Question

AJUTOR ACUM OFER MAX PUNCTE PT ASTEA 2 EX ACUMMMM!!!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

5)

a) 4x³-x²-36x+9 = x²(4x-1)-9(4x-1) = (4x-1)(x²-1) = (4x-1)(x-1)(x+1)

b) ax²-bx²-ay²+by² = x²(a-b)-y²(a-b) = (a-b)(x²-y²) = (a-b)(x-y)(x+y)

c) (3x+1)³-12x-4 = (3x+1)(3x+1)²-4(3x+1) = (3x+1)(9x²+6x+1-4) =

= (3x+1)(9x²+6x-3) = (3x+1)·3·(3x²+2x-1) = 3(3x+1)(3x²+3x-x-1) =

= 3(3x+1)[3x(x+1)-(x+1)] = 3(3x+1)·(x+1)(3x-1)

d) x²+14x+49-11x-77 = (x+7)²-11(x+7) = (x+7)(x+7-11) = (x+7)(x-4)

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6)

a) 4x²-y²-4x+1 =  4x²-4x+1 -y² = (2x-1)²-y² = (2x-1-y)(2x-1+y)

b) x²+2x+1 - x⁴ = (x+1)² - (x²)² = (x+1-x²)(x+1+x²) = (x²+x+1)(-x²+x+1)

c) 4x⁴-4x²-4x-1 = 4x⁴- (2x+1)² = (2x²)²- (2x+1)² =

= (2x²-2x-1)(2x²+2x+1)

d) x⁴+3x²-4 = x⁴+4x²-x²-4 = x²(x²+4)-(x²+4) =

= (x²+4)(x²-1) = (x²+4)(x-1)(x+1)

x⁴+3x²+4 = nu se poate descompune in R