SOLUTIONS
For the polynomial P(x) = 4x^2 + 7x + 8 and c = 1
[tex]P(x)=4x^2+7x+8[/tex]
where c = 1
(a) By direct substitution
[tex]\begin{gathered} P(c)=P(1) \\ P(x)=4x^2+7x+8 \\ P(1)=4(1)^2+7(1)+8=4+7+8=19 \\ P(1)=19 \end{gathered}[/tex]
(b) The Remainder Theorem states that when we divide a polynomial
P(x) by x - c the remainder R equals P(c)
[tex]4x^2+7x+8\div x-1[/tex]
From the remainder theorem , the remainder = 19
