Remainder And Factor Theorems — Mathematics STD 10 — Question
ICSE BoardEnglish MediumSTD 10MathematicsRemainder And Factor Theorems3 Marks
Question
Prove by factor theorem that
$(2x+1)$ is a factor of $4x^3 + 12x^2 + 7x +1$
✓
Answer
$(2 x+1)$ is a factor of $4 x^3+12 x^2+7 x+1$
$
2 x+1 \Rightarrow x=\frac{1}{2}
$
Substituting this value, we get
$
f \left(-\frac{1}{2}\right)=4 \times\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right)+12 \times\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right) \times\left(-\frac{1}{2}\right)+7 \times\left(-\frac{1}{2}\right)+1=0
$
Hence $(2 x+1) 1$ s a factor of $4 x^3+12 x^2+7 x+1$
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