et c(p) be the third derivative of p**9/83160 - p**8/18480 + 49*p**4/24 - p**3/2 - 217*p**2. Let l(t) be the second derivative of c(t). Factor l(r).
2*r**3*(r - 2)/11
Let i = 150 + -148. Let s(u) be the second derivative of -1/135*u**6 + 2/9*u**i - 1/9*u**3 - 1/54*u**4 + 1/30*u**5 + 0 + 20*u. Determine l, given that s(l) = 0.
-1, 1, 2
Let p be 9 - ((-214455)/(-25585) - (-4)/86). Factor 2/7*a**5 - p*a - 6/7*a**3 + 2/7*a**4 - 10/7*a**2 + 0.
2*a*(a - 2)*(a + 1)**3/7
Suppose -3*l**2 - 762*l - 2845 + 1026*l - 2963 = 0. Calculate l.
44
Let i(o) = o**2 + 44*o - 104. Suppose -3*c + 7*u = 11*u + 125, 2*c = -3*u - 85. Let r(b) = 10*b**2 + 395*b - 935. Let y(f) = c*i(f) + 4*r(f). Factor y(s).
5*(s - 2)*(s + 10)
Determine d so that -5/4*d**3 + 318*d**2 + 192 + 2045/4*d = 0.
-1, -3/5, 256
Factor 75/4 + 0*k - 3/4*k**2.
-3*(k - 5)*(k + 5)/4
Let c = 121577/21 + -17363/3. Let -32/7 - 244/7*o**2 + 164/7*o + 124/7*o**3 - c*o**4 = 0. What is o?
1/3, 1, 8
Let g(l) = 11*l**3 - 36*l**2 + 11*l + 34. Let j(h) = 10*h**3 - 35*h**2 + 10*h + 40. Let y(p) = -5*g(p) + 4*j(p). Determine t so that y(t) = 0.
-1/3, 1, 2
Let i(z) be the first derivative of z**3/6 + 163*z**2/4 + 81*z + 515. Determine d so that i(d) = 0.
-162, -1
Suppose 22*w + 42 = 15*w. Let h be (-9)/w + (-58)/(-44)*-1. What is z in -56/11*z - 24/11 - h*z**4 - 46/11*z**2 - 16/11*z**3 = 0?
-3, -2, -1
Let m = 7677 + -53735/7. Let b(g) be the first derivative of m*g**2 + 16/7*g - 17 + 1/21*g**3. Factor b(r).
(r + 4)**2/7
Let v(u) be the second derivative of u**4/12 + 61*u**3/6 - 96*u**2 - 47*u + 17. Factor v(t).
(t - 3)*(t + 64)
Suppose 4*q - 27 + 3 = -2*w, 2*w + 3*q = 19. What is t in t**2 + 37*t - 96 + 5*t**2 - 20*t + 25*t - 3*t**w = 0?
-16, 2
Let x(c) be the first derivative of -c**6/432 + c**5/16 + 2*c**3/3 - c**2 + 112. Let a(l) be the third derivative of x(l). Find w such that a(w) = 0.
0, 9
Let v(d) = -341*d**2 + 166*d + 1161. Let x(c) = 739*c**2 - 331*c - 2323. Let g(h) = -13*v(h) - 6*x(h). Let g(u) = 0. What is u?
-165, -7
Suppose 7*g = 12*g + 115. Let k = -19 - g. Factor -8*v + 15*v**2 - 23*v**5 + 4*v**3 - 12*v**k - 3*v**2 + 27*v**5.
4*v*(v - 2)*(v - 1)**2*(v + 1)
Let p(r) be the third derivative of 5*r**8/28 + 1793*r**7/210 - 34*r**6/15 - 1853*r**5/60 + 53*r**4/6 + 10*r**3 - r**2 - 889. Let p(m) = 0. Calculate m.
-30, -1, -2/15, 1/4, 1
Find t, given that t**5 - 66*t**2 + 0 + 27*t + 199/4*t**3 - 55/4*t**4 = 0.
0, 3/4, 2, 9
Let i = 4685 + -421649/90. Let d(t) be the second derivative of -1/54*t**4 + 0*t**2 + i*t**5 - 18*t + 0 + 0*t**3. Let d(h) = 0. What is h?
0, 1
Let t(y) be the third derivative of y**6/660 - y**5/22 - y**4/4 - 17*y**3/33 - 1797*y**2. What is w in t(w) = 0?
-1, 17
Suppose -3*v + 3*n = 2*n - 16, -4*n = 2*v + 8. Determine c so that -19*c**2 - 80*c**2 - 5*c**3 + 90*c**v - 3*c**5 + 9*c**2 + 8*c**5 = 0.
