 694*l**2. Determine r, given that v(r) = 0.
-9/2, -3, 2
Solve 4/3*v**5 + 780*v**2 - 4/3*v**4 + 864 - 132*v**3 - 1512*v = 0.
-12, 1, 3, 6
Let r = -4 + 6. Find t such that 30*t + 372*t**4 - 180*t**5 + 107*t**4 + 301*t**4 - 85*t**r - 290*t**3 - 135*t**4 = 0.
-1/3, 0, 1/4, 2/3, 3
Let p(y) be the second derivative of -y**4/3 + 498*y**3 + 1496*y**2 - 1683*y - 1. Suppose p(c) = 0. What is c?
-1, 748
Let k(p) be the first derivative of 79/4*p**4 + 80/3*p**3 + 6*p**2 + 11/5*p**5 + 0*p + 245. Suppose k(j) = 0. Calculate j.
-6, -1, -2/11, 0
Solve -123/4*o**3 + 3*o**4 + 141/4*o**2 + 141*o + 72 = 0 for o.
-1, -3/4, 4, 8
Let c be (11/(-2))/(13/(-26)). Suppose 3*w = 3*f - 3, 7*w - 3*w = -f + c. Factor -r + 3*r + 2*r**2 - 2*r**3 + r + r**f.
-r*(r - 3)*(r + 1)
Let l = 829 + -826. Let n(d) be the second derivative of -1/42*d**4 + 4*d + 0 - 2/7*d**2 + 1/7*d**l. What is c in n(c) = 0?
1, 2
Factor -40/7*a - 2/7*a**2 + 6.
-2*(a - 1)*(a + 21)/7
Let a be (-1 - 5/(-1))/((-482)/(-2892)). Let h be ((-3)/a)/((34/16)/(-17)). Factor h + y**2 + 10/3*y.
(y + 3)*(3*y + 1)/3
Let q(d) = 23*d**3 + 6*d - 2*d**3 - 15*d**3 + 33*d**2 + 42*d + 3. Let k(n) = -n**3 - n**2 - 1. Let s(l) = 3*k(l) + q(l). Factor s(t).
3*t*(t + 2)*(t + 8)
Suppose -39 = -3*g - 2*j, 50 + 31 = 5*g - 2*j. Factor -10*q - g*q**3 - 10*q**4 + 34*q**2 + 6*q**2 - 7*q + 2*q.
-5*q*(q - 1)*(q + 3)*(2*q - 1)
Let y(u) be the third derivative of u**5/240 + 7*u**4/24 - 55*u**3/8 + 75*u**2 - 11. Factor y(v).
(v - 5)*(v + 33)/4
Let c(a) be the second derivative of 0*a**2 + 0*a**4 - a - 78 - 1/10*a**6 - 27/20*a**5 + 0*a**3. Factor c(p).
-3*p**3*(p + 9)
Let f be 22/33 - (-2017)/3. Factor 60 - 181*n**2 + 408*n + f*n**2 - 147*n**3 + 159*n**2.
-3*(n - 5)*(7*n + 2)**2
Let w(c) be the second derivative of 1083*c**5/20 - 399*c**4/2 + 78*c**3 - 12*c**2 - 1004*c. Let w(v) = 0. What is v?
2/19, 2
Let a be (-330)/(-100) + -3 - ((-65)/550)/(-1). Determine x, given that -1/11*x**3 + 0 - a*x**2 + 2/11*x**4 + 0*x + 1/11*x**5 = 0.
-2, -1, 0, 1
Let q(c) be the second derivative of -c**4/32 - 25*c**3/8 - 675*c**2/16 - 2*c - 3536. Factor q(v).
-3*(v + 5)*(v + 45)/8
Let k(q) be the second derivative of q**8/10080 - q**7/1260 + 119*q**4/12 + 3*q + 59. Let z(b) be the third derivative of k(b). Let z(x) = 0. Calculate x.
0, 3
Factor -4/7*f**2 + 1296/7*f - 104976/7.
-4*(f - 162)**2/7
Let f be (24732/(-2390))/(-9) - (-16)/(-20). Let u = f + 12/239. Factor -u*z**2 - 2/5*z + 0.
-2*z*(z + 1)/5
Let k(y) be the first derivative of -y**5 + 285*y**4/4 - 1780*y**3 + 17050*y**2 - 29040*y - 6073. Let k(u) = 0. What is u?
1, 12, 22
Let r(c) be the third derivative of -c**5/240 + 185*c**4/48 + 4*c**2 + 242*c - 2. Suppose r(u) = 0. What is u?
0, 370
Let z be (-38)/2641 + (-1778826)/(-51291). Factor z*m - 4/3*m**2 + 0.
