Question

A) Fully factorise x² + 11x + 18

b) Use your answer to part a) to solve
x² + 11x + 18 = 0

Answer 1

To fully factorize the quadratic expression x² + 11x + 18, we can factorize it as (x + 2)(x + 9). To solve the equation x² + 11x + 18 = 0, we can set it equal to zero and use the factored form, which gives x = -2 and x = -9.

Step-by-step explanation:

To fully factorize the quadratic expression x² + 11x + 18, we need to find two numbers whose sum is 11 and product is 18. The numbers are 2 and 9, since 2 + 9 = 11 and 2 * 9 = 18. Therefore, we can factorize the expression as (x + 2)(x + 9).

To solve the equation x² + 11x + 18 = 0, we can set it equal to zero and use the factored form from part a). So, (x + 2)(x + 9) = 0. Then, we can set each factor equal to zero and solve for x. So, x + 2 = 0 and x + 9 = 0. Solving these equations gives x = -2 and x = -9.

Answer 2

a) To fully factorize the quadratic expression x² + 11x + 18, we need to find two numbers that multiply to the constant term (18) and add up to the coefficient of the linear term (11x). These two numbers are 2 and 9 because 2 * 9 = 18 and 2 + 9 = 11.

Now, we can rewrite the quadratic expression as a product of two binomials:

x² + 11x + 18 = (x + 2)(x + 9)

b) To solve the equation x² + 11x + 18 = 0 using the factorization from part a), set each factor equal to zero:

x + 2 = 0 or x + 9 = 0

Solve for x in each equation:

For x + 2 = 0:

x + 2 = 0

x = -2

For x + 9 = 0:

x + 9 = 0

x = -9

So, the solutions to the equation x² + 11x + 18 = 0 are x = -2 and x = -9.