Dezembro 23, 2019

por Joli

Como você fatora $2 x^{2} + 5 x - 3$ $2x ^ 2 + 5x-3$ ?

Responda:

$(x + 3) (2 x - 1)$ $(x+3)(2x-1)$

Explicação:

The standard form of the $quadratic function$ $color(blue)"quadratic function"$ is.

$y = a x^{2} + b x + c$ $y=ax^2+bx+c$

To factorise the function.

• consider the factors of the product ac which sum to give b

$for 2 x^{2} + 5 x - 3$ $"for "2x^2+5x-3$

$a = 2, b = 5 and c = - 3$ $a=2, b=5" and "c=-3$

$\Rightarrow a c = 2 \times - 3 = - 6$ $rArrac=2xx-3=-6$

$the required factors of -6 are + 6 and - 1$ $"the required factors of -6 are "+6" and "-1$

$since 6 \times - 1 = - 6 and + 6 - 1 = + 5$ $"Since " 6xx-1=-6" and " +6-1=+5$

$now express 2 x^{2} + 5 x - 3 as$ $"now express " 2x^2+5x-3" as"$

$2 x^{2} + 6 x - x - 3$ $2x^2color(red)(+6x-x)-3$

Factorise by 'grouping'

$\Rightarrow 2 x (x + 3) - 1 (x + 3)$ $rArr2x(x+3)-1(x+3)$

Take out $common factor of (x + 3)$ $color(blue)"common factor " "of " (x+3)$

$\Rightarrow (x + 3) (2 x - 1) \leftarrow in factorised form$ $rArr(x+3)(2x-1)larr" in factorised form"$