erivative of m**6/6 + 3*m**5/4 + 5*m**4/4 + 5*m**3/6 + 121*m - 106. Let o(y) be the first derivative of a(y). Factor o(v).
5*v*(v + 1)**3
Let i = -40/77 + 1037/1848. Let t(u) be the second derivative of -405/8*u**4 + 15*u - 9/4*u**5 - 32805/8*u**2 - 1215/2*u**3 + 0 - i*u**6. Factor t(q).
-5*(q + 9)**4/4
Let g(n) be the second derivative of -n**8/112 - n**7/70 + 2*n**6/5 - n**5 + 97*n**2/2 + 4*n + 1. Let a(v) be the first derivative of g(v). Factor a(r).
-3*r**2*(r - 2)**2*(r + 5)
Let k = -349 - -373. Let w be 18/k + (-5)/20. Let 1 - 1/2*j + 1/2*j**4 + w*j**3 - 3/2*j**2 = 0. What is j?
-2, -1, 1
Let v(r) = -r**2 + 330*r + 12378. Let x be v(-34). Suppose -1/3*t**3 - 1/9*t**5 + 4/9*t + 0 + 4/9*t**4 - 4/9*t**x = 0. What is t?
-1, 0, 1, 2
Find a, given that -3*a**4 - 675*a**3 + 27582 + 7921*a**2 + 39663*a + 49032 - 45544*a**2 = 0.
-113, -1, 2
Find z, given that -71*z**3 + 14*z**2 - 24 - 8*z + 155*z**3 - 86*z**3 = 0.
-1, 2, 6
Let a(d) = 9*d + 6. Let m = -13240 - -13243. Let q(i) = -i**3 + 2*i**3 + 0*i**3. Let g(f) = m*q(f) - a(f). Solve g(p) = 0.
-1, 2
Let i = 2575/609 - -64/609. Find r, given that -r**3 - 11/3*r**2 - 5/3 - i*r = 0.
-5/3, -1
Let v(o) be the second derivative of -2 - 9/2*o**2 - 4/5*o**3 - 1/20*o**4 - 14*o. Factor v(j).
-3*(j + 3)*(j + 5)/5
Let y be (16*14/(-1400))/(-1 - 1/1). Let l(g) be the third derivative of -17*g**2 - y*g**5 + 1/30*g**4 + 0*g + 0 + 0*g**3. Let l(x) = 0. What is x?
0, 1/6
Let z be 35588/(-868) - (-208)/5. Factor 0 - z*m**2 - 48/5*m.
-3*m*(m + 16)/5
Let u = 7 + -16. Let n be 2/6 + (-33)/u. Suppose 16*t**4 + 17*t**4 - 37*t**n + 4*t**2 + 10*t**5 - 24*t**5 + 14*t**3 = 0. Calculate t.
-1, -2/7, 0, 1
Let i = -20 + 24. Suppose v = -v + i. Suppose 7*f + f**4 - 9*f - f**5 - f**v + 5*f**3 - 2*f**5 + 0*f**5 = 0. Calculate f.
-1, -2/3, 0, 1
Let j be (-5)/(-1) + (-6227)/1287. Let u = j + 2/99. Factor u*w**2 - 36/11*w + 162/11.
2*(w - 9)**2/11
Let p(l) be the third derivative of l**6/120 + 3*l**5/20 + 85*l**3/6 - 66*l**2. Let b(t) be the first derivative of p(t). Find m, given that b(m) = 0.
-6, 0
Let k(v) be the first derivative of -158*v**2 + 5*v**4 - 32/3*v**3 + 83 - 120*v. Factor k(i).
4*(i - 5)*(i + 3)*(5*i + 2)
Let v(f) = 5*f - 4. Let c be v(-7). Let x = c + 43. Solve 48*w**2 + 11*w**4 - 3*w**4 + 34*w**3 + 10 + 26*w - 10 + x = 0 for w.
-2, -1, -1/4
Let a(o) = -21*o**3 - 122*o**2 - 220*o - 10. Let c(x) = -x**3 + 4*x**2 - 2*x - 2. Let i(v) = a(v) - 5*c(v). Determine n, given that i(n) = 0.
-7, -15/8, 0
Let k be (1 - (-8)/(-12))*-3. Let f be 0/(-2) + 8/(3 - k). Solve -y**f - y**2 + 91*y - 87*y + 6 = 0.
-1, 3
Suppose 0 = -2*g - 2*g + 12. Suppose 96 + 53*a + 493*a**g + 32*a**2 - 24 + 31*a - 489*a**3 = 0. What is a?
-3, -2
Let k = 152202 + -152198. Solve k*r - 1/2*r**2 + 10 = 0 for r.
