Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex] ( m > n)
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇒ [tex]\frac{1}{a^{(n-m)} }[/tex] ( n > m )
Given
[tex]\frac{21x^6y^5}{14x^2y^9}[/tex]
= [tex]\frac{21}{14}[/tex] × [tex]x^{(6-2)}[/tex] × [tex]\frac{1}{y^{(9-5)} }[/tex]
= [tex]\frac{3}{2}[/tex] × [tex]x^{4}[/tex] × [tex]\frac{1}{y^{4} }[/tex]
= [tex]\frac{3x^4}{2y^4}[/tex] ← with positive exponents
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(a)
x² + 2x ← factor out x from each term
= x(x + 2)
(b)
2x² - 6x ← factor out 2x from each term
= 2x(x - 3)
(c)
15x - 10x³ ← factor out 5x from each term
= 5x(3 - 2x²)
(d)
9x² + 3x³ ← factor out 3x² from each term
= 3x²(3 + x)
