Question

Given that P(x)=2x²+5x-5

Q(x)=4x²-3x+2,
find...i) P(½)
ii)P(3)-Q(2)
iii) P(x).Q(x)
iv)P(x)+Q(x)​

Answer 1

`(i) P((1)/(2)) = 2*((1)/(2))^2 + 5*(1)/(2) -5`

`=(1)/(2) +(5)/(2) -5\\\\=3-5 = -2`

`(ii) P(3) - Q(2) = 2(3^2)+5(3)-5 -[4(2^2) +3(2) +2]`

`= 18 + 15 -5 -16-6-2= 28-24 =4`

`(iii) P(x)\cdot Q(x) = (2x^2+5x-5)(4x^2-3x+2)`

`=2x^2(4x^-3x+2) +5x(4x^2-3x+2)-5(4x^2-3x+2)\\\\=8x^4 -14x^3 -11x^2 -10x-20x^2+15x-10\\\\=8x^4 - 14x^3 -31x^2 +5 -10`

`(iv) P(x) + Q(x) = 2x^2 +5x -5 + 4x^2 -3x +2`

`= 6x^2 +2x -3`