 2*v(k). Find m such that a(m) = 0.
-682, 0, 1
Factor -2757/2*r - 9/2*r**2 - 459.
-3*(r + 306)*(3*r + 1)/2
Let i = 987/730 + -139/146. Factor -i*p**3 + 0*p + 0 - 2/5*p**2.
-2*p**2*(p + 1)/5
Let t(g) = -g**2 + 4. Let v(b) = 2*b**2 + 1 + b - 4 - 6. Let p(o) = 10*t(o) + 4*v(o). Let j(s) = -s. Let q(a) = -2*j(a) - p(a). Let q(x) = 0. Calculate x.
-1, 2
Let a = -186 + 344. Suppose 300*d - 7 - 24 + 12*d**2 + 453*d - a = 0. What is d?
-63, 1/4
Solve 63 - 255/4*f + 3/4*f**2 = 0 for f.
1, 84
Let c = -303/53 - -24615/106. Let q = 228 - c. Factor -3/2 - q*s**2 - 11/4*s - 1/4*s**3.
-(s + 1)*(s + 2)*(s + 3)/4
Let a(c) be the second derivative of -35*c + 0*c**2 + 0*c**4 + 0 - 1/10*c**6 - 9/20*c**5 + 2*c**3. Factor a(m).
-3*m*(m - 1)*(m + 2)**2
Let x = -410277 + 410282. Factor 8/21*h**4 - 62/21*h + 88/21*h**2 + 16/21 - 52/21*h**3 + 2/21*h**x.
2*(h - 1)**4*(h + 8)/21
Let q(b) = -17*b**3 + 44*b**2 - 445*b + 432. Let p(m) = 9*m**3 - 18*m**2 + 222*m - 216. Let x(t) = -11*p(t) - 6*q(t). Suppose x(c) = 0. What is c?
2, 18
Let n(d) be the first derivative of 3/10*d**4 + 0*d**2 - 2/15*d**3 + 2/25*d**5 + 0*d - 1/5*d**6 + 215. What is q in n(q) = 0?
-1, 0, 1/3, 1
Let b(t) be the first derivative of -3*t**4/28 - 3093*t**3/7 - 3589812*t**2/7 - 7170348*t/7 - 7324. Factor b(s).
-3*(s + 1)*(s + 1546)**2/7
Let l(d) be the second derivative of d**5/450 + d**4/180 - 4*d**3/9 + 85*d**2/2 + 2*d + 29. Let z(r) be the first derivative of l(r). Factor z(s).
2*(s - 4)*(s + 5)/15
Determine u, given that 88 + 1870*u**2 - 12*u - 74*u - 1872*u**2 = 0.
-44, 1
Let c(s) be the first derivative of s**6/60 - 11*s**5/40 + s**4 + s**3/3 - 8*s**2 - 60*s + 62. Let l(h) be the first derivative of c(h). Factor l(y).
(y - 8)*(y - 2)**2*(y + 1)/2
Let y(a) = a**3 + 5*a**2 - 10*a + 4. Let i be y(4). Let v = 110 - i. Factor 137*r**4 + 30*r**3 + 11*r**v - 36*r**2 - 142*r**4.
-5*r**2*(r - 5)*(r - 1)
Let y(m) be the first derivative of -m**4/4 + 245*m**3/3 - 121*m**2 - 488*m - 926. What is k in y(k) = 0?
-1, 2, 244
Let y = 3845/13454 - 1/13454. Determine b, given that 4/7*b**3 - 4/7*b + y*b**4 + 6/7 - 8/7*b**2 = 0.
-3, -1, 1
Let g be (11/4)/((-1)/(-4)). Let m = 1239 + -1227. Solve -2*k**2 - m*k + 4*k**2 + 25*k - g*k = 0.
-1, 0
Suppose 17 = -q - 2*y + 3, -2*y + 4 = 0. Let j be ((-1)/q*-2)/(3/(-18)). Determine k so that j*k**2 + 4/3 + 2*k = 0.
-2, -1
Let q = 54336 + -54334. Factor 26/5*x**q + 2/5*x**4 + 24/5*x + 12/5*x**3 + 8/5.
2*(x + 1)**2*(x + 2)**2/5
Factor -4*n**2 + 50*n**3 - 9691*n - 18*n**3 + 4849*n + 4842*n - 64*n**4.
-4*n**2*(4*n - 1)**2
Solve 3900*o + 5469 - 69*o**3 + 19033 + 18086 - 284*o**2 - 66*o**3 + 139*o**3 = 0.
-7, 39
Let q(z) be the first derivative of 5*z**4/2 + 35*z**3 + 245*z**2/2 - 150*z - 11203. Factor q(c).
