Answer :
Answer:
[tex]{ \bf{let \: \: { \tt{ - {x}^{2} + 5x + 24} \: \: be \: \: { \bf{{y}}}}}} \\ { \tt{y = - {x}^{2} + 5x + 24 }} \\ { \tt{y = (x + 3)(x - 8)}} \\ for \: x - intercept : y = 0 \\ { \tt{(x + 3)(x - 8) = 0}} \\ { \bf{x = - 3 \: and \: 8}}[/tex]
The factors to the given expression are -1(x+3)(x-8)
The x-intercepts are -3, 8
What do we mean by factorization?
Factorization is the process in which we write an expression in its factors which when multiplied results in the original expression.
How do we factorize the given expression?
We equate the given expression to f(x)
(-x² + 5x + 24) = f(x)
⇒ -1(x² - 5x - 24) = f(x)
⇒ -1(x² - (8-3)x - 24) = f(x)
⇒ -1(x² + 3x - 8x -24) = f(x)
⇒ -1(x(x+3) -8(x+3)) = f(x)
⇒ -1(x+3)(x-8) = f(x)
∴The factor to the given expression is -1(x+3)(x-8)
How do we find the x-intercepts?
To find the x-intercepts we equate f(x) = 0
⇒ -1(x+3)(x-8) = 0
⇒ (x+3)(x-8) = 0
x-intercepts are the roots of the above equation.
∴ The x-intercepts occur where x = -3 and x = 8
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