If x – 3 is a factor of p(x), then the remainder is

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If x – 3 is a factor of p(x), then the remainder is p(3)

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पाठ 3: Algebra - Exercise 3.15 [पृष्ठ १३४]

पाठ 3 Algebra
Exercise 3.15 | Q 12 | पृष्ठ १३४

Using the Factor Theorem, show that (x + 5) is a factor of 2x³ + 5x² – 28x – 15. Hence, factorise the expression 2x³ + 5x² – 28x – 15 completely.

What should be subtracted from 3x³ – 8x² + 4x – 3, so that the resulting expression has x + 2 as a factor?

Using the factor Theorem, show that:

2x + 7 is a factor 2x³ + 5x² − 11x – 14. Hence, factorise the given expression completely.

Show that m − 1 is a factor of m²¹ − 1 and m²² − 1.

In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x³ + x² + 3x + 175 and g(x) = x + 5.

Show that 2x + 7 is a factor of 2x³ + 5x² – 11x – 14. Hence factorise the given expression completely, using the factor theorem.

For what value of k is the polynomial p(x) = 2x³ – kx² + 3x + 10 exactly divisible by (x – 2)

Determine the value of m, if (x + 3) is a factor of x³ – 3x² – mx + 24

If (x – 1) divides the polynomial kx³ – 2x² + 25x – 26 without remainder, then find the value of k

If x – 2 is a factor of x³ – kx – 12, then the value of k is ______.