Question

2x³+x²- 23x+20 = (x+4) (_____) find the missing factor.

Answer 1

Answer:

=(2x²-7x+5)

Step-by-step explanation:

thats is the answer

Answer 2

2x³ + x² - 23x + 20 = (x + 4)(2x² - 7x + 5)

Given : 2x³ + x² - 23x + 20 = (x + 4) _____

To find : The missing factor

Solution :

Here the given expression is

2x³ + x² - 23x + 20

Putting x = - 4 in the above expression we get

$\sf = 2 \times {( - 4)}^{3} + {( - 4)}^{2} - 23 \times ( - 4) + 20$

$\sf = - 128+ 16 + 92+ 20$

$\sf = 0$

For x = - 4 the expression vanishes

So x + 4 is a factor of the expression

We factorise the given expression as below

$\sf 2 {x}^{3} + {x}^{2} - 23x + 20$

$\sf = 2 {x}^{3} + 8 {x}^{2} - 7 {x}^{2} - 28x + 5x + 20$

$\sf = 2 {x}^{2} (x + 4) - 7x(x + 4) + 5(x + 4)$

$\sf = (x + 4) (2 {x}^{2} - 7x + 5)$

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