Question

Sendo
A = x-3 / B = x-2 / C = x+1 / D = x+4
Calcule - a) BD + C  b) ABC

Answer 1

sendo

A=x-3
B=x-2
C=x+1
D=x+4

a)
BD+C=

$(x-2)(x+4)+(x+1)= \\ x^2+2x-8+x+1= \\ x^2+3x-7$

b)
ABC=

$(x-3)(x-2)(x+1)= \\ (x^2-5x+6)(x+1)= \\ x^3+x^2-5x^2-5x+6x+6= \\ x^3-4x^2+x+6$

Answer 2

a) $BD+C$

$B=x-2$

$D=x+4$

$C=x+1$

$BD+C=(x-2)(x+4)+(x+1)=x^2+4x-2x-8+x+1=x^2+3x-7$

b) $ABC$

$A=x-3$

$B=x-2$

$C=x+1$

$ABC=\underbrace{(x-3)(x-2)}_{x^2-5x+6}(x+1)=(x^2-5x+6)(x+1)=x^3+x^2-5x^2-5x+6x+6$

$ABC=x^3-4x^2+x+6$