Multiply: $(x - 2) (x^{2} + 3 x + 7)$

x^{3} + 2 x^{2} + 6 x - 14

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x^{3} + x^{2} + 6 x - 14

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x^{3} + x^{2} + x - 14

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x^{3} + 2 x^{2} + 3 x - 14

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Solution

The correct option is B $x^{3} + x^{2} + x - 14$
Resultant multiplication is
$(x - 2) (x^{2} + 3 x + 7)$
$= x (x^{2} + 3 x + 7) - 2 (x^{2} + 3 x + 7)$
$= (x^{3} + 3 x^{2} + 7 x - 2 x^{2} - 6 x - 14)$
$= x^{3} + x^{2} + x - 14$

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Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor = $x - 1$ and remainder = 2. Find the quotient q(x)

$If the dividend = x^{4} + x^{3} - 2 x^{2} + x + 1, divisor = x - 1 and remainder = 2, then find the quotient q(x) .$

(x+1) is a factor of the polynomial
(a) $x^{3} + x^{2} - x + 1$
(b) $x^{3} + 2 x^{2} - x - 2$
(c) $x^{3} + 2 x^{2} - x + 2$
(d) $x^{4} + x^{3} + x^{2} + 1$

lim x \to \infty \frac{x^{3} + x^{2} + 1}{2 x^{2} + 3 x + 4}

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Multiply: (x−2)(x2+3x+7)

The correct option is B x3+x2+x−14Resultant multiplication is(x−2)(x2+3x+7)=x(x2+3x+7)−2(x2+3x+7)=(x3+3x2+7x−2x2−6x−14)=x3+x2+x−14

Multiply: $(x - 2) (x^{2} + 3 x + 7)$

The correct option is B $x^{3} + x^{2} + x - 14$
Resultant multiplication is
$(x - 2) (x^{2} + 3 x + 7)$
$= x (x^{2} + 3 x + 7) - 2 (x^{2} + 3 x + 7)$
$= (x^{3} + 3 x^{2} + 7 x - 2 x^{2} - 6 x - 14)$
$= x^{3} + x^{2} + x - 14$