Form a ppolynomial whose real zeros and degree are given. ​Zeros: negative 2​,negative 1​,3​, 4​; ​ degree: 4

Answer 1

zeros -1, -2, 3, 4

4th degree

(x+1)(x+2)(x-3)(x-4)

= (x^2 +3x +2)(x^2 -7x +12)

= x^4 -7x^3 +12x^2 +3x^3 -21x^2 +36x +2x^2 -14x +24

= x^4 -4x^3 -7x^2 +22x +24

Answer 2

(x+2) opposite sign of -2

(x+1) opposite sign of -1

(x-3) opposite sign of 3

(x-4) opposite sign of 4

multiply these together (x+2) (x+1) (x-3) (x-4)

x⁴ - 4x³ - 7x² + 22x + 24

If you have any trouble multiplying these, do two at a time first using the FOIL method

Answer 3

If a zero is -2 then a factor of the polynomial is (x + 2). If a zero is -1 then a factor of the polynomial is (x + 1). If a zero is 3 then a factor of the polynomial is (x - 3). If a zero is 4 then a factor of the polynomial is (x - 4).

So P(x) = a(x + 2)(x + 1)(x - 3)(x - 4) where "a" is any real number meaning that there are an infinite number of possibilities. But a simple possibility would be when a = 1:

P(x) = 1(x + 2)(x + 1)(x - 3)(x - 4)

P(x) = (x + 2)(x + 1)(x - 3)(x - 4)

You can multiply it out to put the polynomial in standard form if desired:

P(x) = (x² + 3x + 2)(x² - 7x + 12)

P(x) = x⁴ - 7x³ + 12x² + 3x³ - 21x² + 36x + 2x² - 14x + 24

P(x) = x⁴ - 4x³ - 7x² + 22x + 24