Question

examine whether x+2 is a factor of x³ + 2x² + 3x + 6
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Answer 1

Step-by-step explanation:

x+2=0

x=-2

p(x)= x^3+2x^2+3x+6

p(-2)=(-2)^3+2(-2)^2+3(-2)+6

p(-2)=-8+8-6+6

p(-2)=0

Hence (x+2) is a factor

Answer 2

✯Given Expression✯

➝ x³ + 2x² + 3x + 6

✮To examine with✮

➝ x + 2

✭Solution✭

• Let p(x) = x³ + 2x² + 3x + 6
• Given g(x) = x + 2
• The zero of g(x) = -2

➜ p(-2) = (-2)³ + 2(-2)² +3(-2) + 6

➜ -8 + 2(4) - 6 + 6

➜ -8 + 8 -6 + 6

➜ 0

➙∴By Factor Theorem, x+2 is a factor of x³+2x²+3x+6

★Learn more★

• Factor Theorem:

⇾ If p(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then:

• x - a is a factor of p(x) , if p(a) = 0             (or)
• If x-a is a factor of a polynomial p(x) then, p(a) = 0