t x(f) = -9*p(f) + 2*v(f). Suppose x(k) = 0. Calculate k.
-26, -6, -1
Let r = 3856/21 + -968/7. Let x = 46 - r. Suppose 2/9*j**2 - 8/9 + x*j = 0. Calculate j.
-4, 1
Let m(x) be the third derivative of 0*x**3 + 0*x**4 + 1/560*x**8 + 1/8*x**6 + 0*x + 0 + 3/25*x**5 + 1/25*x**7 + 40*x**2. Let m(h) = 0. Calculate h.
-12, -1, 0
Let q(s) be the first derivative of -s**4/4 - 136*s**3/3 - 269*s**2/2 - 134*s + 1717. Let q(c) = 0. What is c?
-134, -1
Let b(m) = -7*m**3 + 61*m**2 + 341*m + 99. Let h(x) = -44*x**3 + 366*x**2 + 2043*x + 593. Let k(v) = -34*b(v) + 6*h(v). Suppose k(l) = 0. Calculate l.
-3, -4/13, 8
Let b(f) = -f**3 - 2*f**2 + f - 1. Let h(r) = 5*r + 48. Let l be h(-8). Let d(i) = 6*i**3 + 10*i**2 - 6*i + 14. Let g(a) = l*b(a) + d(a). Factor g(u).
-2*(u - 1)*(u + 1)*(u + 3)
Suppose 56 = 3*x - 1380*r + 1384*r, 0 = 2*x + 2*r - 30. Solve -1/3*o**3 - 5/3*o - 2*o**2 + x = 0 for o.
-4, -3, 1
Let l(h) be the third derivative of h**9/24192 + h**8/4480 - h**6/720 + 58*h**3/3 + 72*h**2. Let w(j) be the first derivative of l(j). Let w(t) = 0. What is t?
-2, 0, 1
Let s be ((-90)/75)/(92/(-805)). What is v in -27*v + s*v**2 + 12 = 0?
4/7, 2
Factor 17*k**3 + 1/3*k**4 + 0 + 0*k**2 + 0*k.
k**3*(k + 51)/3
Let s(u) be the second derivative of -u**7/42 - u**6/5 + 59*u**5/20 - 12*u**4 + 70*u**3/3 - 24*u**2 - 72*u + 5. Suppose s(c) = 0. Calculate c.
-12, 1, 2
Let w(h) be the second derivative of h**6/20 - 23*h**5/40 + 21*h**4/8 - 73*h**3/12 + 15*h**2/2 + 2398*h. Find z such that w(z) = 0.
1, 5/3, 2, 3
Let s(r) be the third derivative of -4*r**2 + 11 + 25/27*r**3 + 0*r + 10/9*r**4 + 8/15*r**5. Factor s(b).
2*(12*b + 5)**2/9
Let u(z) be the third derivative of z**6/720 + 3*z**5/80 + 3*z**4/8 - 43*z**3/6 + 15*z**2 - 1. Let x(k) be the first derivative of u(k). Factor x(r).
(r + 3)*(r + 6)/2
Let v = 349668/35 - 69928/7. Factor 0 - 1/5*o**3 - v*o + o**2.
-o*(o - 4)*(o - 1)/5
Let s(f) be the second derivative of -f**5/40 + 91*f**4/48 + 23*f**3/12 + 1358*f. Factor s(q).
-q*(q - 46)*(2*q + 1)/4
Let g(z) be the first derivative of 5*z**6/18 + 14*z**5/5 + 121*z**4/12 + 152*z**3/9 + 14*z**2 + 16*z/3 + 2089. Let g(m) = 0. What is m?
-4, -2, -1, -2/5
Let c(j) = 23*j**3 + 80*j**2 + 156*j + 73. Let y(z) = 11*z**3 + 40*z**2 + 77*z + 36. Let o = -58 + 71. Let q(h) = o*y(h) - 6*c(h). What is u in q(u) = 0?
-6, -1
What is g in -165*g - 95*g - 174*g - 110*g**3 - 196 - 2*g**4 - 282*g**2 + 64*g**3 = 0?
-14, -7, -1
Let i = 132 - 127. Let p be 16/(-6) + -1 - (-9 + i). Solve -p*x**3 + 1/3*x**5 + 0*x - 4/3 - x**4 + 7/3*x**2 = 0 for x.
-1, 1, 2
Let k(c) be the third derivative of c**6/720 - c**5/20 - 4*c**4/3 + 896*c**3/9 - 2*c**2 + 252. Factor k(g).
(g - 16)**2*(g + 14)/6
Let p(b) be the second derivative of -b**5/10 + 61*b**4/6 + 125*b**3/3 + 63*b**2 + 2*b + 238. Suppose p(z) = 0. Calculate z.
