factorise 8x⁶ + 5x³ + 1
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Answered by
0
Answer:
Adding and subtracting x^3
=x^6 +5x^3 +8+x^3 −x^3
=x^6 +6x^3 +8−x^3
=(x^2)^3 +(2)^3 +(−x)^3−3(x^2)(2)(−x)
According to the identity
[x^3 +y^3 +z^3 −3xyz=(x+y+z)(x^2 +y^2 +z^2 −xy−yz−zx)]
=(x^2+2−x)[(x^2)^2 +(2)^2 +(−x)^2 −(x^2 )(2)−(2)(−x)−(x^2 )(−x)]
=(x^2 −x+2)(x^4 +x^2 +4−2x^2+2x+x^3 )
= (x ^2 −x+2)(x^4 +x^3−x^2+2x+4)
Thus, factors of x^6+5x^3 +8 are
(x ^2 −x+2)(x^4 +x^3−x^2+2x+4)
Answered by
1
Answer:
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2
2
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1
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4
4
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2
3
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2
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1
)
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