6x^3-16x^2+17x-6?/3x-2
1 answer:
Answer:
2x² − 4x + 3
Step-by-step explanation:
x = 2/3 is a root of both the numerator and the denominator, so it divides evenly. Therefore, one method is to factor by grouping:
6x³ − 16x² + 17x − 6
6x³ − 4x² − 12x² + 17x − 6
2x² (3x − 2) − (12x² − 17x + 6)
2x² (3x − 2) − (4x − 3) (3x − 2)
Divided by 3x − 2:
2x² − (4x − 3)
2x² − 4x + 3
Another method is to use long division (see image).
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Answer: The answer is (B) ∠SYD.
Step-by-step explanation: As mentioned in the question, two parallel lines PQ and RS are drawn in the attached figure. The transversal CD cut the lines PQ and RS at the points X and Y respectively.
We are given four angles, out of which one should be chosen which is congruent to ∠CXP.
The angles lying on opposite sides of the transversal and outside the two parallel lines are called alternate exterior angles.
For example, in the figure attached, ∠CXP, ∠SYD and ∠CXQ, ∠RYD are pairs of alternate exterior angles.
Now, the theorem of alternate exterior angles states that if the two lines are parallel having a transversal, then alternate exterior angles are congruent to each other.
Thus, we have
∠CXP ≅ ∠SYD.
So, option (B) is correct.