-1, 63
Let n be ((-9)/(0 - -9) - 0)*-1*6. Let t(z) be the first derivative of -15 + 10/3*z**3 + 5/2*z**4 - 5*z - 5/6*z**n - 5/2*z**2 - z**5. Factor t(u).
-5*(u - 1)**2*(u + 1)**3
Let w(t) be the second derivative of -t**7/63 - 31*t**6/15 + 16*t**5/5 + 94*t**4/9 + 8*t - 82. Determine g, given that w(g) = 0.
-94, -1, 0, 2
Suppose -4*l + 4 = 0, 5*l = 5*o - 0*o - 20. Factor 4*x**4 - 2*x**5 - 2*x**5 + 2*x**o + 6*x**5.
4*x**4*(x + 1)
Let f(c) be the second derivative of c**6/90 - c**5/6 + 2*c**4/3 - 11*c**3/9 + 7*c**2/6 + 3*c - 140. Factor f(n).
(n - 7)*(n - 1)**3/3
Let u be 9/(0 - 9) - (-2 - -215). Let y = u + 214. Factor -2/3*l**2 + 8/3 + y*l.
-2*(l - 2)*(l + 2)/3
Let b(x) = -x**2 + 5*x - 2. Let f(l) = -l**2 + 4*l - 2. Let y(o) = 3*b(o) - 4*f(o). Let k(u) = -30*u**2 + 25*u - 45. Let a(v) = k(v) + 25*y(v). Factor a(n).
-5*(n - 1)*(n + 1)
Let z be 44 - ((-16)/(-12) - (-1)/(-3)). Suppose x + 3*f = 24, -2*x - 3*f - 2*f = -z. Determine h so that -x*h - 13*h**2 + 0*h**2 + 5*h**2 + 5*h**2 = 0.
-3, 0
Let u(t) be the first derivative of -4*t**5/5 + 33*t**4 - 440*t**3 + 1624*t**2 + 4704*t + 1524. Factor u(s).
-4*(s - 14)**2*(s - 6)*(s + 1)
Factor -1/3*x**2 - 356/3*x - 31684/3.
-(x + 178)**2/3
Let 6/7*p**5 + 306/7*p**3 - 1112/7*p - 16*p**4 + 432/7*p**2 + 480/7 = 0. What is p?
-2, 2/3, 1, 4, 15
Let v(a) be the first derivative of -a**6/6 - 5*a**5/2 - 39*a - 11. Let h(u) be the first derivative of v(u). Factor h(i).
-5*i**3*(i + 10)
Let p(g) = 19*g + 2. Let x be p(2). Let c(b) = 33*b - 559. Let j be c(17). Factor 10*v**3 - 9*v**3 - 20 - x*v - 6*v**3 - 25*v**j.
-5*(v + 1)*(v + 2)**2
Suppose -j - 2*j = -9. Let v be (-120)/(-63) - (-14)/147. Find k, given that -24 + 18 + j*k + 12*k**v - 2*k**3 - 7*k**3 = 0.
-2/3, 1
Let p(h) be the first derivative of -34 - 1/6*h**6 - 5/4*h**4 + 0*h - 2/3*h**3 + 0*h**2 - 4/5*h**5. Factor p(k).
-k**2*(k + 1)**2*(k + 2)
Suppose 31 = -2*k - 5*f, 11 = -37*k + 32*k - 3*f. Determine s, given that 4/5 - 4/5*s**k - 2/5*s + 2/5*s**3 = 0.
-1, 1, 2
Determine n so that 1/9*n**2 + 0 - 98/3*n = 0.
0, 294
What is h in -35*h**2 + 18 + 126*h**3 - 45*h - 74*h**4 - 17*h**2 + 44*h**4 - 25*h**5 + 8*h**2 = 0?
-3, -3/5, 2/5, 1
Let p = 232321/20 - 58074/5. Factor 0 + 1/4*j**4 - 1/2*j**3 - p*j**2 + 3/2*j.
j*(j - 3)*(j - 1)*(j + 2)/4
Let m(v) be the first derivative of 51 - 8*v + 2*v**2 + 2/3*v**6 - 8/5*v**5 + 16/3*v**3 - 2*v**4. Determine x, given that m(x) = 0.
-1, 1, 2
Let l(d) = 11*d**3 + 237*d**2 - 1594*d + 2412. Let q(k) = -13*k**3 - 232*k**2 + 1593*k - 2412. Let r(v) = -6*l(v) - 5*q(v). Find b, given that r(b) = 0.
-268, 3
Let l(c) be the first derivative of c**6/2 - 12*c**5/5 + 15*c**4/4 - 2*c**3 - 1237. Factor l(z).
