Answer:
* The degree of the function is 4 and the leading coefficient is positive
f(x) = (x + 6)(2x - 3)(x - 1)²
* The degree of the function is 5 and the leading coefficient is negative
f(x) = (x - 2)²(-2x - 1)²(-x + 1)
* The degree of the function is 6 and the leading coefficient is negative
f(x) = (-x + 1)³(x + 2)²(x - 3)
* The degree of the function is 5 and the leading coefficient is positive
f(x) = (-2x + 1)²(x - 3)²(x + 1)
Explanation:
∵ f(x) = (x + 6)(2x - 3)(x - 1)²
∵ (x)(2x)(x²) = 2x^4
∴ The degree of the function is 4
∴ The leading coefficient is positive ⇒ (2)
∵ f(x) = (x - 2)²(-2x - 1)²(-x + 1)
∵ (x)²(-2x)²(-x) = (x²)(4x²)(-x) = -4x^5 ⇒ (neglect -ve with even power)
∴ The degree of the function is 5
∴ The leading coefficient is negative ⇒ (-4)
∵ f(x) = (-x + 1)³(x + 2)²(x - 3)
∵ (-x)³(x)²(x) = (-x³)(x²)(x) = -x^6
∴ The degree of the function is 6
∴ The leading coefficient is negative ⇒ (-1)
∵ f(x) = (-2x + 1)²(x - 3)²(x + 1)
∵ (-2x)²(x)²(x) = (4x²)(x²)(x) = 4x^5
∴ The degree of the function is 5
∴ The leading coefficient is positive ⇒ (4)