Question

Given that 2 is a zero of P(x) = x^3 + x – 10

a. (x – 2)(x2 + 2x + 5)

b. (x + 2)(x2 + 2x + 5) c. (x – 2)(x2 – 2x – 5) d. cannot be factored

Answer 1

notice, to do a synthetic division, all terms have to be sorted first, and if any is missing, that simply means they have a coefficient of zero, but they're there.


`\bf P(x)=x^3+x-10\implies P(x)=x^3\underline{+0x^2}+x-10 \\\\\\ \textit{since we know that 2 is a zero, then let's use it as divisor } \begin{cases} x=2\\ x-2=0 \end{cases}\\\\ -------------------------------\\\\ \begin{array}r 2&&1&0&1&-10\\ &&&2&4&10\\ -&&-&-&-&-\\ &&1&2&5&0&\impliedby remainder \end{array} \\\\\\ \stackrel{given~zero}{(x-2)}(1x^2+2x+5)\implies (x-2)(x^2+2x+5)`