Question

Factorize the following:
(i) x3 - 3^x2 + x - 3
(ii) 9y^2 – 12y + 4​

Answer 1

Answer:

x2y2

Step-by-step explanation:

$(i) 12x = 2 × 2 × 3 × x</p><p></p><p>36 = 2 × 2 × 3 × 3</p><p></p><p>The common factors are 2, 2, 3.</p><p></p><p>And, 2 × 2 × 3 = 12</p><p></p><p>(ii) 2y = 2 × y</p><p></p><p>22xy = 2 × 11 × x × y</p><p></p><p>The common factors are 2, y.</p><p></p><p>And, 2 × y = 2y</p><p></p><p>(iii) 14pq = 2 × 7 × p × q</p><p></p><p>28p2q2 = 2 × 2 × 7 × p × p × q × q</p><p></p><p>The common factors are 2, 7, p, q.</p><p></p><p>And, 2 × 7 × p × q = 14pq</p><p></p><p>(iv) 2x = 2 × x</p><p></p><p>3x2 = 3 × x × x</p><p></p><p>4 = 2 × 2</p><p></p><p>The common factor is 1.</p><p></p><p>(v) 6abc = 2 × 3 × a × b × c</p><p></p><p>24ab2 = 2 × 2 × 2 × 3 × a × b × b</p><p></p><p>12a2b = 2 × 2 × 3 × a × a × b</p><p></p><p>The common factors are 2, 3, a, b.</p><p></p><p>And, 2 × 3 × a × b = 6ab</p><p></p><p>(vi) 16x3 = 2 × 2 × 2 × 2 × x × x × x</p><p></p><p>−4x2 = −1 × 2 × 2 × x × x</p><p></p><p>32x = 2 × 2 × 2 × 2 × 2 × x</p><p></p><p>The common factors are 2, 2, x.</p><p></p><p>And, 2 × 2 × x = 4x</p><p></p><p>(vii) 10pq = 2 × 5 × p × q</p><p></p><p>20qr = 2 × 2 × 5 × q × r</p><p></p><p>30rp = 2 × 3 × 5 × r × p</p><p></p><p>The common factors are 2, 5.</p><p></p><p>And, 2 × 5 = 10</p><p></p><p>(viii) 3x2y3 = 3 × x × x × y × y × y</p><p></p><p>10x3y2 = 2 × 5 × x × x × x × y × y</p><p></p><p>6x2y2z = 2 × 3 × x × x × y × y × z</p><p></p><p>The common factors are x, x, y, y.</p><p></p><p>And,</p><p></p><p>x × x × y × y = x2y2</p><p></p><p>$

Answer 2

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