To decompose the polynomial
Next, we can perform synthetic division using
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Write down the coefficients:
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Bring down the leading coefficient (10):
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Multiply
by and add to the next coefficient (11): , and : -
Multiply
by and add to : , and : -
Multiply
by and add to : , and :
The result of the synthetic division is:
Next, we can factor the quadratic
Calculating the discriminant:
Now calculating the roots:
Thus, we can factor the quadratic as:
However, for simplicity, we can also write it as:
The complete factorization can be written as:
Summarizing, the factors of