Factorisation of Polynomials — Flashcards
ICSE · Class 10 · Mathematics
26 flashcards for Factorisation of Polynomials (ICSE Class 10 Mathematics) to test yourself on key terms and facts.
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See them allSolve using the Division Algorithm: If f(x) is divided by a non-zero g(x), what form does the result take?
Answer
Step 1: Write the division form. f(x)=g(x)q(x)+r(x) Step 2: Identify the parts. - f(x) = dividend - g(x) = divisor - q(x) = quotient - r(x) = remainder Step 3: Use the remainder condition. Either r…
Apply the Division Algorithm to this structure: f(x)=g(x)q(x)+r(x). What does each term mean?
Answer
Step 1: Match each symbol. - f(x): dividend polynomial - g(x): non-zero divisor polynomial - q(x): quotient polynomial - r(x): remainder polynomial Step 2: Remember the rule. The remainder is either …
What remainder form is possible when a polynomial is divided by a quadratic polynomial?
Answer
Step 1: Compare degrees. A quadratic divisor has degree 2. Step 2: Use the remainder rule. The remainder must have degree less than 2. Step 3: So the remainder can be written as ax+b where a and b a…
What remainder form is possible when a polynomial is divided by a linear polynomial?
Answer
Step 1: Compare degrees. A linear divisor has degree 1. Step 2: Use the remainder rule. The remainder must have degree less than 1. Step 3: So the remainder is a constant. It is of the form b, where…
Solve: Decide whether x-2 is a factor of x^2-5x+6.
Answer
Step 1: Factorise the polynomial. x^2-5x+6=(x-2)(x-3) Step 2: Look for the given factor. The expression contains (x-2). Step 3: Conclude. So, x-2 is a factor of x^2-5x+6. Verification: The polynom…
Solve: Factorise x^2-5x+6 completely.
Answer
Step 1: Look for two numbers whose product is 6 and sum is -5. The numbers are -2 and -3. Step 2: Split the middle term. x^2-2x-3x+6 Step 3: Group terms. x(x-2)-3(x-2) Step 4: Take common factor. (…
Why does a factor give zero remainder?
Answer
Step 1: Use the factor form. If g(x) is a factor of f(x), then f(x)=q(x)·g(x) Step 2: Compare with division. This means the division has no remainder. Step 3: Connect to the remainder. Zero remainde…
Use substitution to find the value of f(x)=x^2+5x+4 at x=3.
Answer
Step 1: Substitute x=3 everywhere. f(3)=(3)^2+5(3)+4 Step 2: Calculate each part. (3)^2=9 5(3)=15 Step 3: Add the values. 9+15+4=28 Answer: f(3)=28 Check: Always substitute the value in place of …
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