor is (x - 1) and the other is (-c/a = 3/10). #y = 10(x - 1)(x + 3/10) = (x - 1)(10x + 3)#

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Answer 2

Hazel Anglin

To factor completely, you can use the quadratic formula or factoring by grouping. For 10x^2 - 7x - 3, factoring by grouping would be more efficient. First, multiply the leading coefficient (10) by the constant term (-3), resulting in -30. Then, find two numbers that multiply to -30 and add up to the middle coefficient (-7). The numbers are -10 and 3. Rewrite the middle term using these numbers: -10x + 3x. Now, factor by grouping: 10x^2 - 10x + 3x - 3. Group the terms: (10x^2 - 10x) + (3x - 3). Factor out the greatest common factor from each group: 10x(x - 1) + 3(x - 1). Notice that (x - 1) is a common factor, so factor it out: (10x + 3)(x - 1). So, the factored form of 10x^2 - 7x - 3 is (10x + 3)(x - 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.