Answer:
a) The factors of x² + 3·x are x and (x + 3)
x² + 3·x = x·(x + 3)
b) The factors of 2·x² - 8·x are 2, x and (x - 4)
2·x² - 8·x = 2·x·(x - 4)
c) The factors of 6·x + 9·x³ are 3, x and (2 + 3·x²)
6·x + 9·x³ = 3·x·(2 + 3·x²)
d) The factors of 12·x³ - 4·x² are 4, x², and (3·x - 1)
12·x³ - 4·x² = 4·x²·(3·x - 1)
Explanation:
The question relates to resolving a polynomial into its factors;
a) For the polynomial (quadratic) equation, x² + 3·x, we have;
x² + 3·x = x·(x + 3)
Therefore, x² + 3·x in factorized form is x·(x + 3)
b) For the polynomial (quadratic) equation, 2·x² - 8·x, we have;
2·x² - 8·x = 2·x·(x - 4)
Therefore, 2·x² - 8·x in factorized form is 2·x·(x - 4)
c) For the polynomial (cubic) equation, 6·x + 9·x³, we have;
6·x + 9·x³ = 3·x × (2 + 3·x²)
Therefore, 6·x + 9·x³ in factorized form is 3·x·(2 + 3·x²)
d) For the polynomial (cubic) equation, 12·x³ - 4·x², we have;
12·x³ - 4·x² = 4·x²·(3·x - 1)
Therefore, 12·x³ - 4·x² in factorized form is 4·x²·(3·x - 1).