factroize x^3+13x^2+32x+20
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Answered by
1
Answer:
The value of x
3
+13x
2
+32x+20 is
x
3
+x
2
+12x
2
+12x+20x+20
=x
2
(x+1)+12x(x+1)+20(x+1)
=(x−1)(x
2
+12x+20)
=(x−1)(x
2
+10x+2x+20)
=(x+1)[x(x+10)+2(x+10)]
=(x+1)(x+2)(x+10)
Answered by
1
Answer:
(x + 1) (x + 2) (x + 10)
Step-by-step explanation:
Let f(x) = x³ + 13x² + 32x + 20
For x = -1,
f(-1) = (-1)³ + 13(-1)² + 32(-1) + 20
= -1 + 13 - 32 + 20
= 33 - 33 = 0
Thus, (x + 1) is a factor of f(x).
f(x) / (x + 1) = x² + 12x + 20 [Division pic at the top]
f(x) = (x + 1) (x² + 12x + 20)
= (x + 1) (x(x + 10) + 2(x + 10))
= (x + 1) (x + 2) (x + 10)
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