(i) Using remainder and factor theorem, factorize completely, the given polynomial:
2𝑥 ³ − 9𝑥 ² + 7𝑥 + 6

(ii) Each of the letter of the word “HOUSEWARMING”" is written on cards and put in a bag. If a card is drawn at random from the bag after shuffling, what is the probability that the letter on the card is∶
(a) a vowel
(b) one of the letters of the word SEWING.
(c) not a letter from the word WEAR.

(iii) Use graph sheet for this question. Take 2 cm = 1 unit along the axes.
(a) Plot A (1, 2), B(1, 1)and C (2, 1)
(b) Reflect A, B and C about y-axis and name them as Aʹ, Bʹ and Cʹ.
(c) Reflect A, B, C, Aʹ, Bʹ and Cʹ about x-axis and name them as Aʺ, Bʺ, Cʺ, Aʺʹ, Bʺʹ and Cʺʹ respectively.
(d) Join A, B, C, Cʺ, Bʺ, Aʺ, Aʺʹ, Bʺʹ, Cʺʹ, Cʹ, Bʹ, Aʹ and A to form a closed figure.

Solution

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