5x 7x 6 X 3
\left(x-3\right)\left(x-2\correct)\left(x^{2}+i\right)
\left(x-3\right)\left(x-2\correct)\left(ten^{2}+1\right)
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x^{4}-5x^{3}+7x^{2}-5x+half dozen=0
To factor the expression, solve the equation where it equals to 0.
±6,±3,±ii,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term vi and q divides the leading coefficient 1. Listing all candidates \frac{p}{q}.
10=2
Find ane such root by trying out all the integer values, starting from the smallest past accented value. If no integer roots are establish, endeavour out fractions.
10^{3}-3x^{two}+10-3=0
Past Cistron theorem, x-chiliad is a cistron of the polynomial for each root k. Divide x^{4}-5x^{3}+7x^{two}-5x+6 by 10-2 to get x^{3}-3x^{two}+x-three. To factor the result, solve the equation where information technology equals to 0.
±three,±1
By Rational Root Theorem, all rational roots of a polynomial are in the course \frac{p}{q}, where p divides the constant term -3 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.
10=three
Find one such root past trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, endeavor out fractions.
x^{2}+1=0
By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{3}-3x^{2}+x-iii by x-3 to get x^{2}+1. To cistron the upshot, solve the equation where information technology equals to 0.
x=\frac{0±\sqrt{0^{ii}-4\times 1\times 1}}{ii}
All equations of the class ax^{ii}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{ii}-4ac}}{2a}. Substitute 1 for a, 0 for b, and 1 for c in the quadratic formula.
ten=\frac{0±\sqrt{-4}}{2}
Exercise the calculations.
x^{2}+1
Polynomial x^{2}+1 is non factored since information technology does non have whatever rational roots.
\left(x-3\correct)\left(x-2\right)\left(x^{2}+one\correct)
Rewrite the factored expression using the obtained roots.
5x 7x 6 X 3,
Source: https://mathsolver.microsoft.com/en/solve-problem/%7B%20x%20%20%7D%5E%7B%204%20%20%7D%20%20-5%20%7B%20x%20%20%7D%5E%7B%203%20%20%7D%20%20%2B7%20%7B%20x%20%20%7D%5E%7B%202%20%20%7D%20%20-5x%2B6
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