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Let x = 195837 + -1370847/7. What is v in 69/7*v**4 + 0 + 3*v**2 - 90/7*v**3 + x*v - 12/7*v**5 = 0?
-1/4, 0, 1, 4
Let v(q) = 124*q + 141. Let i be v(-1). Let s(b) be the second derivative of -1/2*b**3 + 1/12*b**4 + 0*b**2 + 0 - i*b. Find t, given that s(t) = 0.
0, 3
Let l be (32/40)/(34 - (49 - 16)). Factor -l + 1/5*r**4 - 8/5*r - 3/5*r**2 + 2/5*r**3.
(r - 2)*(r + 1)**2*(r + 2)/5
Determine s so that 72*s + 1/4*s**5 + 56*s**2 + 21*s**3 + 36 + 15/4*s**4 = 0.
-6, -3, -2
Suppose -64/7 - 8/7*i + 2/7*i**3 + 16/7*i**2 = 0. Calculate i.
-8, -2, 2
Suppose -226 + 240 = -2*t. Let o(h) = -15*h**3 + 23*h**2 - 15*h - 7. Let g(w) = 7*w**3 - 11*w**2 + 7*w + 3. Let u(p) = t*g(p) - 3*o(p). Factor u(a).
-4*a*(a - 1)**2
Let q(d) be the third derivative of d**7/6 + 113*d**6/12 + 464*d**5/3 + 320*d**4/3 + 3*d**2 + 134. Suppose q(m) = 0. Calculate m.
-16, -2/7, 0
Let w(y) = -5*y**4 + 41*y**3 + 6*y**2 - 3. Let o(d) = -6*d**4 + 42*d**3 + 8*d**2 - 4. Let v(z) = 3*o(z) - 4*w(z). Let v(l) = 0. Calculate l.
0, 19
Let a(b) be the second derivative of b**7/357 - b**6/51 - 11*b**5/170 + 73*b**4/102 - 98*b**3/51 + 40*b**2/17 + 1048*b - 1. Determine v, given that a(v) = 0.
-4, 1, 2, 5
Let x(i) = -2*i**3 + 19*i**2 + 8*i + 16. Let u be x(10). Let c be (2/(-18))/(u/6). Factor -1/6*y**4 + 0*y + 1/3*y**2 + 0*y**3 - c.
-(y - 1)**2*(y + 1)**2/6
Let w(p) = 3*p**2 + 12*p + 39. Let t(c) = c**2 - c + 3. Let m(x) = 2*t(x) - w(x). Find d such that m(d) = 0.
-11, -3
Let h(j) = -2*j**3 + 8*j**2 + 11*j - 19. Let m be h(4). Let -o**2 + 3*o + 5*o - m*o - 4*o + 46 = 0. Calculate o.
-23, 2
Let a(x) be the third derivative of -1/3*x**3 + 1/60*x**5 - 2*x + 0 - 12*x**2 + 1/24*x**4. Determine r, given that a(r) = 0.
-2, 1
Suppose 0 = 3*q - 3*d - 21, -q - 4*d + 3 - 16 = 0. Let a be (4/(64/120))/(6/4). Factor 21*k**2 + a*k**5 - 3*k**3 + 15*k**4 - 36*k**2 - 2*k**q.
5*k**2*(k - 1)*(k + 1)*(k + 3)
Let x(b) = 14*b**2 - 6*b - 6. Let i(m) = 2*m**2 - m. Let n(u) = -5*i(u) + x(u). Let q be n(2). Factor q + 8/3*g + 2/9*g**2.
2*(g + 6)**2/9
Let a(t) be the third derivative of -t**5/80 + 979*t**4/8 - 958441*t**3/2 - 29*t**2 + 18*t + 2. Factor a(i).
-3*(i - 1958)**2/4
Let m = 53/352 - -439/1760. Factor -4/5*r + m*r**2 + 0.
2*r*(r - 2)/5
Let p = 1027 - 1033. Let f be ((-77)/14 - p)*1*10. Find g such that 5/4*g + 5*g**2 - 5/4*g**3 - f = 0.
-1, 1, 4
Let z be ((-40)/8)/5 - 0. Let f be ((-124)/248)/(z + 2 - 2). Solve 1/2*d - f*d**2 + 1 = 0.
-1, 2
Factor -2178/7*i**2 + 8676/7*i + 3/7*i**3 - 8664/7.
3*(i - 722)*(i - 2)**2/7
Let v = 142827 + -142825. Suppose -2/7 - 4/21*q + 2/21*q**v = 0. What is q?
-1, 3
Let t(f) be the third derivative of f**5/270 - 553*f**4/108 - 2338*f**2. Factor t(r).
