Question

factories by middle term splitting

Answer 1

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•°• Here's your answer •°•

$a) {x}^{2} + 14x + 48 \\ = {x}^{2} + 8x + 6x + 48 \\ = x(x + 8) + 6(x + 8) \\ = (x + 6)(x + 8)$
$b) {x}^{2} + 9x + 20 \\ = {x}^{2} + 5x + 4x + 20 \\ = x(x + 5) + 4(x + 5) \\ = (x + 4)(x + 5)$
$c) {a}^{2} + 15a + 54 \\ = {a}^{2} + 9a + 6a + 54 \\ = a(a + 9) + 6(a + 9) \\ = (a + 6)(a + 9)$
$d) {m}^{2} + 3 \sqrt{3} m + 6 \\ = {m}^{2} + 2 \sqrt{3} m + \sqrt{3}m + 6 \\ = m(m + 2 \sqrt{3}) + \sqrt{3} (m + 2 \sqrt{3} ) \\ = (m + \sqrt{3} )(m + 2 \sqrt{3} )$
$e) {x}^{2} + 7x + 12 \\ = {x}^{2} + 4x + 3x + 12 \\ = x(x + 4) + 3(x + 4) \\ = (x + 3)(x + 4)$
$f) {x}^{2} - 5x - 14 \\ = {x}^{2} - 7x + 2x - 14 \\ = x(x - 7) + 2(x - 7) \\ = (x - 7)(x + 2)$
$g)6 - x - {x}^{2} \\ = { - x}^{2} - x + 6 \\ = { - x}^{2} - 3x + 2x + 6 \\ = - x(x + 3) + 2(x + 3) \\ = (x + 2)(x + 3)$
$h) {x}^{2} - 21x + 108\\ = {x}^{2} - 12x - 9x + 108 \\ = x(x - 12) - 9(x - 12) \\ = (x - 9)(x - 12)$
i) and j) in the pics

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