factorise x⁵+x² plz help me
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What are the factors of x2+x5x2+x5?
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21 Answers
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Jack Smith, lived in Philadelphia, PA
Answered March 26, 2021 · Author has 2K answers and 3.2M answer views
x2+x5x2+x5
x2(x3+1)x2(x3+1)
x2(x+1)(x2−x+1)x2(x+1)(x2−x+1)
Here we have a linear factor and two quadratic factors that seem to be irreducible, but are they really irreducible?
We can reduce the factor x2x2 by rewriting it as x2−0x2−0 and factor it using the difference of squares formula (a2−b2=(a−b)(a+b)a2−b2=(a−b)(a+b)): x2−0⇒(x−0–√)(x+0–√)⇒(x−0)(x+0)x2−0⇒(x−0)(x+0)⇒(x−0)(x+0)
The factor x2−x+1x2−x+1 is irreducible because we cannot complete the square. x2−x+1⇒x2−x+14+34⇒(x−12)2+34x2−x+1⇒x2−x+14+34⇒(x−12)2+34 which cannot be factored because it’s a square plus something.
x2+x5=(x−0)(x+0)(x+1)(x2−x+