4.1 (Function Operations)
Calculate (f + g)(x) given the following:
f(x)=x^2+3
g(x)=-2x-4)
(f+g)(x)=x^2-2x-1
(−3y + y^2 − 8 + 5y^3 ) + ( 7 y^2 + 4y − 2y^3 )
3y^3+8y^2+y-8
(x+1)(x+2)
x^2+3x+2
x^2+2x-15
(x+5)(x-3)
How can you tell if a binomial in (x - a) form is a factor of a polynomial using synthetic division?
If you use synthetic division and have a remainder of zero.
Calculate (g - f)(x) given the following:
f(x)=x^2+3
g(x)=-2x-4)
(g-f)(x)=-x^2-2x-7
(3.2w^2 − 4.1w + 1) + ( 9.3 + 7.4w^2 )
10.6w^2-4.1w+10.3
(y + 4)(y^2 − 1)
y^3+4y^2-y-4
6x^3 + 9x^2 + 3x
3x(2x+1)(x+1)
Use division to determine if (x - 4) is a factor of the following (if it is not a factor, what is the remainder, if it is a factor, what is the quotient)
2x^3+3x^2-5x+8
It is NOT a factor. The remainder is 164.
Calculate (f * g)(x) given the following:
f(x)=x^2+3
g(x)=-2x-4
-2x^3-4x^2-6x-12
(−3t^4 + 6t^2 + 3t) − ( − t^2 − 8t^4 + t)
5t^4+7t^2+2t
(3x^2+2x)(3x^2-2x)
9x^4-4x^2
8x^3 + 125
(2x+5)(4x^2-10x+25)
Given (x - 3) is a factor of the following, find the remaining factors using synthetic division (write final answer out in factored form):
x^3+7x^2-6x-72
(x-3)(x+6)(x+4)
Calculate
(f/g)(x)
given the following:
f(x)=x^2+3
g(x)=-2x-4
(f/g)(x)=(x^2+3)/(-2x-4)
(8.1p^2 − 2.4p − 3) − (0.5p − 7.1p^2 )
15.2p^2-2.9p-3
(c^2 + 6 − c)(3c^2 + c − 1)
3c^4-2c^3+16c^2+7c-6
2x^3+10x^2-x-5
(x+5)(2x^2-1)
Given (x + 5) is a factor of the following, find the remaining factors using synthetic division (write final answer out in factored form):
x^4+6x^3+6x^2+6x+5
(x+5)(x+1)(x^2+1)