Question

Write x(x-2)+3(2-x) as a product of binomials. Hint: you may want to manipulate (2-x) first. Check to see If you have written and equivalent expression by testing x=5. Show your work.

Answer 1

Answer:

x²-5x+6

Step-by-step explanation:

The question is to find product in : x(x-2)+3(2-x)-----------(a)

Make terms in brackets same by introducing a negative sign as;

Collect like terms as : x(x-2) - 3 (x-2)------------ (b)

Note that expression (a) is similar to (b)

Factorize equation (b) as : (x-3)(x-2)

Distribute as : x(x-2) -3 (x-2 ) ------ x²-2x-3x+6

Collect like terms as: x²-5x+6

Final expression : x²-5x+6

Testing with x=5 in original expression

x(x-2)+3(2-x)

5(5-2)+3(2-5)

25-10+6-15

25+6-10-15

31-10-15=6

Using the final expression;

x²-5x+6

5²-5(5)+6

25-25+6

=6