Solving Quadratic Equations Using Common Factors Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
One of the steps needed to solve a quadratic equation by grouping is to split the middle term as a sum of two terms. Given the equation x2−13x+42=0
, which two numbers would be needed to complete this step? Enter the lesser value first.(1 point)
x2−13x+42=0

x2+
x+
x+42=0

Remaining Attempts : 3
Skip to navigation

Answer 1

To solve the quadratic equation \(x^2 - 13x + 42 = 0\) by grouping, we need to split the middle term \(-13x\) into two terms that add up to \(-13\) and multiply to \(42\).

We need two numbers that:

1. Multiply to \(42\) (the constant term).
2. Add up to \(-13\) (the coefficient of the middle term, which is negative).

After checking the pairs of factors of \(42\):

• \(1\) and \(42\) (sum is \(43\))
• \(2\) and \(21\) (sum is \(23\))
• \(3\) and \(14\) (sum is \(17\))
• \(6\) and \(7\) (sum is \(13\))

The pair that works here is \(-6\) and \(-7\):

• \(-6 \times -7 = 42\)
• \(-6 + (-7) = -13\)

Thus, the two numbers needed to complete the step are \(-6\) and \(-7\).

So, you should enter:

-7, -6 (enter the lesser value first).