Question

3. Tenemos los siguientes binomios: N(x): x²-x+7; M(x): x³ + 7x +5; T(x): 5x³ + 2x² - 6x
a) M+N-T
b) T + M - N
c) 2N - 3T + M​

Answer 1

$a)( {x}^{3} + 7x + 5) + ({x}^{2} - x + 7 )- (5 {x}^{3} + 2 {x}^{2} - 6x ) = \\ {x}^{3} + 7x + 5 + {x}^{2} - x + 7 - 5 {x}^{3} - 2 {x}^{2} + 6x = \\ ( {x}^{3} - 5 {x}^{3} ) + ( {x}^{2} - 2 {x}^{2} ) +(7x - x+ 6x ) + (5 + 7) = \\ - 4 {x}^{3} + ( - {x}^{2} ) + 12x + 12 = \\ - 4 {x}^{3} - {x}^{2} + 12x + 12$

$b)(5 {x}^{3} + 2 {x}^{2} - 6x) + ( {x}^{3} + 7x + 5) - ( {x}^{2} - x + 7) = \\ 5 {x}^{3} + 2 {x}^{2} - 6x + {x}^{3} + 7x + 5 - {x}^{2} + x - 7 = \\ (5 {x}^{3} + {x}^{3} ) + (2 {x}^{2} - {x}^{2} ) + ( - 6x + 7x + x) + (5 - 7) = \\ 6 {x}^{3} + {x}^{2} + 2x + ( - 2) = \\ 6 {x}^{3} + {x}^{2} + 2x - 2$

$c)2( {x}^{2} - x + 7) - 3(5 {x}^{3} + 2 {x}^{2} - 6x) + ( {x}^{3} + 7x + 5 ) = \\ 2 {x}^{2} - 2x + 14 - 15 {x}^{3} - 6 {x}^{2} + 18x + {x}^{3} + 7x + 5 = \\ ( - 15 {x}^{3} + {x}^{3} ) + (2 {x}^{2} - 6 {x}^{2} ) + ( - 2x + 18x + 7x) +(14 + 5 ) = \\ - 14 {x}^{3} + ( - 4 {x}^{2} ) + 23x + 19 \\ - 14 {x}^{3} - 4 {x}^{2} + 23x + 19$