Answer:
1. (4x - 3)(x + 6).
2. (2x + 5)(x - 9).
3. (3x - 2)(x + 8).
Explanation:
To factor 4x^2 + 21x - 18, we can start by looking for two numbers whose product is -72 (the product of the leading coefficient 4 and the constant term -18) and whose sum is 21 (the coefficient of x). It's easy to see that these numbers are 24 and -3:
4x^2 + 21x - 18 = 4x^2 + 24x - 3x - 18
= 4x(x + 6) - 3(x + 6)
= (4x - 3)(x + 6)
Therefore, the factored form of the polynomial is (4x - 3)(x + 6).
To factor 2x^2 - 13x - 45, we can again look for two numbers whose product is -90 (the product of the leading coefficient 2 and the constant term -45) and whose sum is -13 (the coefficient of x). These numbers are -18 and 5:
2x^2 - 13x - 45 = 2x^2 - 18x + 5x - 45
= 2x(x - 9) + 5(x - 9)
= (2x + 5)(x - 9)
Therefore, the factored form of the polynomial is (2x + 5)(x - 9).
To factor 3x^2 + 22x - 16, we can use the same method as before, but this time we need to look for two numbers whose product is -48 (the product of the leading coefficient 3 and the constant term -16) and whose sum is 22 (the coefficient of x). These numbers are 24 and -2:
3x^2 + 22x - 16 = 3x^2 + 24x - 2x - 16
= 3x(x + 8) - 2(x + 8)
= (3x - 2)(x + 8)
Therefore, the factored form of the polynomial is (3x - 2)(x + 8).