To expand the polynomial f(x) = (x-3)(x + 2)(x + 3), one common strategy is to use the distributive property of multiplication over addition. This involves multiplying each of the terms in the first binomial (x - 3) with each of the terms in the second binomial (x + 2), and then multiplying the product of these two binomials with the third binomial (x + 3). For example, we can expand the first two binomials and then multiply that expression by the third binomial:
(x - 3)(x + 2) = x^2 + 2x - 3x - 6 = x^2 - x - 6
(x^2 - x - 6)(x + 3) = x^3 + (3 - x)x^2 + (3x - 6)x - 18
So, the expanded form of the polynomial f(x) = (x-3)(x + 2)(x + 3) is x^3 + (3 - x)x^2 + (3x - 6)x - 18.
To expand the polynomial g(x) = 8(x-3)(x + 2)(x + 3)(x-2), the strategy is similar to the one for expanding f(x). However, in this case, we need to first multiply 8 with each of the four binomials in the expression. After that, we can expand the expression using the distributive property of multiplication over addition. For example,
8(x - 3)(x + 2) = 8x^2 + 16x - 24x - 72 = 8x^2 - 8x - 72
(8x^2 - 8x - 72)(x + 3)(x - 2) = 8x^5 + (3x^4 - 10x^3 + x^2 - 20x + 144)x^3 - (72x^2 + 216x - 432)x
So, the expanded form of the polynomial g(x) = 8(x-3)(x + 2)(x + 3)(x-2) is 8x^5 + (3x^4 - 10x^3 + x^2 - 20x + 144)x^3 - (72x^2 + 216x - 432).
The degree of the polynomial f(x) = (x-3)(x + 2)(x + 3) is 3, as the highest degree of the terms in the expanded form is x^3. The degree of the polynomial g(x) = 8(x-3)(x + 2)(x + 3)(x-2) is 5, as the highest degree of the terms in the expanded form is x^5.
The degree of a polynomial expanded from five linear factors would be 5. This is because the degree of a polynomial is equal to the highest degree of the terms in the expanded form, and expanding a polynomial from n linear factors would result in a polynomial with a degree of n