Answer:
(x +3)(1 -10x²) or (1 -x√10)(1 +x√10)(x +3)
Explanation:
You want to factor the expression -10x²(x+3)+(x+3).
Common factor
The factor (x+3) can be brought out to give ...
(-10x² +1)(x +3) . . . . integer factors
This is the factored form of the expression.
Difference of squares
The first factor is not factorable using integers, which is what we usually want to use for factoring. If we allow irrational factors, then we can go one step farther:
= (1 -x√10)(1 +x√10)(x +3) . . . . linear factors
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Additional comment
The difference of squares factors as (a² -b²) = (a -b)(a +b).
We like to avoid leading minus signs, so we have written the x² factor as (1 -10x²), rather than (-10x² +1). This tends to prevent minus signs getting lost when expressions are copied.
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