Rozłóż wielomian w na czynniki liniowe (jak w przykładzie):a) b) c).... Question from @matrod101

September 2018 2 53 Report

Rozłóż wielomian w na czynniki liniowe (jak w przykładzie):

$w(x)=x^{4}-8x^{2}+16=(x^{2}-4)^{2}=[(x-2)(x+2)]^{2}=(x-2)^{2}(x+2)^{2}$

a) $w(x)=x^{4}-18x^{2}+81$

b) $w(x)=32x^{4}-16x^{2}+2$

c) $w(x)=x^{5}-6x^{3}+9x$

sylwek9369

a) W(x)=x⁴ - 18x² + 81 = (x²-9)² = [(x-3)(x+3)]² = (x-3)²(x+3)²

b) W(x)=32x⁴ - 16x² +2 = 32x⁴ - 8x² -8x² +2 = 8x²(4x²-1)-2(4x²-1) = (8x²-2)(4x²-1) = (√8x-√2)(√8x+√2)(2x-1)(2x+1)

c)W(x)=x⁵ - 6x³ + 9x = x(x⁴-6x²+9)=x(x²-3)²=x(x-√3)²(x+√3)²

3 votes Thanks 2

Ines93

a) = (x² - 9)² = [(x - 3)(x + 3)]² = (x - 3)²(x + 2)²

b) = $2(4x^{2} - 1)^{2}$ = $2[(2x - 1)(2x + 1)]^{2} = 2(2x - 1)^{2}(2x + 1)^{2}$

c) $= x(x^{4} - 6x^{2} + 9) = x(x^{2} - 3)^{2} = x[(x - \sqrt{3})(x + \sqrt{3})]^{2} = x(x - \sqrt{3})^{2}(x + \sqrt{3})^{2}$

1 votes Thanks 1

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