+ 3415. Let o(l) be the third derivative of -3/4*l**f - 1/40*l**6 + 3*l**2 + 1/15*l**5 + 1/420*l**7 + 0*l + 1/8*l**4 + 0. Solve o(c) = 0 for c.
-1, 1, 3
Factor 2*b + 12*b**3 + 3*b**2 - 5*b**3 + 3*b**2 - 9*b**3 - 6.
-2*(b - 3)*(b - 1)*(b + 1)
Let v(s) = -2*s**4 + 10*s**3 - 22*s**2 + 14*s - 4. Let o(t) = -t**3 + t - 1. Let c be (-18)/4 + (-6)/(-12). Let z(y) = c*o(y) + v(y). Factor z(a).
-2*a*(a - 5)*(a - 1)**2
Let g be ((-36)/270)/((8 + -18)/30). Factor -8*o + 36/5*o**2 + g*o**4 + 16/5 - 14/5*o**3.
2*(o - 2)**3*(o - 1)/5
Let u(c) be the first derivative of -c**5/10 + 5*c**4/8 - c**3 - c**2 + 4*c - 1031. Factor u(n).
-(n - 2)**3*(n + 1)/2
Let g(a) be the second derivative of a**4/12 + a**3 + 4*a**2 + 15*a. Let m be g(-5). Factor -5*y**4 - 9*y - 5*y + 10*y**3 + m*y - 20 - 9*y + 15*y**2.
-5*(y - 2)**2*(y + 1)**2
Let n(p) be the second derivative of 0 + 0*p**2 - 1/3*p**3 - 1/6*p**4 + 95*p. Factor n(y).
-2*y*(y + 1)
Let v(m) be the first derivative of m**7/140 - 7*m**6/16 - m**5/40 + 35*m**4/16 - 9*m**2/2 - 7*m + 265. Let q(h) be the second derivative of v(h). Factor q(j).
3*j*(j - 35)*(j - 1)*(j + 1)/2
Determine i so that -1/5 + 4324/5*i**3 - 2116/5*i**4 - 2301/5*i**2 + 94/5*i = 0.
1/46, 1
Let o be (-1 + 5)/(0 + 2/5). Let y = 35 - o. Factor -12*d**2 + 27 + y - 64 + 51*d.
-3*(d - 4)*(4*d - 1)
Let f(l) be the first derivative of 2*l**3/9 - 322*l**2/3 + 214*l - 181. Factor f(k).
2*(k - 321)*(k - 1)/3
Determine k, given that 2/5*k**4 - 1/5*k**5 + 0 + 3*k**3 + 4/5*k**2 - 4*k = 0.
-2, 0, 1, 5
Let a = 48 + -52. Let t(n) = -5*n**3 + 18*n**2 - 53*n + 4. Let r(w) = 6*w**3 - 19*w**2 + 54*w - 5. Let x(b) = a*r(b) - 5*t(b). Suppose x(k) = 0. What is k?
0, 7
Suppose 0 = -2*f + u + 3, 4*u = -3*f - 16 + 4. Let l = -155688 + 467068/3. Determine s, given that -16/3 + 4/3*s**3 + f*s + 28/3*s**2 - l*s**5 - 4*s**4 = 0.
-2, -1, 1
Let y(o) be the second derivative of -o**7/21 - 9*o**6/5 - 114*o**5/5 - 392*o**4/3 - 320*o**3 - 8119*o. Determine b so that y(b) = 0.
-15, -4, 0
Let c be ((-235)/(-47))/(-8 + 58). Factor -1/5 - c*x**2 + 3/10*x.
-(x - 2)*(x - 1)/10
Let q(j) be the first derivative of 5*j**4/2 + 256*j**3/3 - 55*j**2 - 156*j + 179. Factor q(y).
2*(y - 1)*(y + 26)*(5*y + 3)
Let b(x) = -x**3 + 4*x**2 - 6*x + 9. Let t(n) = 2*n + 43. Let y be t(-20). Let m be b(y). Factor m*p**2 - 2/9*p**5 - 2/9*p**3 + 0*p + 4/9*p**4 + 0.
-2*p**3*(p - 1)**2/9
Let m(w) = -62*w - 212. Let v be m(-22). Find o such that -39*o**3 + 354*o**3 + 9*o**3 - v + 119*o**3 - 1472*o**2 + 37*o**3 + 2112*o + 4*o**5 - 72*o**4 = 0.
2, 6
Suppose 0 = -131*q - 173*q. Suppose 5*x - 16 = -2*m - 0*m, -x = 5*m - 17. Factor 0 + 1/2*k**4 + q*k + 2*k**2 + x*k**3.
k**2*(k + 2)**2/2
Suppose 1107 = 17*m + 24*m. Suppose -27 = 4*o - 151. Solve o*a**3 + 4*a - 7*a**2 - a**2 - m*a**3 = 0.
