Determine whether (x – 1) is a factor of the following polynomials: x3 + 5x2 – 10x + 4 - Mathematics

Determine whether (x – 1) is a factor of the following polynomials:

x³ + 5x² – 10x + 4

Sum

Let P(x) = x³ + 5x² – 10x + 4

By factor theorem (x – 1) is a factor of P(x), if P(1) = 0

P(1) = 1³ + 5(1²) – 10(1) + 4 = 1 + 5 – 10 + 4

P(1) = 0

∴ (x – 1) is a factor of x³ + 5x² – 10x + 4

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Chapter 3: Algebra - Exercise 3.3 [Page 96]

Chapter 3 Algebra
Exercise 3.3 | Q 7. (i) | Page 96

If x + a is a common factor of expressions f(x) = x² + px + q and g(x) = x² + mx + n; show that : `a = (n - q)/(m - p)`

Find the value of ‘a’, if (x – a) is a factor of x³ – ax² + x + 2.

Find the value of m ·when x³ + 3x² -m x +4 is exactly divisible by (x-2)

Prove that ( p-q) is a factor of (q - r)³ + (r - p) ³

Use the factor theorem to factorise completely x³ + x² - 4x - 4.

Show that (x – 1) is a factor of x³ – 5x² – x + 5 Hence factorise x³ – 5x² – x + 5.

Show that (x – 3) is a factor of x³ – 7x² + 15x – 9. Hence factorise x³ – 7x² + 15 x – 9

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

Find the value of 'a' if x – a is a factor of the polynomial 3x³ + x² – ax – 81.

Is (x – 2) a factor of x³ – 4x² – 11x + 30?