3*z**2*(z - 2)*(z - 1)**2
Factor 0 + 46/7*b + 94/7*b**2 + 50/7*b**3 + 2/7*b**4.
2*b*(b + 1)**2*(b + 23)/7
Let a = -473 + 476. Let s be (-2964)/(-1197) + (-7)/a. Factor -5/7*n**2 - s*n**3 - 3/7 - n.
-(n + 1)**2*(n + 3)/7
Let v(o) be the second derivative of -o**4/3 - 20*o**3 + 2016*o. Suppose v(y) = 0. What is y?
-30, 0
Let c(k) be the third derivative of -10/3*k**3 - 7/12*k**4 - 94*k**2 - 1/30*k**5 + 0 + 0*k. Let c(d) = 0. Calculate d.
-5, -2
Let z(b) = -30*b**3 + 2466*b**2 - 725*b - 1607. Let h(y) = -12*y**3 + 986*y**2 - 291*y - 643. Let p(t) = -13*h(t) + 5*z(t). What is l in p(l) = 0?
-2/3, 1, 81
Let b(c) = 14*c**3 + 142*c**2 + 570*c + 616. Let k(i) = 5*i**3 + 47*i**2 + 188*i + 204. Let t(v) = 6*b(v) - 17*k(v). Find g, given that t(g) = 0.
-2, 57
Let i(x) be the first derivative of -x**4 - 16*x**3/3 + 24*x**2 + 14172. Find y such that i(y) = 0.
-6, 0, 2
Let w(h) be the third derivative of h**5/660 - 29*h**4/264 + 20*h**3/11 + 1095*h**2. Suppose w(j) = 0. What is j?
5, 24
Let o(k) = 20*k**2 - 200*k - 2090. Let b(p) = -29*p**2 + 288*p + 3135. Let f(d) = 5*b(d) + 7*o(d). Factor f(w).
-5*(w - 19)*(w + 11)
Let i = -1602/149 + 16578/1043. Factor 6/7*w**5 + 72/7*w**3 - 60/7*w**2 - i*w**4 + 18/7*w + 0.
6*w*(w - 3)*(w - 1)**3/7
Let r(s) be the first derivative of -1/30*s**5 - 263/9*s**3 + 38 - 147/2*s + 11/6*s**4 + 77*s**2. Factor r(x).
-(x - 21)**2*(x - 1)**2/6
Let s(w) be the second derivative of -w**6/40 - 633*w**5/40 - 43669*w**4/16 + 44943*w**3/2 - 136107*w**2/2 - 128*w - 13. Solve s(p) = 0.
-213, 2
Find h such that 402/17*h**2 - 76/17*h**3 + 2/17*h**4 + 256/17 - 584/17*h = 0.
1, 4, 32
Let k(o) = o**3 + 4*o**2 - 6*o + 11. Let h be k(-5). Determine z, given that -45*z**3 - 80*z - 23*z**2 - h*z**4 + 21*z**4 + 26*z**2 + 117*z**2 = 0.
0, 1, 4
Let b(s) be the third derivative of s**5/30 + 41*s**4/24 + 10*s**3 - 2*s**2 + 40*s. Let j(g) = 25*g**2 + 535*g + 780. Let x(u) = -40*b(u) + 3*j(u). Factor x(o).
-5*(o + 3)*(o + 4)
Suppose -3*q = -378*u + 369*u + 3, 4*u + 2*q - 48 = 0. Factor 3*b + 3/4*b**u - 3/2*b**4 + 3*b**2 - 9/4*b**3 + 0.
3*b*(b - 2)**2*(b + 1)**2/4
Suppose 82*h - 85*h + 6 = 0. Factor 498*m**2 + 502*m**2 + 504*m**2 + m**3 - 31*m - 1518*m**h - 16.
(m - 16)*(m + 1)**2
Let n(t) be the third derivative of -t**7/945 + 11*t**6/180 - 17*t**5/18 + 575*t**4/108 + 59*t**2 + 19. Factor n(j).
-2*j*(j - 23)*(j - 5)**2/9
Let u = -1920 + 1920. Let m(j) be the third derivative of -1/420*j**6 + u + 0*j**5 - 4*j**2 + 0*j + 0*j**3 + 0*j**4 - 1/735*j**7. Let m(i) = 0. What is i?
-1, 0
Suppose 0 = 3*v - 3*h, 5*v - 36 = -5*h - 6. Find d such that 18*d - 4*d**v - 21*d - d**2 + 7*d**3 + 1 = 0.
-1, 1/3, 1
Let m = 1/22982 - -34471/45964. What is q in -2*q**2 + 0 - 3/4*q + 1/2*q**4 - m*q**3 = 0?
-1, -1/2, 0, 3