2*r*(r - 553)/9
Suppose -24 = 37*s - 98. Let z(f) be the third derivative of 0 + 1/10*f**6 + 0*f**3 + 1/70*f**7 - 9*f**s + 0*f - 1/2*f**4 - 1/20*f**5. Factor z(p).
3*p*(p - 1)*(p + 1)*(p + 4)
Let k(h) = 1. Let n(i) = -2*i**3 + 8*i**2 + 12*i - 11. Let p(g) = g - 3. Let l(o) = -n(o) - 2*p(o). Let s(t) = 6*k(t) + 2*l(t). Find z such that s(z) = 0.
-2, 1, 5
Let j(o) = -150*o**2 + 8*o - 6. Let x be j(1). Let z be (-222)/x + 1 + (-4)/2. Factor 3/4*a**2 + 7/4*a + z.
(a + 2)*(3*a + 1)/4
Let t(p) = -5*p**2 + 10*p + 13. Let c(b) be the second derivative of -25*b**4/12 + 25*b**3/3 + 32*b**2 - 10*b. Let v(s) = 2*c(s) - 11*t(s). Factor v(q).
5*(q - 3)*(q + 1)
Let s be 12930/(-6896)*(-4)/10. Factor s*c**3 - 9/2*c + 0 - 15/4*c**2.
3*c*(c - 6)*(c + 1)/4
Suppose 0 = 29*h - 298 + 95. Let d be 12/42 - (-12)/h. Determine t so that 2/19*t + 2/19*t**d + 0 = 0.
-1, 0
Suppose -2*i - i + p = -i, -5*p = 2*i. Let m(f) be the third derivative of -1/450*f**5 + 0 + i*f + 0*f**3 + 20*f**2 + 1/45*f**4. What is n in m(n) = 0?
0, 4
Let h be (2 + -8)*(-2)/6. Let q = 451 + -449. Factor -8*g + 2*g - h*g**q + 3*g**2 - 4*g**2.
-3*g*(g + 2)
Let l be -4*(-6)/(-12)*-1. Let -1978*u - u**l + 10 - u**2 + 1970*u = 0. Calculate u.
-5, 1
Factor -31941 - 3/7*g**2 + 234*g.
-3*(g - 273)**2/7
Suppose 3*p - 56 + 29 = 0. Let y be (5*8/20)/(p/15). Factor -2/9*s**5 + 250/9*s**2 + 0*s + y*s**4 + 0 - 50/3*s**3.
-2*s**2*(s - 5)**3/9
Let l(z) = -z**3 + 14*z**2 - 11*z - 20. Let d be l(13). Determine i, given that -30193*i**4 + 8*i**2 - d*i**3 + 30195*i**4 - 2*i**3 = 0.
0, 2
Let a(c) = -c**2 - 8*c - 5. Let l be a(-7). Suppose -4 - l = -2*n. Find r, given that 4*r + 109 + 5*r**2 - 109 + r**2 + 2*r**n = 0.
-2, -1, 0
Let j(m) = m**4 + 3*m**3 + m**2 + m. Let h(v) = -4*v**5 - 4*v**4 + 9*v**3 + 4*v**2 + 5*v. Let p be 2/(-6) - (-76)/57. Let b(i) = p*h(i) - 5*j(i). Factor b(r).
-r**2*(r + 1)**2*(4*r + 1)
Let s = -826 - -828. Let a be 1*7 + 57/(-95). Factor -a - 16/5*g - 2/5*g**s.
-2*(g + 4)**2/5
Let f(v) = v**2 + 5*v - 4. Let u be f(1). Factor -3*a + 5*a**u - 194 + 184 + 8*a.
5*(a - 1)*(a + 2)
Let f(u) = -20*u**3 + 45*u**2 - 6*u - 4. Let l(x) = -x**3 - x**2 - 3*x. Let n(g) = -f(g) - 3*l(g). Factor n(s).
(s - 1)**2*(23*s + 4)
Let v(j) be the second derivative of -1/18*j**4 + 2/35*j**5 + 0*j**2 + 0 + 1/63*j**3 + 22*j. Factor v(f).
2*f*(3*f - 1)*(4*f - 1)/21
Let v(k) = -2*k**2 - 8*k + 45. Let s be v(5). Let h be (-19 - -10)/s + 9/5. Determine y, given that -9/4*y**3 + 0 + 3/2*y**h + 3/4*y**4 + 0*y = 0.
0, 1, 2
Let a(d) = 5*d**2 + 23*d + 26. Let w(u) = 8*u**2 + 21*u + 25. Suppose 8 + 3 = -2*x - z, 3*z + 30 = -5*x. Let n(c) = x*a(c) + 2*w(c). Let n(m) = 0. What is m?
-1, 28
Let n(t) be the first derivative of -t**4/18 + 14*t**3/9 - 8*t**2 + 136*t/9 + 1164. Factor n(k).
