Adding and Subtracting Polynomials

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Presentation transcript:

Adding and Subtracting Polynomials Really just means “Combine Like Terms” Adding: Combine the terms with Same Variable and Same Exponent. DO NOT change the variable or exponent… just add coefficients (5x3 + 7x2 – 6x + 8) + (2x3 – x2 – 2) Subtracting: The subtraction gets distributed through the entire 2nd polynomial CHANGE ALL THE SIGNS Then add like above (9x2 – 7x + 2) - (4x2 – 2x – 8) (9x2 – 7x + 2) + - 4x2 + 2x + 8

Multiply by a Monomial Distribute the monomial to EVERY term of the polynomial. Multiply the coefficients Add the exponents Watch out for signs Examples: 4t (t + 6) 4t2 + 24t (c+8) 2c 2c2 + 16c 6y(y2 + 7y + 2) 6y3 + 42y2 + 12y -3g2 (-9g3 + 4g) 27g5 – 12g3 You Try: 10x (-4x2 + x – 3) CHALLENGE: find the shaded area 6x3 ( 3x2 – x + 10) 3x2 + 5x - 1 8z2 (4z3 + 2z2 – 5z) 2x2 + 4x 7x 3x

Multiply binomials Method #1: List each binomial along top and side of a box In each section, multiply the monomials together Check for “like terms” to add List answers in standard form x +2 Exp 1: (x + 2) (x+1) x2 +3x +2 x x2 2x +1 x 2 b -4 Exp 5: (5b+9)(b-4) 5b2 -20b 5b 5b2 -11b -36 9 9b -36 7y -3x 9 14xy -6x2 2x Exp 9:(2x+5y)(7y-3x) 5y 35y2 -15xy -6x2 – 1xy + 35y2

Multiplying Binomials (Part 2) F.O.I.L. (A shortcut) This is an option for multiplying binomials WITHOUT drawing a box. The letters remind us which terms to multiply so that we include all of them. First Outside Inside Last Still Multiply each set of terms together then ADD all the parts. Look for LIKE terms to combine in the middle. (3x + 6) (2x + 5) FIRST: (3x)(2x) = 6x2 OUTSIDE: (3x)(5) = 15x (3x + 6) (2x + 5) (3x + 6) (2x + 5) INSIDE: (6)(2x) = 12x 6x2 + 27x + 30 (3x + 6) (2x + 5) LAST: (6)(5) = 30 EX: (4x+5)(3x-7) 12x2 -28x +15x -35 12x2 -13x - 35 EX: (6x+1)(4x-9) 24x2 -54x +4x -9 24x2 -50x - 9