Question

$resolve \: into \: factors. \\ 2 {x}^{2} + 9x + 4 \\ plese \: resolve \: in \: full \: prosses$
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Answer 1

Step-by-step explanation:

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$\sf{:}\implies$Factor the expression by grouping. First, the expression needs to be rewritten as 2x$^2$ +ax+bx+4. To find a and b, set up a system to be solved.

a+b=9

ab=2×4=8

$\sf{:}\implies$As ab is positive, a and b have the same sign. As a+b is positive, a and b are both positive. List all such integer pairs that give product 8.

1,8

2,4

$\sf{:}\implies$Calculate the sum for each pair.

1+8=9

2+4=6

$\sf{:}\implies$The solution is the pair that gives sum 9.

a=1

b=8

$\sf{:}\implies$Rewrite 2x$^2$+9x+4 as (2x$^2$) +(8x+4).

(2x$^2$) +(8x+4)

x(2x+1)+4(2x+1)

$\sf{:}\implies$Factor out common term 2x+1 by using distributive property.

(2x+1)(x+4)

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