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Which geometric model using algebra tiles represents the factorization of x2 - 5x + 6?

Which geometric model using algebra tiles represents the factorization of x2 - 5x-example-1
User Dominik Seibold
by
2.4k points

1 Answer

29 votes
29 votes

ANSWER:

(x - 2) • (x - 3)

Step by Step Solution:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring x2-5x+6

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is +6

Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6

Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + -1 = -7

-3 + -2 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -2

x2 - 3x - 2x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-3)

Add up the last 2 terms, pulling out common factors :

2 • (x-3)

Step-5 : Add up the four terms of step 4 :

(x-2) • (x-3)

Which is the desired factorization

Final result :

(x - 2) • (x - 3)

User James Holderness
by
3.1k points