# How do you factor #10x^2+29x+10#?

First let's find the zeros of the polynomial by the quadratic formula:

Since

you get

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To factor the quadratic expression 10x^2 + 29x + 10, you can use the factoring by grouping method. Here's how:

- Multiply the coefficient of the x^2 term (10) by the constant term (10). This gives you 100.
- Find two numbers that multiply to give you 100 and add to give you the coefficient of the x term (29). The numbers are 5 and 20.
- Rewrite the middle term (29x) using these two numbers: 29x can be written as 5x + 20x.
- Group the terms: 10x^2 + 5x + 20x + 10.
- Factor by grouping: Group 1: 5x(2x + 1) Group 2: 10(2x + 1)
- Factor out the common factor from each group: Group 1: 5x(2x + 1) Group 2: 10(2x + 1)
- Factor out the common binomial factor (2x + 1): (2x + 1)(5x + 10)
- Simplify: (2x + 1)(5x + 10) = (2x + 1)(5)(x + 2)

Therefore, the factored form of 10x^2 + 29x + 10 is (2x + 1)(5)(x + 2).

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To factor the quadratic expression (10x^2 + 29x + 10), you need to find two binomials that multiply to give this quadratic. You can do this by breaking down the middle term (29x) into two terms that, when added or subtracted, yield (29x), and then factor by grouping or using other factoring techniques.

One way to factor this quadratic is by splitting the middle term. Here's the process:

- Multiply the leading coefficient (10) by the constant term (10). You get (10 \times 10 = 100).
- Find two numbers that multiply to give 100 and add to give the coefficient of the middle term (29). These numbers are 5 and 20.
- Rewrite the middle term (29x) as (5x + 20x).
- Now, rewrite the expression with four terms: (10x^2 + 5x + 20x + 10).
- Group the terms: ((10x^2 + 5x) + (20x + 10)).
- Factor out the greatest common factor from each group: (5x(2x + 1) + 10(2x + 1)).
- Now, you can see that both groups have a common factor of ((2x + 1)).
- Factor out ((2x + 1)): ((2x + 1)(5x + 10)).
- Finally, simplify further if possible. In this case, you can factor out 5 from the second binomial: ((2x + 1)(5(x + 2))).

So, the factored form of (10x^2 + 29x + 10) is ((2x + 1)(5x + 2)).

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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.

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.

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.

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