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olga2289 [7]
3 years ago
13

How to Factor 3x^2-x-10

Mathematics
1 answer:
adoni [48]3 years ago
5 0

Solution

( − 2)(3 + 5)

Step-by-step solution:

Use the sum-product pattern

3x^2−−10

3^2+5−6x−10

Common factor from the two pairs

3^2+5−6−10

(3+5)−2(3+5)

Rewrite in factored form

(3+5)−2(3+5)

(−2)(3+5

hope this was good! <3

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Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?
QveST [7]
<span>I note that this problem starts out with "Which is a factor of ... "  This implies that you were given several answer choices.  If that's the case, it's unfortunate that you haven't shared them.

I thought I'd try finding roots of this function using synthetic division.  See below:

f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
Please use " ^ " to denote exponentiation.  Thanks.

Possible zeros of this poly are factors of 35:  plus or minus 1, plus or minus 5, plus or minus 7.  Use synthetic division; determine whether or not there is a non-zero remainder in each case.  If none of these work, form rational divisors from 35 and 6 and try them:  5/6, 7/6, 1/6, etc.

Provided that you have copied down the function 
</span>f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35  properly, this approach will eventually turn up 1 or 2 zeros of this poly.  Obviously it'd be much easier if you'd check out the possible answers given you with this problem.

By graphing this function, I found that the graph crosses the x-axis at 7/2.  There is another root.

Using synth. div. to check whether or not 7/2 is a root:

         ___________________________
7/2   /   6    -21    -4    24    -35
                   21      0   -14     35           
        ----------- ------------------------------
           6        0     -4    10       0

Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial.  Thus, (x-3.5), or (x-7/2), is a factor.

7 0
2 years ago
Read 2 more answers
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