-18, -1, 0, 1
What is b in b**2 - 32*b - 16*b + 20*b - 8*b = 0?
0, 36
Let q = -104 + 96. Let v(g) = -2*g**3 - 15*g**2 + 9*g + 12. Let n be v(q). Factor -3*y**4 + 3*y**4 + 13*y - 21*y + 2*y**n + 6*y**3.
2*y*(y - 1)*(y + 2)**2
Determine s so that 8/3*s + 0 - 8/3*s**3 + 2/3*s**4 - 2/3*s**2 = 0.
-1, 0, 1, 4
Let c(j) be the third derivative of -15/8*j**3 + 0 - 1/80*j**5 + 0*j + 95*j**2 + 1/4*j**4. Factor c(m).
-3*(m - 5)*(m - 3)/4
Let w = 285 + -85. Suppose 4*d - w = -v, 3*d - 6*d = -5*v - 150. Determine r so that -r**2 + 4*r**3 + r**2 + 44*r**4 - d*r**4 = 0.
0, 2/3
Let w be (((-84)/(-70))/(-2 + 3))/((-6)/(-90)). Find n such that 108/5 + w*n + 24/5*n**2 + 2/5*n**3 = 0.
-6, -3
Let n be -5 + 30/12 + (-1)/(-2). Let u be ((-385)/(-15) + n/3)/1. Factor -5*s**3 - 200*s**2 - 18*s**5 + u*s**4 - 2*s**5 + 200*s**2.
-5*s**3*(s - 1)*(4*s - 1)
Let i = 1 - -8. Let k be i*1/6*(-20)/(-6). Solve 3*q**k - 12*q**3 + 9*q**3 - 12*q**2 + 9*q**2 + 3*q**4 = 0 for q.
-1, 0, 1
Let a be (-1 - (-1 + -2)) + (-474)/553. Let j(w) be the first derivative of 2/21*w**3 + 11 + a*w - 4/7*w**2. Find g, given that j(g) = 0.
2
Factor 1941*a - 88 + 3*a**3 + 7144 + 88*a**2 + 159*a - 2*a**3.
(a + 4)*(a + 42)**2
Let z(o) be the first derivative of 0*o - 6/5*o**2 + 9/25*o**5 + 21/20*o**4 + 0*o**3 - 19. Suppose z(l) = 0. What is l?
-2, -1, 0, 2/3
Let p = 769 - 598. Factor -37464*u + 48*u**3 + 7*u**4 + 37626*u - p*u**2 - 48 + 2*u**4.
3*(u - 1)**2*(u + 8)*(3*u - 2)
Let j(f) be the first derivative of -f**6/2 + 111*f**5/5 - 1269*f**4/4 + 1507*f**3 - 2832*f**2 + 2304*f - 4600. Determine q, given that j(q) = 0.
1, 3, 16
Let n(b) be the third derivative of -76*b**2 - 2/51*b**5 + 2/51*b**3 + 1/68*b**4 + 0 + 0*b. Factor n(u).
-2*(4*u + 1)*(5*u - 2)/17
Let q = 91 - 94. Let g be (-4 - q) + 1090/2. Suppose -166*c**4 - 146*c**4 + 1870*c**2 - 88*c**4 - g*c + 755*c**3 - 1196*c + 360 - 125*c**5 = 0. What is c?
-3, 2/5, 2
Let x(b) = 4*b - 2*b**2 + b**3 - 1 + 0*b**2 + 3 - 2*b**2. Let c be x(4). Factor -10*j**3 + 5*j**2 + 5*j**3 - 3 + c + 25*j.
-5*(j - 3)*(j + 1)**2
Let x be -2 - ((-44)/(-110))/(2/(-30)). Let k = -14 - -24. Factor 12*r - k*r**2 - r - x + 3*r.
-2*(r - 1)*(5*r - 2)
Let -1/3*y**2 - 88804/3 + 596/3*y = 0. Calculate y.
298
Let u(a) be the first derivative of a**6/2 + 6*a**5 + 99*a**4/4 + 44*a**3 + 30*a**2 + 967. Solve u(l) = 0.
-5, -2, -1, 0
Let u be ((-32)/(-24))/(-2) + 17/3. Suppose 4*r + u - 13 = 0. Suppose -7*m**2 + 3*m + r*m**2 + 0*m - 8*m + 30 = 0. Calculate m.
-3, 2
Factor 115118 + 115799 - 76*s + 2*s**2 - 230203.
2*(s - 21)*(s - 17)
Let m = 28 + -13. Suppose 16 = -11*n + m*n. Factor -4*q + 4*q**3 + 1724 - 1722 - 4*q**n + 2*q**4.
