Can you help me with this

Mathematics

1 answer:

MrRa [10]2 years ago

3 0

Answer:

p(x - 4) = x³ - 12x² + 48x - 69

Step-by-step explanation:

To evaluate p(x - 4), substitute a = x - 4 into p(a), that is

p(x - 4) = (x - 4)³ - 5

= (x - 4)(x - 4)(x - 4) - 5 ← expand 2nd/ 3rd factors using FOIL

= (x - 4)(x² - 8x + 16) - 5 ← distribute parenthesis

= x³ - 8x² + 16x - 4x² + 32x - 64 - 5 ← collect like terms

= x³ - 12x² + 48x - 69

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$\bigstar\:{\underline{\sf{In\:right\:angled\:triangle\:ABC\::}}}\\\\$

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$\bf{\dag}\:{\underline{\frak{By\:using\:Pythagoras\: Theorem,}}}\\\\$

$\star\:{\underline{\boxed{\frak{\purple{(Hypotenus)^2 = (Perpendicular)^2 + (Base)^2}}}}}\\\\\\ :\implies\sf (AB)^2 = (AC)^2 + (BC)^2\\\\\\ :\implies\sf (AB)^2 = (AB)^2 = (7)^2 = (4)^2\\\\\\ :\implies\sf (AB)^2 = 49 + 16\\\\\\ :\implies\sf (AB)^2 = 65\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{AB = \sqrt{65}}}}}}\:\bigstar\\\\$