Question

If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

• A. $x^2 + 5x - 4$
• B. $(x + 3) (-x + 8)$
• C. $a(x^2 + 5x - 24)$
• D. $x^2 - 24$

Hint:

If you are unsure of the algebraic expansion, simply substitute the given zeroes into the options.
For option (B), at $x = -3$, $(x+3)(-x+8) = 0$, and at $x = 8$, $(x+3)(-x+8) = 0$.
Since both values satisfy the polynomial, it must be the correct option!

Answer 1

The Correct Option is B

Step 1: Test each option by substituting the zeroes directly, instead of expanding first.
A correct $p(x)$ must become $0$ when $x=-3$ and also when $x=8$.
Step 2: Try option (B), $(x+3)(-x+8)$.
At $x=-3$: $(0)(11) = 0$. At $x=8$: $(11)(0) = 0$. Both check out.
Step 3: Rule out the other options quickly.
Option (A) $x^2+5x-4$ gives $9-15-4=-10\neq0$ at $x=-3$. Option (D) $x^2-24$ gives $9-24=-15\neq0$ at $x=-3$. Option (C) has a stray unexplained constant $a$ with wrong sign on the middle term.
Step 4: Conclude.
Option (B) is the only one satisfying both zeroes.
\[ \boxed{p(x) = (x+3)(-x+8)} \]