Question

Find the value of the polynomial x² + 2x + 5 when,

(i) x = 0
(ii) x = 3
(iii) x = $-$ 1
(iv) x = $-$ 3
(v) x = a

Answer 1

Let p(x) = x² + 2x + 5

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{To}\mathrm{finding}\mathrm{the}\mathrm{value}\mathrm{of}p\left(x\right)\mathrm{when}x=0,\mathrm{put}x=0\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \\ p\left(x\right)=x^2+2x+5 \\ \Rightarrow p\left(0\right)=0^2+2\times 0+5 \\ =5 \\ \Rightarrow p\left(0\right)=5 \\ \therefore \mathrm{The}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{polynomial}\mathrm{is}5\mathrm{when}x=0 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)\mathrm{To}\mathrm{finding}\mathrm{the}\mathrm{value}\mathrm{of}p\left(x\right)\mathrm{when}x=3,\mathrm{put}x=3\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \\ p\left(x\right)=x^2+2x+5 \\ \Rightarrow p\left(3\right)=3^2+2\times 3+5 \\ =9+6+5 \\ =20 \\ \Rightarrow p\left(3\right)=20 \\ \therefore \mathrm{The}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{polynomial}\mathrm{is}20\mathrm{when}x=3 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}p\left(x\right)\mathrm{when}x=-1,\mathrm{put}x=-1\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \\ p\left(x\right)=x^2+2x+5 \\ \Rightarrow p\left(-1\right)={\left(-1\right)}^2+2\times \left(-1\right)+5 \\ =1-2+5 \\ =4 \\ \Rightarrow p\left(-1\right)=4 \\ \therefore \mathrm{The}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{polynomial}\mathrm{is}4\mathrm{when}x=-1 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}p\left(x\right)\mathrm{when}x=-3,\mathrm{put}x=-3\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \\ p\left(x\right)=x^2+2x+5 \\ \Rightarrow p\left(-3\right)={\left(-3\right)}^2+2\times \left(-3\right)+5 \\ =9-6+5 \\ =8 \\ \Rightarrow p\left(-3\right)=8 \\ \therefore \mathrm{The}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{polynomial}\mathrm{is}8\mathrm{when}x=-3 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{v}\right)\mathrm{To}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}p\left(x\right)\mathrm{when}x=a,\mathrm{put}x=a\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{polynomial}. \\ p\left(x\right)=x^2+2x+5 \\ \Rightarrow p\left(a\right)=a^2+2\times a+5 \\ =a^2+2a+5 \\ \Rightarrow p\left(a\right)=a^2+2a+5 \\ \therefore \mathrm{The}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{polynomial}\mathrm{is}{a}^2+2a+5\mathrm{when}x=a \end{gathered}$$