Question

Practice Set 6.1
(2) x2 - 10x + 9
(5) p2 - 2p - 35
(8) m² - 25m + 100
(11) 20x2 - 26x + 8
(3) y2 + 24y + 144
(6) p2 - 7p - 44
(9) 3x2 + 14x + 15
(12) 44x2 - x - 3​

Answer 1

Step-by-step explanation:

$2) \: {x}^{2} - 10x + 9 \\ = {x}^{2} - x - 9x + 9 \\ = x(x - 1) - 9(x - 1) \\ = (x - 9)(x - 1)$

$5) {p}^{2} - 2p - 35 \\ = {p}^{2} - 7p + 5p - 35 \\ = p(p - 7) + 5(p - 7) \\ = (p + 5)(p - 7)$

$8) {m}^{2} - 25m + 100 \\ = {m}^{2} - 5m - 20m + 100 \\ = m(m - 5) - 20(m - 5) \\ = (m - 20)(m - 5)$

$11)20 {x}^{2} - 26x + 8 \\ = 20 {x}^{2} - 10x - 16x + 8 \\ = 10x(2x - 1) - 8(2x - 1) \\ = (10x - 8)(2x - 1)$

$3) {y}^{2} + 24y + 144 \\ = {y}^{2} + 12y + 12y + 144 \\ = y(y + 12) + 12(y + 12) \\ = (y + 12)(y + 12) = {(y + 12)}^{2}$

$6) {p}^{2} - 7p - 44 \\ = {p}^{2} + 4p - 11p - 44 \\ = p(p + 4) - 11(p + 4) \\ = (p - 11)(p + 4)$

$9)3 {x}^{2} + 14x + 15 \\ = 3 {x}^{2} + 9x + 5x + 15 \\ = 3x(x + 3) + 5(x + 3) \\ = (3x + 5)(x + 3)$

$12)44 {x}^{2} - x - 3 \\ = 44 {x}^{2} + 11x - 12x - 3 \\ = 11x(4x + 1) - 3(4x + 1) \\ = (11x - 3)(4x + 1)$

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