Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: [tex](7x+4)[/tex] and [tex](x-1)[/tex]
If the given quadratic expression is of the form [tex]ax^2 + bx + c[/tex],
then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha - \beta[/tex]
The given expression is [tex]7x^2 - 3x - 4[/tex]
Comparing it with the standard form of quadratic expression [tex]ax^2 + bx + c[/tex], we get: a = 7, b = -3, c = -4
ac = -28
-28 = -2 times 14
-28 = -7 times 4 (-7 + 4 = -3 = b)
Thus, [tex]\alpha = -7, \beta = 4[/tex]
Thus, we get:
[tex]7x^2 - 3x - 4 = 7x^2 - 7x + 4x - 4 = 7x(x-1) + 4(x-1) = (7x+4)(x-1)\\7x^2 - 3x - 4 = (7x+4)(x-1)[/tex]
Thus, The factors of given expression are: [tex](7x+4)[/tex] and [tex](x-1)[/tex]
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