-2*(q - 1)**3*(q + 1)
Let d(s) be the third derivative of s**8/16 + 66*s**7/7 + 1483*s**6/40 + 507*s**5/10 + 23*s**4 + 63*s**2 + 5*s + 9. Suppose d(b) = 0. What is b?
-92, -1, -2/7, 0
Let y(s) = -s**2 - 8*s + 21. Let w be y(-10). Let f be 0 + 4 - (w + -1)/3. Factor 0*g**5 - 6*g**4 - 4*g - 2*g**f - g**5 + 5*g**5 + 8*g**2.
4*g*(g - 1)**3*(g + 1)
Let r = -31 - -36. Suppose -r*k - 50 = -15*k. Suppose 12*h**5 + 6*h**2 - 6*h**4 - 33*h**5 + 16*h**3 + k*h**3 = 0. What is h?
-1, -2/7, 0, 1
Let i(q) be the second derivative of q**6/900 - 7*q**5/300 + q**4/10 + 17*q**3/2 - 56*q. Let w(l) be the second derivative of i(l). Find t such that w(t) = 0.
1, 6
Suppose -188 + 194 = -b, 2*f - 2*b - 18 = 0. Let p(d) be the first derivative of 14 + 0*d + d**2 + 1/2*d**4 - 4/3*d**f. Factor p(t).
2*t*(t - 1)**2
Let c(g) = 17*g**3 + 175*g**2 + 1965*g + 3226. Let f(y) = -15*y**3 - 174*y**2 - 1959*y - 3222. Let b(d) = -6*c(d) - 7*f(d). Solve b(x) = 0.
-41, -13, -2
Let q be 10 - -1*(3 + -7 + 6) - 3. Let l(n) be the first derivative of -14 - 54*n + q*n**2 - 1/2*n**3. Factor l(v).
-3*(v - 6)**2/2
Factor 78*p**2 - 5*p**3 - 8*p**2 + 30*p + 42*p + 3*p.
-5*p*(p - 15)*(p + 1)
Determine l, given that 3/4*l**4 - 243/4 - 81/2*l + 0*l**2 + 9/2*l**3 = 0.
-3, 3
Suppose 17447*m**2 - 274598*m - m**3 - 20247*m + 609628 - 24266 - 16363*m**2 = 0. What is m?
2, 541
Suppose w + 19 = -0*w - 4*j, -w = 3*j + 19. Let q be (-8 - -2)*(114/60)/w. Factor q*m**2 - 3/5 + 0*m.
3*(m - 1)*(m + 1)/5
Let k(w) be the second derivative of 3*w**5/20 + 199*w**4/4 + 295*w**3 + 588*w**2 - 2*w - 240. Suppose k(s) = 0. What is s?
-196, -2, -1
Let l(j) be the third derivative of j**7/630 - j**6/12 + 83*j**5/180 - 3*j**4/4 - 2*j**2 + j - 3. Suppose l(t) = 0. Calculate t.
0, 1, 2, 27
Let o be 54 - (30/8 - 10/(-8)). Determine f so that 15895*f - 3825*f**2 + 182*f**3 + 14*f**3 + 2*f**4 + 49130 - 7*f**4 + o*f**3 = 0.
-2, 17
Suppose 802*b - 48 = 806*b. Let m(h) = h**4 - h**3 - h**2 - 1. Let r(l) = 2*l**4 - 14*l**3 - 3*l**2 - 3. Let k(f) = b*m(f) + 4*r(f). Factor k(z).
-4*z**3*(z + 11)
Let s(h) be the third derivative of 0*h - 1/385*h**7 - 2/11*h**3 + 14*h**2 - 1 - 1/220*h**6 + 3/110*h**5 + 1/44*h**4. Suppose s(l) = 0. What is l?
-2, -1, 1
Let o(k) be the third derivative of 5*k**8/336 + 23*k**7/42 - 175*k**6/24 - 23*k**5/12 + 145*k**4/4 + 11614*k**2. Suppose o(a) = 0. What is a?
-29, -1, 0, 1, 6
Let a(r) be the first derivative of r**5/15 - 29*r**4/6 + 407*r**3/3 - 5510*r**2/3 + 36100*r/3 - 1440. Factor a(x).
(x - 19)**2*(x - 10)**2/3
Let m(r) be the third derivative of -35*r**8/12 - 19*r**7/30 + 31*r**6/150 - r**5/75 - 3690*r**2. Solve m(t) = 0 for t.
-1/4, 0, 2/35
Let r(q) be the second derivative of q**4/28 - 33*q**3/14 + 48*q**2/7 - 276*q. Let r(p) = 0. What is p?
1, 32
Let u(g) be th