Math PicnicEvery sheet is a promise

Factoring x² − bx + c

Practice Practice sheetNew questions
The question

x² − 29x + 138

x² − 29x + 138

x² − 29x + 138
multiply to138· add to−29
138 > 0→same sign
−29 < 0→both −
1·1382·693·466·23
1·1382·693·466·23
−6and−23
x² − 29x + 138=(x − 6)(x − 23)
  1. Factoring this means finding two numbers to put in (x + ▢)(x + ▢). They multiply to 138, the last term, and add to −29, the number in front of x.
  2. 138 is positive, so the two numbers share a sign — a product is only positive that way. And −29 is negative, so the sign they share is negative: two negatives multiply to a positive and add to a negative.
  3. Now list the pairs that multiply to 138. There are only 4: 1 and 138, 2 and 69, 3 and 46, 6 and 23.
  4. Which of them adds to −29? −6 × −23 = 138 and −6 + −23 = −29. So the two numbers are −6 and −23.
  5. Put them in the brackets: x² − 29x + 138 = (x − 6)(x − 23). Multiply back out to check.

How it works.

  1. 01

    Factoring this means finding two numbers to put in (x + ▢)(x + ▢). They multiply to 138, the last term, and add to −29, the number in front of x.

  2. 02

    138 is positive, so the two numbers share a sign — a product is only positive that way. And −29 is negative, so the sign they share is negative: two negatives multiply to a positive and add to a negative.

  3. 03

    Now list the pairs that multiply to 138. There are only 4: 1 and 138, 2 and 69, 3 and 46, 6 and 23.

  4. 04

    Which of them adds to −29? −6 × −23 = 138 and −6 + −23 = −29. So the two numbers are −6 and −23.

  5. 05

    Put them in the brackets: x² − 29x + 138 = (x − 6)(x − 23). Multiply back out to check.

Pick another skill