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Polynomials

Home > PowerPoint Slides > Polynomials
Published in: Mathematics
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Topic of this ppt is about Polynomials of Class IX.

Chetan G / Delhi

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Qualification: B.Tech/B.E. (Kurukshetra University , Kurukshetra - 2016)

Teaches: Chemistry, Mathematics, All Subjects, English, Science

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  1. 5.3 — Polynomials and Polynomial Functions Definitions Term: a number or a product of a number and variables raised to a power. 3, 5x2 — 2x, 9x2y Coefficient: the numerical factor of each term. 5x2 — 2x, 9x2y Constant: the term without a variable. -6, 5, 32 3, Polynomial: a finite sum of terms of the form axn, where a is a real number and n is a whole number. -15x3 + -5 21y6 -7/-2/ +6y
  2. 5.3 — Polynomials and Polynomial Functions Definitions Monomial: a polynomial with exactly one term. 2 2x4 ax —9m, 9x2y Binomial: a polynomial with exactly two terms. X — 8, r —3, 5X2 + 2X, -—2X -k 9X2y Trinomial: a polynomial with exactly three terms. r5 + 3 r — 3, 5x2 -k 2x — 7
  3. 5.3 — Polynomials and Polynomial Functions Definitions The Deqree of a Term with one variable is the exponent on the variable. 4 The Deqree of a Term with more than one variable is the sum of the exponents on the variables. —7X2y 2X4y2 —9mn z 6 3 10 The Deqree of a Polynomial is the greatest degree of the terms of the polynomial variables. 2x3 — 3x+7 3, 2x4y2 + 5x2y3 — 6x 6
  4. 5.3 — Polynomials and Polynomial Functions Practice Problems Identify the degrees Of each term degree Of the and the polynomial. 3 4a2b4 + 3a3b5 — 9b 4 +4 2 1 3 4x5y4 + 5x4y6 6 8 8 9 10 — 6X3y3 -k y 6 2 10
  5. 5.3 — Polynomials and Polynomial Functions Practice Problems Evaluate each polynomial function f (x) = 3x2 —10 f(-l) 3(-1) —10 3-1—10 3—10 6 y 2 1 y — 20 54 33 —20 87 — 20 67
  6. 5.4 — Polynomials and Polynomial Functions Multiplication Multiplying Monomials by Monomials 10x 9x = Examples: 90x2 8x3 1 -88x10 5x5
  7. 5.4 — Polynomials and Polynomial Functions Multiplication Multiplying Monomials by Polynomials Examples: 4X(X2 + + 3) = 4 X 3 +16X2 -k 12X 8X(7X4 -k 56X5 -I-8x -x + 2) = -15x5+5x 4—10x3
  8. 5.4 — Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples: (x + 5) (x2 + lox — 3) = x3 +10x2_3x+5x2+50x —15 12x 12x X3 +15X2 +47 X —15 3 —16X2+3X2—4X +15X —20 = 3 —13X2 +1 IX —20
  9. 5.4 — Multiplying Polynomials Special Products Multiplying Two Binomials using FOIL First terms Outer terms Inner terms Last terms (x +3) (x +4) = x 2+4 x +3 x +12 x2 +7 x +12 -28 = -28
  10. 5.4 — Multiplying Polynomials Special Products Multiplying Two Binomials using FOIL First terms Outer terms Inner terms Last terms 2y2 -4) = 2y3-8y2+3y -12 2 y 3—8y2+3y +4)2 -1-4 y 2-l-4y2 +16 = y -12 +8y2 +16
  11. 5.4 — Multiplying Polynomials Special Products Squaring Binomials 2 — a2 — 2ab + b2 = 16x2 +2(-20x) +25 = (—3x — 6) 2 16X2 — 40X + 25 — 9X2 +2 (18X) +36 =
  12. 5.4 — Multiplying Polynomials Special Products Multiplying the Sum and Difference of Two Binomials 2 x2 —81 = 9x2-15x +15x-25 = 9x2 -25 x 2 — 64 25x2 -169
  13. 5.4 — Multiplying Polynomials Special Products Dividing by a Monomial where c 0 6 —12x4 21x8 + 9x 21x8 12x4 7x5 +3x
  14. Extra Problems
  15. 5.4 — Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples: x2 +10x + 5x +50 (x + + 10) x2 +15 x +50 — 12X2— 16X-k 15X— 20 12x2 —x —20
  16. 5.4 — Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples: x + 3) (2x2 —5x+4) 2X3 —5X2 -k4x+6X2 —15X +12 = 2X3 -I-X2 —1 IX +12
  17. 5.4 — Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples: 2

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