0, 1
Let m(f) be the third derivative of -1/2*f**4 + 0*f**5 + 0*f - 38 - 4/3*f**3 + 1/30*f**6 + f**2. Let m(b) = 0. What is b?
-1, 2
Let n = 2305/1652 - -55/1652. Factor 4/7 - n*z + 6/7*z**2.
2*(z - 1)*(3*z - 2)/7
Let x = 431/1075 - 1/1075. Let z(l) be the first derivative of -1/15*l**3 + x*l**2 + 0*l - 18. Factor z(t).
-t*(t - 4)/5
Let b(c) be the first derivative of c**6/3 - 16*c**5/5 + 8*c**4 - 4*c**3/3 - 17*c**2 + 20*c + 15246. What is j in b(j) = 0?
-1, 1, 2, 5
Let x = 98 + -95. Solve m**x - 20 - 16*m + 2*m**3 - m**2 - 2*m**3 = 0.
-2, 5
Let c(m) = 2*m**5 - 16*m**4 + 27*m**3 + 105*m**2 - 378*m + 324. Let u(g) = -g**3 + g**2. Let r(p) = -2*c(p) - 6*u(p). Factor r(l).
-4*(l - 3)**3*(l - 2)*(l + 3)
Suppose 0 = -180*p + 279 + 171 + 270. Let o(j) be the third derivative of 18*j**2 + 0*j + 5/8*j**p + 0 + 0*j**3 + 1/12*j**5. Factor o(n).
5*n*(n + 3)
Let z(w) = -w**3 - w + 4. Let l(r) = 19*r**2 - 27*r**2 + 24*r + 22*r - 5*r**2 - 37*r**2 + 6*r**3 - 4. Let o(v) = -l(v) - z(v). Factor o(f).
-5*f*(f - 9)*(f - 1)
Suppose -3*b + 7*f - f + 24 = 0, 8 = -2*f. Factor b - 8/5*n**3 + 48/5*n + 44/5*n**2 - 4/5*n**4.
-4*n*(n - 3)*(n + 1)*(n + 4)/5
Let f = -202 + 211. What is o in 16 - 7 + 4 + 3*o**3 + 34*o + 8*o**2 + 7 - f*o**3 = 0?
-1, 10/3
Let s(j) be the third derivative of -164*j**2 + 2/105*j**7 + 1/2*j**4 - 1/10*j**6 + 0*j + 0*j**3 + 0 - 1/15*j**5. Determine q so that s(q) = 0.
-1, 0, 1, 3
Suppose 4*s - 6*s = 4*g - 112, s - 29 = -g. Let a = g - 25. Factor 3/2*c - 7/2*c**a + 5/2*c**4 - 3/2*c**3 + 1.
(c - 1)**2*(c + 1)*(5*c + 2)/2
Let l(c) = -c**2 + 4*c + 7. Let o = 471 - 472. Let k be l(o). Suppose 14/5*s**5 - 2/5*s - 52/5*s**4 + 4/5 + 68/5*s**3 - 32/5*s**k = 0. What is s?
-2/7, 1
Let m(b) be the third derivative of -b**6/120 - 19*b**5/60 - 25*b**4/8 + 10*b**3/3 + 8*b**2 + 15*b. Let s be m(-6). Find k such that -1/4*k**s + 0 - 7/4*k = 0.
-7, 0
Let s be ((-74)/3)/((-12)/18). Let b = s + -35. Determine m so that -4*m - m**2 - 2*m**b + 4*m + 5*m + 2 = 0.
-1/3, 2
Let k(f) = 20*f**3 - 56*f**2 - 192*f - 128. Let b(i) = i**4 + 38*i**3 - 112*i**2 - 384*i - 256. Let m(t) = 4*b(t) - 7*k(t). Determine q so that m(q) = 0.
-4, -2, -1, 4
Let o(s) be the first derivative of -3*s**2/2 + 15*s - 7. Let n be o(4). Let 0*z + 14*z**3 + 3*z**4 + 0*z - 8*z**n = 0. What is z?
-2, 0
Let s(x) = 5*x**2 - 3*x + 1. Let w be s(1). Let c be ((-80)/(-60))/(-4 + w + 2). Factor -1/3*r**4 - 1/3*r**3 + c*r**2 + 0 + 4/3*r.
-r*(r - 2)*(r + 1)*(r + 2)/3
Factor 3*b**4 + 2*b**4 + 125*b**2 - 1218 - 2018 - 105*b**3 - 8594 + 6045*b.
5*(b - 13)**2*(b - 2)*(b + 7)
Let v(h) be the second derivative of h**5/190 - 163*h**4/57 + 26569*h**3/57 + 3985*h. Solve v(m) = 0.
0, 163
Let w(v) be the second derivative of 2*v**6/135 - 5*v**5/9 + 119*v**4/27 - 190*v**3/27 + 2*v + 2068. Suppose w(r) = 0. What is r?