5*(c + 5)*(c + 6)*(2*c - 1)
Let d = 326 + -326. Suppose 4*u = 2*u + 4. Factor -4*w**3 + 2*w**2 - 3*w**u + 3*w**3 + d*w**2.
-w**2*(w + 1)
Factor 0 + 201/5*l**3 + 40*l**2 + 0*l + 1/5*l**4.
l**2*(l + 1)*(l + 200)/5
Let s(f) be the second derivative of -f**4/6 - 125*f**3/3 + 63*f - 2. Factor s(y).
-2*y*(y + 125)
Let f(n) = -28*n - 43. Let x(k) = 4*k - 1. Let o(m) = 2*f(m) + 10*x(m). Let q be o(-6). Solve q*d**2 - 32/15 + 2/15*d**4 + 32/15*d - 8/15*d**3 = 0.
-2, 2
Let a be 0/(-1)*(-5)/10. Suppose -7*r = -a*r - 14. Factor -10*b - 35*b**r + 7*b - 4 + 14 - 22*b.
-5*(b + 1)*(7*b - 2)
Let j = -561 - -553. Let z(t) = -t**2 - 14*t - 44. Let s be z(j). Factor 0 + 8/5*v - 8/5*v**2 + 4/5*v**s - 6/5*v**3 + 2/5*v**5.
2*v*(v - 1)**2*(v + 2)**2/5
Let j(g) = -5*g**2 - 80*g + 90. Let t(x) = 8*x**2 + 120*x - 135. Let a be (-3)/(-2)*(-8)/(-6) + 3. Let y(c) = a*t(c) + 7*j(c). Factor y(h).
5*(h - 1)*(h + 9)
Let p(y) = -y**5 - 3*y**3 - y**2 - y. Let w(f) = -5*f**5 - 4*f**4 - 18*f**3 - 8*f**2 - 5*f. Let u(h) = -20*p(h) + 5*w(h). Factor u(n).
-5*n*(n + 1)**4
Suppose -3*z - 6 = 3*i, -z + 2*z - i + 10 = 0. Let n be (z/4)/(3/4) + 4. Factor -10*v**4 - 14 - 12*v**n - 26*v**3 + 14.
-2*v**2*(v + 2)*(5*v + 3)
Let c be 2/((-14)/(-404)*(-100)/(-175)). Determine v, given that -c - 32*v**3 - 112*v + 92*v**2 - 137 + 286 + 4*v**4 = 0.
1, 2, 3
Let h(n) be the first derivative of 49*n**6/2 + 3213*n**5/20 - 459*n**4/4 + 107*n**3/4 - 9*n**2/4 - 817. Let h(q) = 0. What is q?
-6, 0, 1/7, 1/4
Let m = 636 + -534. Suppose -79*j - 46 = -m*j. Factor -1/3*t**j - 2*t - 8/3.
-(t + 2)*(t + 4)/3
Let i(u) be the third derivative of 0*u + 3/4*u**4 - 2 - 3/70*u**7 + 5*u**2 + 0*u**3 + 19/20*u**5 + 1/20*u**6. Factor i(y).
-3*y*(y - 3)*(y + 2)*(3*y + 1)
Let v(d) be the first derivative of -d**6/3 + 146*d**5/5 - 140*d**4 + 184*d**3 + 4812. Suppose v(s) = 0. Calculate s.
0, 2, 69
Solve -524*a**2 - 1090*a - 806*a + 1166*a + 177*a**3 - 28 - 515*a**3 - 4260*a**2 = 0 for a.
-14, -1/13
Suppose 2/13*x**5 - 8/13*x**2 + 6/13*x**3 + 8/13*x**4 + 0 - 8/13*x = 0. What is x?
-2, -1, 0, 1
Let s(k) be the third derivative of -k**5/300 - k**2 + 131*k. Let s(a) = 0. What is a?
0
Let t be 2599/1695 + (-25)/125*(1 + 0). Solve t*g**2 - 14*g + 0 = 0.
0, 21/2
Let h be 44*27/2376 - ((-2)/24*278 - 3). Factor 2/3*w**2 + 800/3 + h*w.
2*(w + 20)**2/3
Suppose 0*x - 6*x + 12 = 0. Factor -12*u**2 + 22*u**3 + 9*u + u - 18*u**3 - x*u.
4*u*(u - 2)*(u - 1)
Let q be (-18)/(-21)*42/9. Find i such that -6562 + 15*i**q + 97*i**2 + 5*i**4 + 41*i + 88*i**3 + 6568 = 0.
-3, -1/2, -2/5
Let x(f) be the second derivative of -f**7/1260 + f**6/90 - f**5/20 + f**4/9 - 4*f**3/3 + 15*f. Let s(p) be the second derivative of x(p). Factor s(v).
