Răspuns:
Explicație pas cu pas:
a) x³+3x²-16(x+3) = x²(x+3) - 16(x+3) = (x+3)(x²-16) = (x+3)(x-4)(x+4)
c) 16(5-x)²- 9(2x+3)² = [4·(5-x)]² - [3·(2x+3)]² = (20-4x)² - (6x+9)²=
(20-4x-6x-9)(20-4x+6x+9) = (11-10x)(29+2x)
e) 9(2x+5)² - 4(4x+3)² = [3·(2x+5)]² - [2·(4x+3)]² = (6x+15)²-(8x+6)²=
= (6x+15-8x-6)(6x+15+8x+6) = (9-2x)(21+14x) = 7(2x+3)(9-2x)
g) 9(x+2)² - 4(3x-7)² = [3·(x+2)]²-[2·(3x-7)]² = (3x+6)²-(6x-14)²=
= (3x+6-6x+14)·(3x+6+6x-14) = (20-3x)(9x-8)
i) (3x²-2x+5)² - (x²+2x+2)² = (3x²-2x+5-x²-2x-2)(3x²-2x+5+x²+2x+2) =
= (2x²-4x+3)(4x²+7)
k) 36x² - (x²-2x+3)² = (6x)² - (x²-2x+3)² =
= (6x-x²+2x-3)(6x+x²-2x+3) = (-x²+8x-3)(x²+4x+3)
