Question

1) 5a⁵-30a³+15a 2) 3x²+12x-2x-8=3x²+10x-8 3) 42m²+35mn-18mn-15n²=42m²+17mn-15n² 4) x³+x²-6x+5x²=5x-30=x³+6x²-x-30

Answer 1

5a (a^4-6a^2+3) 2) (x+4) (3x-2) 3) (6m+5m) (7m-3n) 4) (x+5) (x^2+x-6)

Answer 2

Let's simplify each of the given expressions step by step:

1. 5a⁵ - 30a³ + 15a

Factor out the common factor, which is 5a: 5a(a⁴ - 6a² + 3)

Now, let's simplify the expression inside the parentheses: a⁴ - 6a² + 3 is a quadratic expression.

2. 3x² + 12x - 2x - 8

Combine like terms in the expression: (3x² + 12x) - (2x + 8)

Now, simplify each group of terms separately: 3x² + 12x can be factored out as 3x(x + 4) 2x + 8 can be factored out as 2(x + 4)

So, the simplified expression is: 3x(x + 4) - 2(x + 4)

Now, you can factor out the common factor, which is (x + 4): (x + 4)(3x - 2)

3. 42m² + 35mn - 18mn - 15n²

Combine like terms in the expression: (42m² + 35mn) - (18mn + 15n²)

Now, simplify each group of terms separately: 42m² + 35mn can be factored out as 7m(6m + 5n) 18mn + 15n² can be factored out as 3n(6m + 5n)

So, the simplified expression is: 7m(6m + 5n) - 3n(6m + 5n)

Now, you can factor out the common factor, which is (6m + 5n): (6m + 5n)(7m - 3n)

4. x³ + x² - 6x + 5x² = 5x - 30

Combine like terms on the left side of the equation: x³ + (x² + 5x²) - 6x = 5x - 30

x³ + 6x² - 6x = 5x - 30

Now, move all terms to one side of the equation: x³ + 6x² - 6x - 5x + 30 = 0

Combine like terms again: x³ + 6x² - 11x + 30 = 0

So, the simplified equation is: x³ + 6x² - 11x + 30 = 0