78 = 0. Let c be (-6)/14 + (-8)/p. Factor -3/7 + c*f**2 + 2/7*f.
(f - 1)*(f + 3)/7
Suppose -25*p = -73*p + 480. Let r(l) be the first derivative of 36 - 15/2*l**2 - p*l - 5/3*l**3. Factor r(b).
-5*(b + 1)*(b + 2)
Let a(q) = 255*q + 765. Let l be a(-3). Let j(t) be the first derivative of 15 + 4/5*t**5 + 2*t**4 + l*t + 4/3*t**3 + 0*t**2. Factor j(g).
4*g**2*(g + 1)**2
Let k = 159784000/394602663 - 7/333561. Let p = k + 4/169. Find z, given that 5/7*z**2 + p*z - 2/7 = 0.
-1, 2/5
Let j be 35/21*(-1 - -4). Let 19*y**5 + 20*y**5 + 16 - 2*y**4 - 11*y**3 + 26*y**5 + 40*y**2 - 64*y**j - 44*y = 0. Calculate y.
-4, 1, 2
Factor -352 - 436 - 505 - 4*m**2 + 107 + 412*m - 398.
-4*(m - 99)*(m - 4)
Factor -59168/5 - 688/5*m - 2/5*m**2.
-2*(m + 172)**2/5
Determine l, given that l**5 - 3*l**4 + 28*l**2 + 17*l**2 - 9*l**3 - 12*l + 39*l**2 - 61*l**2 = 0.
-3, 0, 1, 4
Let b(c) be the second derivative of 3 - 1/12*c**4 - 7/2*c**3 + 23*c + 0*c**2. Determine m, given that b(m) = 0.
-21, 0
Suppose -50*v - 6 = -6. Let c(r) be the first derivative of 0*r**2 + 2/21*r**3 + 1/14*r**4 - 1 + v*r. Solve c(s) = 0 for s.
-1, 0
Let v(k) be the second derivative of -4*k**2 - 7/9*k**3 - 221*k + 1/36*k**4 + 1/60*k**5 + 0. Factor v(z).
(z - 4)*(z + 2)*(z + 3)/3
Find c, given that -2*c**4 + 5*c**2 + c - 36*c - 274*c + 305*c**3 - 3*c**4 + 4*c = 0.
-1, 0, 1, 61
Factor -650*m**2 + 645*m**2 - 11*m + 2020 - 474*m.
-5*(m - 4)*(m + 101)
Factor -k**2 - 3*k**3 - 3*k**2 + 4*k + 4*k**4 - 135770*k**5 + 135769*k**5.
-k*(k - 2)**2*(k - 1)*(k + 1)
What is a in 0 - 1/7*a**3 - 92/7*a**2 - 85*a = 0?
-85, -7, 0
Let c(t) be the second derivative of -t**4/18 + 61*t**3/9 - 1256*t. What is s in c(s) = 0?
0, 61
Let u = 1023 + -778. Suppose -u = 4*v - i - 247, -3*v - i - 2 = 0. Factor 0 + 2/15*f**5 + v*f**3 - 4/15*f**2 - 2/15*f + 4/15*f**4.
2*f*(f - 1)*(f + 1)**3/15
Let -273/8*l + 1/8*l**2 + 0 = 0. Calculate l.
0, 273
Suppose -5*q = -4*w, 2*w - 6 = -0*w + 4*q. Let c = w - -25. Determine u, given that c*u**4 - 10*u**4 + u**3 - 13*u**4 = 0.
0, 1/3
Let l(q) be the third derivative of 0*q - 3/40*q**5 + 5/16*q**4 + 1/140*q**7 - 1/80*q**6 + 0 - 108*q**2 - 1/2*q**3. Factor l(k).
3*(k - 1)**3*(k + 2)/2
Let b(h) = -2*h**3 - 30*h**2 - 870*h - 3030. Let p(r) = -4*r**3 - 92*r**2 - 2608*r - 9088. Let j(n) = -8*b(n) + 3*p(n). Factor j(u).
4*(u - 21)*(u + 6)**2
Let r(g) be the third derivative of -g**7/90 + g**6/90 + 43*g**5/180 - g**4/18 - 2*g**3 + 14*g**2 + g. Find z such that r(z) = 0.
-2, -1, 1, 18/7
Let w(h) be the first derivative of 22/5*h**3 - 2/5*h**6 + 51/25*h**5 + 3/5*h - 18 - 21/5*h**4 - 12/5*h**2. Factor w(g).
-3*(g - 1)**4*(4*g - 1)/5
Suppose -1736/11*n - 622/11*n**2 - 1176/11 - 64/11*n**3 - 2/11*n**4 = 0. Calculate n.