-2, 10
Find f, given that 99 - 37*f - 9 - 62 - 52 - 54 + 21*f**2 = 0.
-26/21, 3
Suppose -7*c - 9 = -4*c. Let j be ((-3)/(-2))/(c/(-6)). Find u such that -10 - 4*u**5 - 3*u**4 - 65*u**j + 24*u**5 - 8*u**4 + 85*u**2 - 15*u - 4*u**4 = 0.
-2, -1/4, 1
Let b(h) be the second derivative of h**4/3 + 388*h**3 - 1166*h**2 + 94*h + 30. Factor b(x).
4*(x - 1)*(x + 583)
Let j(g) = 7*g**2 + 142*g + 138. Let l(x) = -19*x**2 - 425*x - 414. Let s(a) = 8*j(a) + 3*l(a). Factor s(k).
-(k + 1)*(k + 138)
Let c be 37 - 41 - 704/((-4)/(-2)). Let f = c + 359. Factor -3/2*v - 3/2*v**2 + f.
-3*(v - 1)*(v + 2)/2
Let y(l) be the second derivative of 4*l + 5/12*l**4 + 0*l**2 + 5/6*l**3 + 10. Factor y(m).
5*m*(m + 1)
Factor 1/3*u**4 + 104*u + 118/3*u**2 + 169/3 - 8*u**3.
(u - 13)**2*(u + 1)**2/3
Let y(h) be the second derivative of h**6/50 - 51*h**5/25 + 19*h**4 - 248*h**3/5 - 2*h + 2022. Factor y(x).
3*x*(x - 62)*(x - 4)*(x - 2)/5
Suppose 118*g - 2*l = 116*g + 8, 0 = -l - 2. Let -3/8*w**g + 15/2*w - 27/2 = 0. What is w?
2, 18
Let n(d) be the second derivative of d**7/280 + d**6/20 + 3*d**5/20 - 67*d**2 + 70*d. Let a(f) be the first derivative of n(f). Let a(k) = 0. What is k?
-6, -2, 0
Let i(a) be the second derivative of -a**5/60 + 13*a**4/36 - 22*a**3/9 + 16*a**2/3 + 324*a + 3. Let i(v) = 0. Calculate v.
1, 4, 8
Let v(x) = x**3 - 8*x**2 + 6*x + 9. Let a be v(7). Factor -4*y**3 + 20*y**2 - 21*y**a - 3*y**2.
-4*y**2*(y + 1)
Suppose -166 + 407 = 319*q - 397. Suppose -20/3*w + q*w**2 - 16/3 = 0. Calculate w.
-2/3, 4
Suppose -1/10*v**4 - 7/10*v**2 - 3/10*v + 0 - 1/2*v**3 = 0. What is v?
-3, -1, 0
Let t = 2/117341 + 586701/234682. Let -15/8*v**2 + 5/2*v**3 + 11/8*v**4 + 1/2 - t*v = 0. What is v?
-2, -1, 2/11, 1
Let x(t) = 15*t**2 - 10*t + 1. Let w be x(-2). Suppose w*a + 6 = 84*a. Suppose 0*o - 2/11*o**a + 8/11 = 0. Calculate o.
-2, 2
Let r(g) = -3*g**3 - 3069*g**2 - 1046537*g - 118955455. Let v(x) = 2*x**3 + 2046*x**2 + 697691*x + 79303637. Let q(y) = 5*r(y) + 8*v(y). Factor q(s).
(s + 341)**3
Factor -9*w**2 - 40*w**3 + 31 + 112*w**2 - w**2 + 3*w**4 - 13*w - 83*w.
(w - 1)**3*(3*w - 31)
Let g be (790/(-110) + 7)*-22. Let x(d) be the first derivative of -9/4*d**2 + 6 + 27/2*d - 5/2*d**3 - 3/8*d**g. Suppose x(v) = 0. Calculate v.
-3, 1
Let r(x) = -26*x**3 - 111*x**2 - 56*x + 64. Let a(k) = 84*k**3 + 334*k**2 + 168*k - 194. Let t(c) = -5*a(c) - 16*r(c). Factor t(n).
-2*(n - 27)*(n + 1)*(2*n - 1)
Let f = -34858/101 + 177522/505. Let z = 7 + -3. Determine s, given that -12/5*s**2 - 8*s + 16/5*s**3 + 4/5*s**z + f = 0.
-4, -2, 1
Let u(q) be the third derivative of q**6/300 - 16*q**5/75 + q**4 - 1864*q**2. Factor u(v).
2*v*(v - 30)*(v - 2)/5
Suppose 170 = 65*q - 33*q + 53*q. Let l(c) be the first derivative of 0*c - 2/3*c**3 - 14 - q*c**2. Factor l(g).
