Question

which expression is equivalent to $10x^{2}-19x + 6$? a) $(10x - 3)(x - 2)$ b) $(10x + 1)(x + 6)$ c) $(5x + 3)(2x - 2)$ d) $(5x - 2)(2x - 3)$

Explanation:

Step1: Expand Option A

Using the distributive property (FOIL method):
$(10x - 3)(x - 2) = 10x \cdot x + 10x \cdot (-2) - 3 \cdot x + (-3) \cdot (-2) = 10x^2 - 20x - 3x + 6 = 10x^2 - 23x + 6$.
This does not match $10x^2 - 19x + 6$.

Step2: Expand Option B

Using the distributive property (FOIL method):
$(10x + 1)(x + 6) = 10x \cdot x + 10x \cdot 6 + 1 \cdot x + 1 \cdot 6 = 10x^2 + 60x + x + 6 = 10x^2 + 61x + 6$.
This does not match $10x^2 - 19x + 6$.

Step3: Expand Option C

Using the distributive property (FOIL method):
$(5x + 3)(2x - 2) = 5x \cdot 2x + 5x \cdot (-2) + 3 \cdot 2x + 3 \cdot (-2) = 10x^2 - 10x + 6x - 6 = 10x^2 - 4x - 6$.
This does not match $10x^2 - 19x + 6$.

Step4: Expand Option D

Using the distributive property (FOIL method):
$(5x - 2)(2x - 3) = 5x \cdot 2x + 5x \cdot (-3) - 2 \cdot 2x + (-2) \cdot (-3) = 10x^2 - 15x - 4x + 6 = 10x^2 - 19x + 6$.
This matches the given expression.

Answer:

D) $(5x - 2)(2x - 3)$