-14, -3, -1
Let 387/7*g**3 + 24 - 102/7*g**2 - 27/7*g**4 - 348/7*g = 0. Calculate g.
-1, 2/3, 14
Let x(l) be the first derivative of l**6/120 - 3*l**5/40 + l**4/16 + 5*l**3/12 + 20*l - 45. Let m(v) be the first derivative of x(v). Factor m(o).
o*(o - 5)*(o - 2)*(o + 1)/4
Let f(g) be the third derivative of 4*g**7/315 + 13*g**6/900 - g**5/45 - g**4/60 + 9781*g**2. Determine j, given that f(j) = 0.
-1, -1/4, 0, 3/5
Let h be 1078/55 + (-6)/10. Let c = h + -17. Determine y, given that 28*y**4 - 60*y**3 + 18*y**2 + 20*y**2 - 4*y**5 + 18*y**c - 20*y**2 = 0.
0, 1, 3
Factor -1736/13*d**3 - 2258/13*d**2 - 744/13*d - 72/13 - 392/13*d**4.
-2*(d + 2)**2*(14*d + 3)**2/13
Let a be 3 + 32/(-12)*3 + -1 + (-560)/(-90). Factor -6 + 52/9*m + a*m**2.
2*(m - 1)*(m + 27)/9
Let t(a) be the first derivative of -a**6/3 - 33*a**5/2 - 653*a**4/8 - 901*a**3/6 - 483*a**2/4 - 37*a - 1997. Let t(y) = 0. What is y?
-37, -2, -1, -1/4
Let -25 + 174*z - 164 - z + 190*z - 180*z**2 + 7 - z**3 = 0. What is z?
-182, 1
Let u = -19 + 20. Let i be (1/(-2) + u)*8. Factor -5*g**2 + 8*g + 3*g**3 + g**2 - 11*g**3 + 4*g**i.
4*g*(g - 2)*(g - 1)*(g + 1)
Let k(c) be the third derivative of -c**6/780 + 127*c**5/390 - 295*c**4/12 - 325*c**3 - 212*c**2. Determine t so that k(t) = 0.
-3, 65
Suppose 3*w = 8*w - 110. Suppose w = 3*l + 5*c, 0 = -4*c - 22 + 6. What is z in -l*z + 8*z - 3*z**2 + 0*z**2 = 0?
-2, 0
Let h(v) = -275*v**2 + 5589*v + 9889. Let q(o) = 55*o**2 - 1118*o - 1978. Let w(i) = 2*h(i) + 11*q(i). Let w(n) = 0. Calculate n.
-18/11, 22
Let d(a) be the first derivative of 5*a**3/6 + 35*a**2 + 2187. Suppose d(r) = 0. What is r?
-28, 0
Let r(z) be the second derivative of -23*z**4/60 - 49*z**3/30 - 3*z**2/5 - 2016*z. Determine u so that r(u) = 0.
-2, -3/23
Let t(b) be the first derivative of 8*b + 0*b**3 - 19 + 1/5*b**5 + 0*b**4 + 0*b**2. Let c(l) be the first derivative of t(l). Solve c(s) = 0.
0
Suppose -1075 = 14*t + 4413. Let z be (-12)/21*t/36 + -6. Factor 4/9 - 2/9*x**2 + z*x.
-2*(x - 2)*(x + 1)/9
Let h(k) be the third derivative of -k**5/30 + 65*k**4/6 - 256*k**3/3 - 464*k**2. Factor h(p).
-2*(p - 128)*(p - 2)
Let c(y) = 2*y**3 - 78*y**2 + 333*y + 248. Let b be c(34). Factor 9/2*a**3 - 3*a**2 - 4 - b*a.
(a - 2)*(3*a + 2)**2/2
Factor -16/5*v + 1/10*v**2 + 87/10.
(v - 29)*(v - 3)/10
Let k(i) be the first derivative of -i**4/22 - 644*i**3/33 - 641*i**2/11 - 640*i/11 - 2397. Determine d, given that k(d) = 0.
-320, -1
Let v(o) be the second derivative of 1 + 1/22*o**4 - 2/33*o**3 + 22*o - 4/11*o**2 + 1/220*o**5 - 1/330*o**6. Factor v(h).
-(h - 2)**2*(h + 1)*(h + 2)/11
Let s be (-100)/90 + 2 + (-3 - (-814)/198). Factor -22/5*o**3 + 0 - 2/5*o**s + 24/5*o.
-2*o*(o - 1)*(11*o + 12)/5
Let n(p) = 25*p**2 + 30*p - 20. Let y(j) = 1 - j**2 + 32*j - 122*j + 36*j + 53*j. Let h be ((-2)/(-6))/(2/6). Let v(k) = h*n(k) + 20*y(k). Factor v(a).