-2*(v - 4)*(v - 1)**2/3
Let j = -214 - -269. Suppose b**3 + 16*b**3 - j*b**2 + 215*b - 50 - 37*b**3 = 0. What is b?
-5, 1/4, 2
Suppose 11 = 4*m - 5*o, 46 = m + 3*m + 2*o. Let c(y) be the first derivative of 1/15*y**5 - 1/9*y**3 - 1/18*y**6 - m + 1/12*y**4 + 0*y**2 + 0*y. Factor c(a).
-a**2*(a - 1)**2*(a + 1)/3
Suppose 202*a = -94*a + 45*a. Let g(r) be the second derivative of 6 - r + a*r**2 - 1/66*r**4 + 1/33*r**3. What is z in g(z) = 0?
0, 1
Let h(d) be the second derivative of 6615*d**5/16 - 5565*d**4/4 + 421*d**3/8 - 3*d**2/4 - 1256*d. What is c in h(c) = 0?
1/105, 2
What is w in 6/7*w**2 - 5/7*w**3 + 0*w + 0 + 1/7*w**4 = 0?
0, 2, 3
Let l be (2/(-247))/(((-2884)/364)/103). Suppose -l*y**3 + 24/19 + 26/19*y + 0*y**2 = 0. Calculate y.
-3, -1, 4
Factor -4*a**3 - 1415*a**2 - 3205512 + 626459*a - 632714*a + 6471*a**2 - 1586373*a.
-4*(a - 633)**2*(a + 2)
Let j(s) be the first derivative of -s**6/450 + s**5/75 + s**4/10 - 16*s**3/3 + 3*s**2/2 + 97. Let k(t) be the third derivative of j(t). Factor k(w).
-4*(w - 3)*(w + 1)/5
Solve -65*c**2 + 0 - 42*c - 3/7*c**5 + 31/7*c**4 + 1/7*c**3 = 0.
-3, -2/3, 0, 7
Suppose 1054 = -8*c + 3710. Let l = 338 - c. Factor -3/2*n**3 - l*n**2 + 0 - 9/2*n.
-3*n*(n + 1)*(n + 3)/2
Suppose -4*r + 175 - 42 = 5*n, 0 = 2*n + 3*r - 49. Factor 7 - 30*p + 6 - n - 12*p**2 + 2*p**3.
2*(p - 8)*(p + 1)**2
Let z be 12/8 - 13765/14. Let c = z + 982. Determine b, given that c*b**2 + 8/7*b - 8/7*b**3 - 2/7*b**4 + 0 = 0.
-4, -1, 0, 1
Let c be (-3555)/948*12/(-5)*(-7)/(-12). Let -c + 1/4*z**2 + z = 0. Calculate z.
-7, 3
Let b(u) be the first derivative of -21/5*u**3 + 0*u + 69/20*u**4 - 3/5*u**2 - 23. Factor b(d).
3*d*(d - 1)*(23*d + 2)/5
Let q(b) = 6*b**2 - 6183*b + 9572906. Let a(v) = 7*v**2 - 6182*v + 9572920. Let f(j) = 5*a(j) - 6*q(j). Solve f(t) = 0 for t.
3094
Let i(r) be the third derivative of 8*r**2 + 0*r - 2/9*r**3 + 0 - 1/270*r**5 + 5/108*r**4. Factor i(l).
-2*(l - 3)*(l - 2)/9
Suppose -99*d + 222*d = 90*d. Solve 2/3*c**2 - 1/3*c**3 + d*c + 0 = 0 for c.
0, 2
Let n(v) be the third derivative of -v**7/1575 - 17*v**6/900 + v**5/25 + 8*v**2 - 9. Factor n(q).
-2*q**2*(q - 1)*(q + 18)/15
Let r be (-8)/((59 + -56)/((-7)/4 + 1)). Let p(l) be the second derivative of 0*l**r - 4/39*l**3 - 26*l - 1/78*l**4 + 0. Suppose p(u) = 0. Calculate u.
-4, 0
Suppose -139*y - 12 = -143*y. What is j in -16*j**5 - 20*j + 217*j**4 + 28*j**y - 44*j**2 + 8*j - 173*j**4 = 0?
-1, -1/4, 0, 1, 3
Suppose -2/11*m**3 + 382/11*m**2 + 53016/11 - 18800/11*m = 0. What is m?
3, 94
Let i(j) be the third derivative of j**6/300 + j**5/15 - 11*j**4/60 - 2739*j**2. Factor i(u).
2*u*(u - 1)*(u + 11)/5
Let w(y) = y**3 - 31*y**2 + 28*y + 62. Let m be w(30). Factor 10*r**m + 85956 - 5*r**3 + 125*r - 85891 + 45*r**2.
-5*(r - 13)*(r + 1)**2
Factor -5*c**5 + 17*c**3 - 25*c**3 - 25*c**4