p(w)=4(w)^3-3w-4; find p(-4) and p(1/4)
p( - 4 )= 4 * ( - 4 ) ^ 3 - 3 * ( - 4 ) - 4 =
4 * ( - 64 ) + 3 * 4 - 4 =
-256 + 12 - 4 = - 248
p( 1 / 4 )= 4 * ( 1 / 4 ) ^ 3 - 3 * ( 1 / 4 ) - 4 =
4 * 1 / 64 - 3 / 4 - 4 =
4 / ( 4 * 16 ) - 3 / 4 - 4 =
1 / 16 - ( 3 * 4 ) / ( 4 * 4 ) - ( 4 * 16 / 16 ) =
1 / 16 - 12 / 16 - 64 / 16 =
- 75 / 16
thank you very much
To find the values of p(-4) and p(1/4), substitute the given values into the equation p(w) = 4(w)^3 - 3w - 4 one at a time.
1. To find p(-4), replace w with -4 in the equation:
p(-4) = 4(-4)^3 - 3(-4) - 4
Simplifying the equation:
p(-4) = 4(-64) + 12 - 4
p(-4) = -256 + 12 - 4
p(-4) = -248
Therefore, p(-4) = -248.
2. To find p(1/4), replace w with 1/4 in the equation:
p(1/4) = 4(1/4)^3 - 3(1/4) - 4
Simplifying the equation:
p(1/4) = 4(1/64) - 3/4 - 4
p(1/4) = 1/16 - 3/4 - 4
p(1/4) = 1/16 - 12/16 - 4
p(1/4) = -11/16 - 4
p(1/4) = -11/16 - 64/16
p(1/4) = -75/16
Therefore, p(1/4) = -75/16.