Values Of A Polynomial Function For a polynomial f(x) = 3x2 – 4x + 2. Values Of A Polynomial To find its value at x = 3; replace x by 3 everywhere. So, the value of f(x) = 3x2 – 4x + 2 at x = 3 is f(3) = 3 × 32 – 4 × 3 + 2 = 27 – 12 + 2 = 17. Similarly, the value of polynomial f(x) = 3x2 – 4x + 2, (i) at x = –2 is f(–2) = 3(–2)2 –4(–2) + 2 = 12 + 8 + 2 = 22 (ii) at x … [Read more...] about Values Of A Polynomial Function
Polynomials
How Do You Use The Factor Theorem
Factor Theorem Theorem: If p(x) is a polynomial of degree n ≥ 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x). Proof: By the Remainder Theorem, p(x) = (x – a) q(x) + p(a). (i) If p(a) = 0, then p(x) = (x – a) q(x), which shows that x – a is a factor of p(x). (ii) Since x – a is a factor of … [Read more...] about How Do You Use The Factor Theorem
What Are The Types Of Factorization
Types Of Factorization Example Problems With Solutions Type I: Factorization by taking out the common factors. Example 1: Factorize the following expression 2x2y + 6xy2 + 10x2y2 Solution: 2x2y + 6xy2 + 10x2y2 =2xy(x + 3y + 5xy)Type II: Factorization by grouping the terms. Example 2: Factorize the following expression a2 – b + ab – a Solution: … [Read more...] about What Are The Types Of Factorization
Factorization Of Algebraic Expressions
Factorization Of Algebraic Expressions Of The Form a3 + b3 + c3, When a + b + c = 0 Example 1: Factorize (x – y)3 + (y – z)3 + (z – x)3 Solution: Let x – y = a, y– z = b and z – x = c, then, a + b + c = x – y + y – z + z –x = 0 ∴ a3 + b3 + c3 = 3abc ⇒ (x – y)3 + (y – z)3 + (z – x)3 = 3 (x–y)(y – z)(z–x)Example 2: Factorize (a2–b2)3 + (b2–c2)3+ … [Read more...] about Factorization Of Algebraic Expressions
Relationship Between Zeros And Coefficients Of A Polynomial
Relationship Between Zeros And Coefficients Of A Polynomial Consider quadratic polynomial P(x) = 2x2 – 16x + 30. Now, 2x2 – 16x + 30 = (2x – 6) (x – 3) = 2 (x – 3) (x – 5) The zeros of P(x) are 3 and 5. Sum of the zeros = 3 + 5 = 8 = =Product of the zeros = 3 × 5 = 15 = = So if ax2 + bx + c, a ≠ 0 is a quadratic polynomial and α, β are two zeros of polynomial … [Read more...] about Relationship Between Zeros And Coefficients Of A Polynomial