5*a*(a + 2)
Let l(k) be the third derivative of -k**5/240 + 37*k**4/16 - 4107*k**3/8 + 53*k**2. Suppose l(w) = 0. Calculate w.
111
Factor 387*k**4 - 51772 + 8039*k**2 + 166*k**3 - 1682*k**2 - 23634*k - 774*k**4 + 388*k**4 - 21946*k.
(k - 7)*(k + 1)*(k + 86)**2
Let o be (2 - (-11)/(-4)) + (-117)/(-156). Suppose o = -30*h - 7*h + 74. Factor 4*i - 8/3 - 4/3*i**h.
-4*(i - 2)*(i - 1)/3
Let a be -2 - (117/(-273) + (-18)/7). Suppose -d + 2 = -u, -4*u + a = d - 6. Suppose 4/11*v**d - 16/11*v - 2/11*v**4 + 8/11*v**2 + 0 = 0. Calculate v.
-2, 0, 2
Let h(w) = w**2 + w. Let u be h(-5). Suppose 11 = -r + u. Let -2 - 2 + 4*x**2 + 5*x - r*x**2 + 4*x**2 = 0. Calculate x.
1, 4
Let 180/7*f**3 + 354/7*f**2 + 2/7*f**4 + 0 + 176/7*f = 0. Calculate f.
-88, -1, 0
Let i(d) = -6*d**2 + 5*d. Let g = -40 + 42. Suppose -3 = 4*z + 3*m + 2*m, -3*m = g*z + 1. Let t(s) = -s**2 + s. Let q(b) = z*i(b) + 10*t(b). Factor q(h).
2*h**2
Let j(s) be the second derivative of 0*s**2 + 2/21*s**4 + 1/105*s**6 + 0*s**3 + 2/35*s**5 + 11*s + 4. Suppose j(t) = 0. What is t?
-2, 0
Let f(c) be the second derivative of c**4/12 - 3694*c**3/3 + 6822818*c**2 + 2457*c. Solve f(n) = 0 for n.
3694
Let b(q) be the second derivative of -q**8/840 + q**7/42 - 5*q**6/36 - 67*q**3/6 - 8*q + 1. Let j(v) be the second derivative of b(v). Solve j(a) = 0 for a.
0, 5
Factor 36/7*n**2 + 33/7*n**3 + 0*n + 0 - 3/7*n**4.
-3*n**2*(n - 12)*(n + 1)/7
Let j(t) be the first derivative of t**9/6048 + t**8/480 + t**7/112 + t**6/80 + 145*t**3/3 + 126. Let u(l) be the third derivative of j(l). Factor u(f).
f**2*(f + 1)*(f + 3)**2/2
Suppose 12*x = 2*x + 20. Factor 8*z**x - 12*z**2 + 84*z - 24*z.
-4*z*(z - 15)
Let c(k) = -72*k - 349. Let x be c(-5). Let r be (-3)/(-4) + x/(-44). Factor 3/4*s - r - 1/4*s**2.
-(s - 2)*(s - 1)/4
Let a be ((-4)/(-2))/((-11)/110*-10). Suppose -c + a = 2. Determine d so that 3/4*d + c + 1/4*d**2 = 0.
-3, 0
Let v be (-4372)/(-14) + -11 + 10. Let b = v + -311. Determine n, given that 2/7 + 2/21*n**3 - 2/21*n - b*n**2 = 0.
-1, 1, 3
Let b = -526833 + 526838. Let 0*x - 6/7*x**4 + 0*x**3 - 2/7*x**b + 8/7*x**2 + 0 = 0. What is x?
-2, 0, 1
Let r(y) be the first derivative of 0*y**5 - 20/3*y - 76/9*y**3 - 11*y**2 - 8/3*y**4 + 282 + 1/9*y**6. Find b such that r(b) = 0.
-2, -1, 5
Factor -9*z**3 + 0 + 3/4*z**4 + 0*z + 27*z**2.
3*z**2*(z - 6)**2/4
Suppose 1532 = 19*h + 1076. Let r(m) = 2*m + 1. Let f be r(1). Solve -11*k**2 - 4*k**3 + k**2 + h*k**f + 10*k**4 - 15*k - 5*k**5 = 0.
-1, 0, 1, 3
Let a(i) be the first derivative of i**6/6 + 8*i**5/5 - 39*i**4/4 - 38*i**3/3 + 142*i**2 - 264*i - 11692. Find v, given that a(v) = 0.
-11, -3, 2
Let k(x) = -2*x**3 - 2*x**2. Let s(r) = 2*