Factor, if possible. Show your complete working. a. x2 + 7x + 10b. j2 + 12j + 27c. m2 − 7m + 10d. x2 − 5x + 7

Sure, here are the solutions:

a. x² + 7x + 10 This can be factored into (x + 2)(x + 5). Here's how: We're looking for two numbers that multiply to 10 and add to 7. Those numbers are 2 and 5. So, we write: x² + 2x + 5x + 10 = x(x + 2) + 5(x + 2) = (x + 2)(x + 5)

b. j² + 12j + 27 This can be factored into (j + 3)(j + 9). Here's how: We're looking for two numbers that multiply to 27 and add to 12. Those numbers are 3 and 9. So, we write: j² + 3j + 9j + 27 = j(j + 3) + 9(j + 3) = (j + 3)(j + 9)

c. m² − 7m + 10 This can be factored into (m - 2)(m - 5). Here's how: We're looking for two numbers that multiply to 10 and add to -7. Those numbers are -2 and -5. So, we write: m² - 2m - 5m + 10 = m(m - 2) - 5(m - 2) = (m - 2)(m - 5)

d. x² − 5x + 7 This cannot be factored using integers because there are no two numbers that multiply to 7 and add to -5.