For the given polynomial [tex]x^{3} + 3x^{2} - 7x + 2[/tex],[tex]x(-2)=20, x(-1)=11, x(0)=2, x(1)= -1, x(2)=8.[/tex]
Step-by-step explanation:
Step 1:
We substitute the values of x as -2, -1, 0, 1, and 2 in the given polynomial.
The important thing to remember is a negative number powered to an even number will result in an even number and a negative number powered to an odd number will be negative. i.e [tex]-2^{4} = 16, -2^{5} = -32.[/tex]
Step 2:
When x = -2, [tex]x^{3} + 3x^{2} - 7x + 2 = -2^{3} + 3(-2)^{2} - 7(-2) + 2 = -8+12+14+2 = 20.[/tex]
When x = -1, [tex]x^{3} + 3x^{2} - 7x + 2 = -1^{3} + 3(-1)^{2} - 7(-1) + 2 = -1+3+7+2 = 11.[/tex]
When x = 0,
[tex]x^{3} + 3x^{2} - 7x + 2 = 0^{3} + 3(0)^{2} - 7(0) + 2 = 0+0+0+2 =2.[/tex]
When x = 1,
[tex]x^{3} + 3x^{2} - 7x + 2 = 1^{3} + 3(1)^{2} - 7(1) + 2 = 1+3-7+2 = -1.[/tex]
When x = 2,
[tex]x^{3} + 3x^{2} - 7x + 2 = 2^{3} + 3(2)^{2} - 7(2) + 2 = 8+12-14+2 = 8.[/tex]
Step 3:
So for the given polynomial
[tex]x(-2)=20, x(-1)=11, x(0)=2, x(1)= -1, x(2)=8.[/tex]