-2*g*(g + 2)
Let -17*p - 8/7 + 127/7*p**2 = 0. What is p?
-8/127, 1
Factor 24 - 46/5*a + 2/5*a**2.
2*(a - 20)*(a - 3)/5
Let l(r) = r**2 - 18*r + 76. Let n be l(12). Suppose 3*u**4 + 8*u**4 + 11*u - 4*u**4 + 25*u**2 + 5*u + 19*u**3 + u**5 + n = 0. Calculate u.
-2, -1
Let j(h) be the third derivative of h**6/96 - 215*h**5/48 + 2135*h**4/96 - 355*h**3/8 + h**2 + 1021*h + 1. Suppose j(n) = 0. What is n?
1, 213
Let l(t) = t**3 - 3*t**2 - 5*t + 2. Let w be l(5). Let k = -25 + w. Factor -13*x + x + 14*x**3 - 16*x**2 + 3*x**4 - k*x**3 + 18 - 5*x**4.
-2*(x - 3)**2*(x - 1)*(x + 1)
Factor 0 + 0*d**3 - 1/4*d**4 - 1/2*d + 3/4*d**2.
-d*(d - 1)**2*(d + 2)/4
Let p(n) = 9*n**4 - 6665*n**3 + 12*n**2 - 12*n + 4. Let d(l) = 26*l**4 - 19995*l**3 + 33*l**2 - 33*l + 11. Let g(q) = 4*d(q) - 11*p(q). What is a in g(a) = 0?
0, 1333
Let w(t) be the first derivative of 2*t**3/39 - 3606*t**2/13 + 6501618*t/13 - 5596. Factor w(p).
2*(p - 1803)**2/13
Let b(j) be the third derivative of j**6/60 + 503*j**5/150 - 881*j**4/30 + 208*j**3/5 + j**2 - 98*j. Find c such that b(c) = 0.
-104, 2/5, 3
Let n(o) be the second derivative of -9 + 1/36*o**4 - 7/18*o**3 - 6*o + 0*o**2. Suppose n(w) = 0. Calculate w.
0, 7
Let x be ((-344)/(-3860))/(112/320). Let y = x - -6/193. Factor -y*w**2 + 2/7 + 0*w.
-2*(w - 1)*(w + 1)/7
Factor 236/11*k**2 + 2/11*k**3 - 734/11*k - 88.
2*(k - 4)*(k + 1)*(k + 121)/11
Let g(l) = l**3 - 17*l**2 - 67*l + 6. Let h be g(21). Solve -h + 292*a + 369*a - 83*a**2 - 25*a**2 - 265*a = 0 for a.
11/6
Let t(g) be the second derivative of 0*g**2 - 1/28*g**4 - 31 + 1/70*g**6 - 2*g + 3/70*g**5 - 1/7*g**3. Solve t(u) = 0 for u.
-2, -1, 0, 1
Let 5/2 + 8/3*i + 1/6*i**2 = 0. Calculate i.
-15, -1
Suppose -26993 + 27041 = 6*s. Factor 28/5*w + s + 4/5*w**2.
4*(w + 2)*(w + 5)/5
Let q(p) be the second derivative of -1/48*p**4 - 1/4*p**2 + 1/8*p**3 + 2 - 10*p. Find x, given that q(x) = 0.
1, 2
Let u(j) be the first derivative of -3*j**5/35 + 11*j**4/42 - 5*j**3/21 + 110*j - 170. Let g(o) be the first derivative of u(o). Factor g(y).
-2*y*(y - 1)*(6*y - 5)/7
Suppose -5*v + 3*q + q - 5 = 0, 3*q = v + 12. Let j be 2 - 0*(-3)/6. Factor z**v - 3*z**3 + 31*z**2 + 6*z - 36 - 23*z**j.
-2*(z - 3)**2*(z + 2)
Let n(l) be the first derivative of 0*l + 1/150*l**5 - 9/2*l**2 + 1/15*l**3 + 1/30*l**4 + 7. Let y(b) be the second derivative of n(b). Factor y(v).
2*(v + 1)**2/5
Factor -1836 - 267/2*z - 3/2*z**2.
-3*(z + 17)*(z + 72)/2
Let y = -60 - -429. Let x = y - 369. Let 4/7*z**3 - 6/7*z**4 + 2/7*z**5 + x*z + 0 + 0*z**2 = 0. What is z?
0, 1, 2
Let p(b) be the second derivative of b**7/63 - b**6/9 + 4*b**5/15 - 2*b**4/9 + 283*b - 2. Factor p(s).
2*s**2*(s - 2)**2*(s - 1)/3
Let n be 5688/6636