Question

factorise
3a2 - 2a - 16​

Answer 1

Step-by-step explanation:

3a^2 -2a -16

3a^2 + 6a - 8a - 16

3a(a+2) - 8(a+2)

(3a-8)(a+2)=0

3a-8=0

3a=8

a=8/3

a+2=0

a=-2

Answer 2

$\huge \mathbb \red {ANSWER}$

$\bold {by \: using \: direct \: methods \: } \\ \\ \bold {in \: this \: methord \:we \: have \:to \: convert \: equation \: into \: form \: of \: {x}^{2} + bx + c } \\ \\ \bold{on \: dividing \:given \: equation \: by \: 3 } \\ \\ \bold { \frac{3 {a}^{2} - 2a - 16 }{3} } \\ \\ \bold{ {a}^{2} - \frac{2}{3} - \frac{16}{3} } \\ \\ \bold{now \: we \: divide \: b \: (here \: 2) \: by2}$

$\bold{then \: \frac{2}{3 \times 2} = \frac{1}{3} } \\ \\ \bold {then \: add \: and \: substract \: \frac{1}{3} \:from \: u(where \: u \: is \: some \: unknown \: integer )} \\ \\ \bold { (\frac{1}{3} - u)( \frac{1}{3} + u) - - (1)= ( { \frac{1}{3} }^{2} - {u}^{2} ) = \frac{1}{9} - {u}^{2} } \\ \\ \bold {let \: above \: equation \:be \: = \frac{16}{3} } \\ \\ \bold {\frac{1}{9} - {u}^{2} = \frac{16}{3} } \\ \\ \bold { - {u}^{2} = \frac{16}{3} - \frac{1}{9} } \\ \\ \bold { - {u}^{2} = \frac{ - 48 - 1}{9} }$

$\bold {u^{2} = \frac{49}{9} = u = \sqrt{ \frac{49}{9} } = u = \frac{7}{3}}$

$\bold { now \: we \: have \:put \: value \: u\: in \: equation \: 1} \\ \\ \bold { \frac{1}{3} - \frac{7}{3}and \: \frac{1}{3} + \frac{7}{3} } \\ \\ \bold { \frac{6}{3}and \: \frac{8}{3} } \\ \\ \bold {then \:let \: x = \frac{6}{3} = x = 2 \: then \: factor \: will \: be \: x + 2 } \\ \\ \bold {x = \frac{8}{3} = then \: factor \: 3x - 8 } \\ \\ \bold { therefore \: factors \: are \: x + 2 \: and \: 3x - 8}$

$\large \underline \green {methord \:2 \: \: \: by \: factorising} \\ \\ \bold {here \: given \: equation \: is \: 3 {a}^{2} - 2a - 16 } \\ \\ \bold {3 {a}^{2} + 6a - 8a it - 16} \\ \\ \bold {3a(a - 2) - 8(a + 2)} \\ \\ \bold {(3a - 8)(a + 2)}$

hope it helps

be brainly