Write a polynomial of least degree with roots 3 and – 4. Write your answer using the variable x and in standard form with a leading coefficient of 1.

Answer 1

(x-3)(x+4) = x^2 + x -12

is a polynomial of least degree with roots or zeros 3 and -4

(3)^2 +3 -12 = 9+3-12 = 12-12 = 0

(-4)^2 -4 -12 = 16-4-12 = 12-12 = 0

Just take each zero, change its sign, then stick an x in front of it to get the factors. Then multiply the factors together. Use the FOIL method

(x-3)(x+4) = x^2 +4x -3x -12 = x^2 +x -12

If you graph this polynomial f(x) = y = x^2 +x -12, it's an upward opening parabola with x intercepts 3 and -4 or the points (3,0), (-4,0) That's where the parabola intersects the x axis.