Butinthecaseofpolynomialsyouaredividingnumbers

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Unformatted text preview: the polynomials get big. For bigger multiplications, vertical is usually faster, and is much more likely to give you a correct answer. Simplify (4x2 – 4x – 7)(x + 3) Here's what it looks like when done horizontally: (4x2 – 4x – 7)(x + 3) = (4x2 – 4x – 7)(x) + (4x2 – 4x – 7)(3) = 4x2(x) – 4x(x) – 7(x) + 4x2(3) – 4x(3) – 7(3) = 4x3 – 4x2 – 7x + 12x2 – 12x – 21 = 4x3 – 4x2 + 12x2 – 7x – 12x – 21 = 4x3 + 8x2 – 19x – 21 4x2 – 4x – 7 X x + 3 12x2 – 12x – 21 + 4x3 – 4x2 – 7x . 4x3 + 8x2 – 19x ­21 Vertical Method Products of Sums and Differences Difference of two squares: (x+y)(x­y) = x2­xy +xy –y2=x2–y2 Example: (t+5)(t­5) = t2­25 (2x+3y)(2x­3y)=4x2­9y2 (x+y)2= x2 + xy + xy + y2 = x2 + 2xy + y2 (t+6)2 = t2 + 12t + 36 (2a+4b)2= 4a2 +16ab + 16b2 Squaring a Binomial Simplify (t+3)(t­1)(t+2) (t­1)(t+2)= t2 + 2t – 1t – 2 = t2 + 1t – 2 (t+3)(t2 + 1t – 2)= t(t2 + 1t – 2)+ 3(t2 + 1t – 2)= t3 + 1t2 – 2t + 3t2 + 3t – 6= t3 + 4t2 + t ­ 6 Given f(x) = 2x2 + 3...
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