Question

1b. True or False? Explain your answer without multiplying. 2 points

(2x - 3)(5x^2 - 2x + 6) = (3x-2)(5x^2 - 2x + 6)
ANSWER AND EXPLANATION:​

Answer 1

False

How?

Let 5x^2-2x+6 be A

The expression will be

`\\ \sf\longmapsto A(2x-3)=A(3x-2)`

`\\ \sf\longmapsto 2x-3=3x-2`

But it's impossible

`\\ \sf\longmapsto 2x-3\\eq 3x-2`

Answer 2

• False

Explanation:

Solution 1

The easy way is to compare the leading terms or constants.

LHS

The leading term is:

• 2x*5x² = 10x³

The constant is:

• (-3)*6 = -18

RHS

The leading term is:

• 3x*5x² = 15x³

The constant is:

• (-2)*6 = -12

We see both the leading terms (10x³ ≠ 15x³) and constants (-18 ≠ -12) are different so the equation is false.

Solution 2

We see one of the factors is same on both sides:

• 5x² - 2x + 6

The other factors are:

• 2x - 3 = 3x - 2

Since this factor is different on both sides, the equation is false