0, 1, 5, 19
Let v(r) = 4*r - 22. Let j be v(6). Suppose j*q = 4 + 2, 2*q - 4 = y. Factor -5*p**y + 7*p**2 - 5*p**3 + 3*p**2.
-5*p**2*(p - 1)
Suppose 882*l = 884*l - 3*b - 13, -6*l - 3*b + 3 = 0. Solve -8*w - 5/3*w**2 - 1/3*w**4 + 12 + l*w**3 = 0.
-2, 2, 3
Let t(h) be the first derivative of 6*h**2 + 1/9*h**3 + 108*h - 70. Factor t(c).
(c + 18)**2/3
Let -29768/13 + 7434/13*a**2 - 976/13*a + 2/13*a**4 + 244/13*a**3 = 0. Calculate a.
-61, -2, 2
Suppose 8*p = 27*p + 152. Let h be (-3)/14 + (p - 102/(-12)). Factor 8/7*s + h*s**2 + 8/7.
2*(s + 2)**2/7
Let d be (-10 - -12)*(-9 - (-168)/16). Find j such that -11/7*j - 4/7 + 1/7*j**4 - 1/7*j**d - 9/7*j**2 = 0.
-1, 4
Let -4*a**3 - 13099*a**2 + 30*a**3 + 13055*a**2 + 192 - a**4 - 104*a = 0. What is a?
-2, 2, 24
Suppose -11*s = 49*s - 4 - 116. Suppose 24 = -x + 9*x. Factor 80/7*v**s - 16/7*v + 0 - 100/7*v**x.
-4*v*(5*v - 2)**2/7
Let f be -4 - (-18)/3 - (-2)/1. Find s, given that s**f + 2101*s**2 + 15972*s + 132*s**3 - s**4 + 3*s**4 + 77*s**2 + 43923 = 0.
-11
Let r(f) be the third derivative of f**8/784 - 6*f**7/245 + 9*f**6/280 + 11*f**5/70 - 313*f**2. What is l in r(l) = 0?
-1, 0, 2, 11
Let d = -1069567 - -4278313/4. Factor 11/4*v**3 + 27/2 + 1/4*v**4 + 81/4*v + d*v**2.
(v + 2)*(v + 3)**3/4
Let u(j) be the third derivative of j**6/80 + 33*j**5/40 + 59*j**4/16 - 93*j**3/4 + 2*j**2 - 553. Find w such that u(w) = 0.
-31, -3, 1
Let q(j) = -4*j**4 + 83*j**3 - 781*j**2 + 2322*j - 2344. Let x(s) = s**4 - s**3 + 5*s**2 - 1. Let d(h) = -3*q(h) - 15*x(h). Factor d(v).
-3*(v - 3)**3*(v + 87)
Suppose 5 = -3*k + 4*h + 2, -1 = 2*k - 3*h. Let q be 42/24 + 1/(-20)*k. Factor 4/11 - 2*w**3 - 14/11*w - 40/11*w**q.
-2*(w + 1)**2*(11*w - 2)/11
Let s be (-1696)/318*(-9)/12. Solve 16/5*r**2 + 2/15*r**s + 32/15 - 16/15*r**3 - 64/15*r = 0 for r.
2
Factor -2 + 11154*p**3 + 238*p + 6695/2*p**2.
(13*p + 2)**2*(132*p - 1)/2
Suppose -4*o - 20 = 64. Let b be 140/o - (1 + -8). Suppose 0 - b*i - 5/3*i**2 - 7/3*i**3 - i**4 = 0. Calculate i.
-1, -1/3, 0
Let j(z) = 2*z**3 + 14*z - 44. Let s be j(6). Let d = s - 468. Factor 0 + 0*x**2 + 0*x + 2/11*x**3 - 2/11*x**d.
-2*x**3*(x - 1)/11
Let v(s) = 4*s**3 + 21*s**2 - 64*s - 156. Let q(z) = -z**3 - 5*z**2 + 16*z + 40. Let u(f) = -9*q(f) - 2*v(f). Solve u(g) = 0 for g.
-4, -3, 4
Let q(a) = 2*a**2 - 2*a - 4. Let d = 50 + -42. Let m(b) = -5*b + 8*b + 4*b**2 - d - 7*b. Let y(i) = -3*m(i) + 5*q(i). Factor y(z).
-2*(z - 2)*(z + 1)
Let i = -167/412 + 135/206. Factor -i*q**2 - 3/2*q + 0.
-q*(q + 6)/4
Let m be (-36)/378 - (1 + -8 - (4 - (-935)/(-105))). Suppose -79/9*g**3 + 19/9*g**4 - 100/9*g - 1/9*g**5 + 133/9*g**m + 28/9 = 0. Calculate g.
1, 2, 14
Find p 