-2*(k - 17)*(k - 2)**2/9
Factor 3*c**2 + 6 - 948*c + 227*c - 726 - 2*c**2 - 2*c**2.
-(c + 1)*(c + 720)
Let g(n) = -2*n**3 - n + 1. Let s(a) = 35*a**4 + 275*a**3 + 580*a**2 + 115*a + 25. Let v(x) = -25*g(x) + s(x). Factor v(c).
5*c*(c + 2)*(c + 7)*(7*c + 2)
Let i(z) be the second derivative of 2/3*z**4 - 1/5*z**5 + 0*z**2 - 1/21*z**7 - 52*z + z**3 - 4/15*z**6 + 1. Suppose i(n) = 0. Calculate n.
-3, -1, 0, 1
Let l be (-275)/(-30) - (-25)/30. Factor -20*h**2 + 79*h**5 - 10*h**4 - 5*h - 30*h**3 - 84*h**5 - l*h**4.
-5*h*(h + 1)**4
Let a(b) be the second derivative of b**8/20160 - b**6/720 - b**5/180 + 29*b**4/12 + b**3/6 - b + 9. Let g(h) be the third derivative of a(h). Factor g(j).
(j - 2)*(j + 1)**2/3
Let 260/3*i + 2/3*i**5 + 6*i**3 + 22/3*i**4 - 32 - 206/3*i**2 = 0. Calculate i.
-8, -6, 1
Let y(o) be the third derivative of -o**7/70 + 27*o**6/40 + 363*o**5/20 + 277*o**4/8 - 333*o**3 - 1955*o**2. Suppose y(x) = 0. What is x?
-9, -2, 1, 37
Let n(q) be the third derivative of -2/9*q**4 + 0*q - 32/27*q**3 + 1/36*q**5 - 1/1080*q**6 - 9*q**2 - 10. Factor n(k).
-(k - 8)**2*(k + 1)/9
Let i(c) be the third derivative of c**6/40 - 19*c**5/20 + 99*c**4/8 - 81*c**3/2 + 25*c**2 + 20*c. Determine n, given that i(n) = 0.
1, 9
Let j be (46/5 - (-18 - -27))*220/24. Factor 1/6*b**2 - 2*b + j.
(b - 11)*(b - 1)/6
Let p(w) = -5*w**2 + 1367*w - 4. Let z(k) = -k**2 - 113*k - 1. Let m(x) = p(x) - 4*z(x). What is l in m(l) = 0?
0, 1819
Let l(u) be the first derivative of -6*u**5/25 + 39*u**4/20 + 23*u**3/5 + 12*u**2/5 + 377. Let l(x) = 0. Calculate x.
-1, -1/2, 0, 8
Let c(a) be the second derivative of -a**8/420 + a**7/210 - a**3/6 - 86*a**2 + 3*a + 34. Let w(n) be the second derivative of c(n). Factor w(v).
-4*v**3*(v - 1)
Let c be 595/(-2312) - 3/(-8). Suppose -c*t**2 - 56/17*t - 392/17 = 0. Calculate t.
-14
Let g(a) be the second derivative of a**5/150 + 11*a**4/30 + 59*a**3/45 - 31*a**2/5 - 950*a. Factor g(m).
2*(m - 1)*(m + 3)*(m + 31)/15
Let p be 4*-3*(1005/(-60) - -18)*(-2)/10. Solve -1/5*c**p - 11/5*c**2 - 38/5*c - 8 = 0.
-5, -4, -2
Let f(p) = -p + 10. Let q be f(8). Suppose -4*u + 108 = 4*m + 80, 0 = 4*m - 28. Factor -7/3*c**3 + u - 2/3*c - 3*c**q.
-c*(c + 1)*(7*c + 2)/3
Let h(f) be the third derivative of 5*f**5/12 + 445*f**4/2 - 1070*f**3/3 + 2743*f**2. Factor h(z).
5*(z + 214)*(5*z - 2)
Factor -25856/5*u + 4/5*u**2 + 41783296/5.
4*(u - 3232)**2/5
Determine j, given that 207/2*j**2 + 9/8*j**5 + 813/4*j**3 + 51 - 309/2*j**4 - 1635/8*j = 0.
-1, 1/3, 1, 136
Let t(c) be the second derivative of 1/6*c**6 + 0 + 0*c**2 + 40*c**3 + 50/3*c**4 - 21*c + 11/4*c**5. Solve t(i) = 0.
-4, -3, 0
Let w(f) be the second derivative of -f**5/240 + 7*f**4/48 + 5*f**3/8 - 203*f**2/2 + 3*f - 59. Let c(y) be the first derivative of w(y). What is m in c(m) = 0?
-1, 15
Let z(c) =