Question: 17. $y^2 + 7y + 12$ 18. $x^2 - 15x + 14$ 19. $u^2 + 11u + 18$ 20. $r^2 + 9r + 20$ 21. $x^2 - 12x +…

17. $y^2 + 7y + 12$
18. $x^2 - 15x + 14$
19. $u^2 + 11u + 18$
20. $r^2 + 9r + 20$
21. $x^2 - 12x + 20$
22. $x^2 - 14x + 24$
23. $y^2 + 25y + 24$
24. $x^2 + 11x + 28$
25. $n^2 - 17n + 30$

Written Exercises

Factor. Check by multiplying the factors. If the polynomial is not factorable, write prime.

1. $x^2 + 5x + 4$
2. $z^2 + 9z + 8$
3. $r^2 - 6r + 8$

Solution

The image contains a series of algebraic problems asking to factor polynomials. Below, I will factor problem 1 as requested: 1. \( x^2 + 5x + 4 \) First, identify two numbers that multiply to 4 (the constant term) and add to 5 (the coefficient of the linear term). The numbers 1 and 4 satisfy these conditions because: \[ 1 \cdot 4 = 4 \] \[ 1 + 4 = 5 \] Therefore, the factors of the polynomial \( x^2 + 5x + 4 \) are: \[ (x + 1)(x + 4) \] To verify, expand the factors: \[ (x + 1)(x + 4) = x^2 + 4x + 1x + 4 = x^2 + 5x + 4 \] Thus, the polynomial is factored correctly as \( (x + 1)(x + 4) \).