-4*m*(m - 26)/3
Let b(v) be the first derivative of 7/3*v**3 - 3/5*v**5 + 29 + 1/4*v**4 - 1/6*v**6 - 4*v + 0*v**2. Determine n so that b(n) = 0.
-2, -1, 1
Let h be 37/(8325/36)*4*(-4)/(-32). Factor -24/25*d - 26/25 + h*d**2.
2*(d - 13)*(d + 1)/25
Let k = -19 + 33. Let c(h) = h**3 + 11*h**2 + 10*h + 2. Let t be c(-10). Factor k*v**2 + 27 + 18*v**2 - 47*v**t - 9*v - 3*v**3 + 0*v**3.
-3*(v - 1)*(v + 3)**2
Let v = 1847112/6464941 - -2/923563. Factor -46/7*n - 18/7*n**2 - 30/7 - v*n**3.
-2*(n + 1)*(n + 3)*(n + 5)/7
Let d(y) be the second derivative of 3*y**5/100 + 7*y**4/10 - 199*y**3/10 + 276*y**2/5 - 3*y - 261. What is i in d(i) = 0?
-23, 1, 8
Let n(d) be the third derivative of -d**6/160 - 17*d**5/40 - 265*d**4/32 - 75*d**3 - 2*d**2 + 5*d. Find u, given that n(u) = 0.
-24, -5
Let m(w) be the second derivative of 13/75*w**6 + 0*w**2 + 0 - 24/25*w**5 + 34/15*w**4 - 149*w - 1/105*w**7 - 32/15*w**3. Find r, given that m(r) = 0.
0, 1, 2, 8
Solve -880/3 - 148*x - 2/3*x**2 = 0 for x.
-220, -2
Let a(m) be the second derivative of -m**7/21 - 7*m**6/15 + m**5/10 + 55*m**4/6 + 28*m**3 + 36*m**2 - 3*m - 2936. Find v such that a(v) = 0.
-6, -2, -1, 3
Let f = 131732/45 + -26332/9. Factor -14/15*t**3 + 4/15 - f*t**2 - 2/5*t.
-2*(t + 1)**2*(7*t - 2)/15
Factor 83/4*q**3 - 1224*q**2 - 1/8*q**4 - 1724463/8 + 117045/4*q.
-(q - 51)**3*(q - 13)/8
Let f be -3*((-5921)/(-465) - ((9 - 1) + 5)). Suppose 2/15*l**2 + f*l + 0 = 0. Calculate l.
-6, 0
Suppose 0 = -4*n + 20, 4*x - x + 1 = 2*n. Suppose 2*a + 104 = x*a. Factor -12*w**2 - a*w + 4*w**3 + 3 + 112*w - 3.
4*w*(w - 2)*(w - 1)
Suppose 1685*g - 167*g = -198*g + 5148. Let t**2 + 0 - 1/3*t**4 + 0*t - 2/3*t**g = 0. Calculate t.
-3, 0, 1
Let x be 3 + (-8 + 0)*316/2528. Let 2*h**4 + 0 + 8/5*h**x + 0*h + 16/5*h**3 + 2/5*h**5 = 0. What is h?
-2, -1, 0
Let x(a) be the second derivative of -a**6/90 + a**5/20 + 3*a**4/4 - 17*a**3/3 + 27*a + 1. Let k(t) be the second derivative of x(t). Factor k(q).
-2*(q - 3)*(2*q + 3)
Let j be (920/780 - (-6)/39)*12. Let g(t) be the third derivative of j*t**2 + 0*t + 0 - 1/6*t**3 - 1/72*t**4 + 1/60*t**5 + 1/360*t**6. Factor g(y).
(y - 1)*(y + 1)*(y + 3)/3
Let b be 286/1260 - (-72)/(-324). Let g(k) be the third derivative of 0*k + b*k**7 - 1/60*k**5 + 0*k**3 - 22*k**2 + 0*k**6 + 0*k**4 + 0. Factor g(n).
n**2*(n - 1)*(n + 1)
Let l(v) = -92 - 2*v + 17 + 9*v + 0*v. Let s be l(11). Factor 0 - 3/2*p**s + 3*p**3 + 3/2*p**4 - 3*p.
3*p*(p - 1)*(p + 1)*(p + 2)/2
Let m(v) = 15*v**2 + 2011*v + 6. Let f(j) = -50*j**2 - 6031*j - 21. Let n(k) = -2*f(k) - 7*m(k). Factor n(p).
-5*p*(p + 403)
Let p(s) be the first derivative of -4*s**3/3 - 72*s**2 + 148*s + 1567. Solve p(c) = 0.
-37, 1
Let s(w) be the third derivative of w**5/150 + 224*w**4/3 + 1003520*w**3/3 + 10658*w**2. Determine o, given that s(o) = 0.
