The Factor And Remainder Theorems
Muhtasari
How can you tell whether a linear expression divides exactly into a polynomial without carrying out the full long division? The factor theorem and the remainder theorem give you a direct shortcut: substitute a single value, and the answer tells you everything you need. These two results are the key tools for breaking cubic and higher-degree polynomials into simpler factors.
In this topic you will learn to test whether a given linear expression is a factor, find the remainder from any linear divisor, and combine these techniques with algebraic division to factorise cubics completely. These skills appear frequently on both papers of the Edexcel 4PM1 exam and connect directly to solving polynomial equations.
Malengo
- Know that if f(x) = 0 when x = a, then (x - a) is a factor of f(x)
- Factorise cubic expressions when a factor has been provided
- Determine the remainder when the polynomial f(x) is divided by (ax + b) or (ax - b)
Maelezo ya Somo
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Tathmini ya Somo
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- If f(x) = x^3 - 3x^2 + 2x - 6 and f(3) = 0, which of the following is a factor of f(x)? A) (x + 3) B) (x - 3) C) (x - 6) D) (x + 1) Answer: B
- When f(x) = x^3 + x^2 - 2x + 1 is divided by (x - 1), the remainder is: A) 0 B) 1 C) -1 D) 3 Answer: B
- Which value of x should you substitute to test whether (x + 4) is a factor of f(x)? A) x = 4 B) x = -4 C) x = 1/4 D) x = -1/4 Answer: B
- The polynomial f(x) = 2x^3 - x^2 + kx + 6 has (x - 2) as a factor. What is k? A) -5 B) -7 C) 5 D) 7 Answer: A
- If the remainder when f(x) is divided by (x - a) is equal to zero, then: A) a is a coefficient of f(x) B) (x - a) is a factor of f(x) C) f(x) has degree a D) f(x) has no real roots Answer: B
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Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Inapatikana kwenye programu ya Green Bridge
Pakua programu ya Green Bridge CBT kwenye simu yako au kompyuta yako ili kupata maelezo kamili ya masomo, maswali ya mazoezi, na mengi zaidi.
Vitabu Vinavyopendekezwa
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