Question

Factorise by splitting the middle term
3x² + 2x - 8

Answer 1

Given Equation

• 3x² + 2x - 8

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Solution

• By middle term spiliting.

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→ 3x² + 2x - 8

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→ 3x² + 6x - 4x - 8

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→ 3x(x + 2) - 4(x + 2)

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→ (x + 2) ( 3x - 4)

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• We get

⇛ x = -2

⇛ x = 4/3

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☆Know more☆

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★ Quadratic equation :-

• A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

Answer 2

Question -

Factorise by splitting the middle term 3x² + 2x - 8

Required Answer -

$\red{\bigstar}\sf 3x^2 + 2x - 8 \large\leadsto{\tt\purple{ [ x + 2x ] [ 3x - 4]}}$

Step By Step Solution -

3x² + 2x - 8 , now we need to replace ( 3 * 8 = 24 ) from the numbers which are factors of 24 and while adding or subtracting gives 2

Factors of 24

• 2 and 12
• 3 and 8
• 4 and 6

Let's give a try to each ,

1) 2 and 12 ; 12 + 2 = 14 ☒ , 12 - 2 = 10 ☒

now by adding and subtracting 12 and 2 we are not getting 2

2) 3 and 8 ; 8 + 3 = 11 ☒ , 8 - 5 = 5 ☒

now by adding and subtracting 3 and 8 we are not getting 2

3) 4 and 6 ; 6 + 4 = 10 ☒ , 8 - 5 = 5 ☑

now by adding 6 and 4 we are not getting 2 but by subtracting 6 and 4 we are getting 3 its mean we will replace it with 4 and 6 .

$\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \: 3x ^{2} + 6x - 4 x - 8 \\ \end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf \:( 3x ^{2} + 6x )-( 4 x - 8 )\\ \end{gathered} \end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf 3x( x + 2x )-4( x - 2 )\\ \end{gathered} \end{gathered}\end{gathered}$

Now we will take (x + 2x) and (3x - 4x) common

$\begin{gathered}\begin{gathered}\begin{gathered} \\ \\ : \implies \displaystyle \sf ( x + 2x )(3x - 4)\\ \end{gathered} \end{gathered}\end{gathered}$