-2240
Suppose 33*t - 55*t = -1056. Suppose -t*x + 114*x = 198. Suppose -25/3*o + 0 - 10/3*o**2 - 1/3*o**x = 0. Calculate o.
-5, 0
Let h(x) = x**4 + 3*x**3 + x**2 - x. Let v(t) = 2*t**5 + t**4 - 71*t**3 - 34*t**2 + 6*t. Let l(d) = 6*h(d) + v(d). Factor l(f).
f**2*(f - 4)*(f + 7)*(2*f + 1)
Let z(r) be the third derivative of r**8/168 - r**7/35 - r**6/30 + 2*r**5/5 - 2*r**4/3 - 414*r**2 + r. Factor z(n).
2*n*(n - 2)**2*(n - 1)*(n + 2)
Let y(j) be the first derivative of 5*j - 16*j - 93 - j + j**3. Factor y(q).
3*(q - 2)*(q + 2)
Determine l, given that 22*l + 3*l + l + 18*l**2 - 3*l**4 - 50*l + l**3 + 8*l**3 = 0.
-2, 0, 1, 4
Let n(s) = 35*s - 770. Let j be n(22). Suppose -2*u + 5*y = 10, j = 2*u - y - 26 + 28. Factor u + 2/3*q**4 + 4/3*q**3 - 10/3*q**2 - 4*q.
2*q*(q - 2)*(q + 1)*(q + 3)/3
Let m be 224/280 - 15/50*52/(-3). Let -3/4*h**4 + 3*h + 15/4*h**3 + 0 - m*h**2 = 0. What is h?
0, 1, 2
Factor 118*v**3 - 10252*v + 127*v**3 + 0 - 175*v**2 + 10207*v - 25*v**4 + 0.
-5*v*(v - 9)*(v - 1)*(5*v + 1)
Let l(n) = -2*n**4 + 5*n**3 - 2*n**2 - n. Let q(p) = -4*p**4 - 101*p**3 - 1052*p**2 - 763*p + 6600. Let s(x) = -6*l(x) + 2*q(x). Factor s(c).
4*(c - 66)*(c - 2)*(c + 5)**2
Let w = 542213 + -542211. Factor 6/7 + 9/7*c + 3/7*c**w.
3*(c + 1)*(c + 2)/7
What is l in 156*l**2 + 12561*l**3 + 1056*l - 25120*l**3 + 12563*l**3 - 9680 = 0?
-22, 5
Let u = 1329 - 1324. Let w(n) be the second derivative of 0*n**3 + 0 - 1/90*n**u + 0*n**2 + 2/135*n**6 + 7*n - 1/27*n**4 + 1/189*n**7. Let w(h) = 0. What is h?
-2, -1, 0, 1
Let q be ((-5166)/(-6027))/(6 + -3). Factor -q*r**3 - 1350/7*r + 1250/7 + 102/7*r**2.
-2*(r - 25)**2*(r - 1)/7
Suppose 2*f = -4*j - 12, 0 = -3*j - 2*j - 20. Suppose 40 - 10*b + 11*b**f + 38*b - 13*b**2 + 6*b**2 = 0. Calculate b.
-5, -2
Let b be 150/120 + (-6)/(-8). Suppose -10*w**2 - 151*w**4 + 5*w**b + 152*w**4 - w**3 - 3*w = 0. What is w?
-1, 0, 3
Suppose -5*y + 1 = 3*b - 0*b, -2*b = -3*y - 7. Suppose -b*k - k + 3 = 0. Factor 7/3*m**2 - 14/3*m + 4/3*m**3 + k.
(m - 1)*(m + 3)*(4*m - 1)/3
Let -1440*k - 6912 - 3/2*k**3 - 84*k**2 = 0. What is k?
-24, -8
Let n(z) be the first derivative of z**6/12 + 3*z**5/2 + 53*z**4/8 - 43*z**3/6 - 69*z**2/2 + 56*z + 922. What is o in n(o) = 0?
-8, -7, -2, 1
Factor -167 + 3165*d**2 + 1067 - 902*d - 3163*d**2.
2*(d - 450)*(d - 1)
Let z(m) be the first derivative of -4*m**5/5 + m**4/4 + 11*m**3/3 + 3*m**2 - 3215. Factor z(i).
-i*(i - 2)*(i + 1)*(4*i + 3)
Let j(u) be the third derivative of -u**8/100800 - u**7/25200 + u**5/15 - 5*u**3/6 + 45*u**2. Let m(d) be the third derivative of j(d). Factor m(h).
-h*(h + 1)/5
Let t = -157 - -117. Let l be t/(-70) + (90/14 - 2). Solve 5/3*v**4 + 10/3*v + 0