Given: y = -(x-1)(x^2+6)(x+5)^2y=−(x−1)(x2+6)(x+5)2
Standard form of a polynomial requires distribution and putting terms in descending order:
Note: (a +b)^2 = (a^2 + 2ab + b^2)(a+b)2=(a2+2ab+b2)
y = -(x-1)(x^2+6)(x+5)^2 y=−(x−1)(x2+6)(x+5)2
= -(x-1)(x^2+6)(x^2+10x+25)=−(x−1)(x2+6)(x2+10x+25)
y = -(x-1)(x^4 +10x^3 +25x^2 + 6x^2 +60x + 150)y=−(x−1)(x4+10x3+25x2+6x2+60x+150)
Add like terms:
y = -(x-1)(x^4 + 10x^3 + 31x^2+60x + 150)y=−(x−1)(x4+10x3+31x2+60x+150)
Distribute again:
y = -(x^5+ 10x^4 + 31x^3+60x^2 + 150x -x^4-10x^3-31x^2-60x-150)y=−(x5+10x4+31x3+60x2+150x−x4−10x3−31x2−60x−150)
Add/Subtract like terms:
y = -(x^5 + 9x^4 + 21x^3 + 29x^2 + 90x - 150)y=−(x5+9x4+21x3+29x2+90x−150)
Distribute the negative sign:
y = -x^5 - 9x^4 -21x^3 -29x^2 - 90x + 150y=−x5−9x4−21x3−29x2−90x+150
