. Factor x**4 + u*x**4 - 20*x - x**4 + 3*x**4 + 24 - 92*x**2 - 28*x**3.
4*(x - 3)*(x + 1)**2*(5*x - 2)
Let h(m) = 3*m**2 + 59*m. Let c be h(9). Let v be c/(-86) + (12 - -1). Determine x, given that 1/2*x**v + 0 - x**3 + 0*x + 1/2*x**2 = 0.
0, 1
Let k(j) be the second derivative of 2*j**6/135 - j**5/15 + 2*j**4/27 - 781*j + 1. Factor k(h).
4*h**2*(h - 2)*(h - 1)/9
Let p(j) be the second derivative of 0*j**2 + 0 + 176*j - 1/24*j**4 - 1/12*j**3. Factor p(w).
-w*(w + 1)/2
Let h(c) = -12*c**4 + 112*c**3 - 1100*c**2 + 3208*c - 2696. Let j(a) = -a**4 - a**3 + a**2 + 11*a + 1. Let s(l) = -h(l) + 8*j(l). Let s(r) = 0. Calculate r.
2, 13
Let w(f) be the second derivative of 1 + 77*f - f**3 + 1/12*f**4 + 4*f**2. Find r, given that w(r) = 0.
2, 4
Let k = 4/16493 - -263876/49479. Let j(u) be the second derivative of 8/9*u**3 + 7 + 2*u - k*u**2 - 1/18*u**4. Factor j(n).
-2*(n - 4)**2/3
Let 0 - 1/5*p**4 - 64/5*p + 127/5*p**2 - 62/5*p**3 = 0. What is p?
-64, 0, 1
Let j = -943 - -943. Suppose -5*w = 4*x + 6, j*x = -3*w - x + 2. Find u, given that 14/5*u**4 - 2/5*u**3 + 0*u - 6/5*u**2 + w*u**5 + 0 = 0.
-1, 0, 3/5
Factor 978*m**4 - 9108*m**2 - 2935*m**4 - 360*m**3 + 975*m**4 + 978*m**4 - 63504 - 45360*m.
-4*(m + 3)**2*(m + 42)**2
Let b(r) be the first derivative of -2/3*r**2 + r - 62 - 7/9*r**3. Determine h so that b(h) = 0.
-1, 3/7
Let o(q) be the third derivative of -q**7/630 + 11*q**6/180 + 83*q**5/180 - 187*q**4/6 - 578*q**3 + 354*q**2 + 1. Factor o(r).
-(r - 17)**2*(r + 6)**2/3
Let m be 2 + -1 + 0 + 4 + 33. Solve -m*l**3 - 5*l**4 + 48*l**3 - 56*l + 20*l**2 + 16*l = 0.
-2, 0, 2
Let z(w) be the second derivative of w**5/300 - w**4/120 - 6*w**2 + 2*w + 45. Let q(i) be the first derivative of z(i). Factor q(u).
u*(u - 1)/5
Let w(t) = -4 - 4*t + t**2 + 8*t + 8 + 4*t. Let u be w(-8). Factor 3 + 2*b**3 - b + 6*b**5 - 6*b**2 + u*b**4 - b**4 - 7*b**5.
-(b - 3)*(b - 1)**2*(b + 1)**2
Let n(r) = 0*r**2 - 4 - r - 4*r**3 - r**2 + 3*r**3. Let y be n(-2). Factor 32*a + 10*a**y + 0 + 25 - 4 + 11 + a**3.
(a + 2)*(a + 4)**2
Suppose -6*b - 13 = 47. Let o be ((-12)/b)/((-24)/(-80)). Find f such that -7*f**4 + 3*f**3 + 11*f**o - 7*f**3 = 0.
0, 1
Let b(c) = 9*c**3 - 15*c**2 + 6*c - 4. Let g(x) = -21*x**3 + 16*x + 90*x**2 + 25 - 34*x**3 - 35*x - 16*x. Let t(o) = -25*b(o) - 4*g(o). What is y in t(y) = 0?
0, 1, 2
Let l(x) be the third derivative of 3*x**7/350 + 5*x**6/12 + 421*x**5/300 + 16*x**4/15 - 26*x**3/15 - 517*x**2. Let l(v) = 0. Calculate v.
-26, -1, 2/9
Let u = -5414 + 5419. Let b(m) be the third derivative of -2/3*m**3 - 1/4*m**4 - 1/30*m**u + 0*m + 19*m**2 + 0. Let b(s) = 0. What is s?
-2, -1
Let j(f) be the third derivative of -f**6/30 - 4*f**5/15 + 10*f**4 + 1113*f**2. Factor j(y).
-4*y*(y - 6)*(y + 10)
Let n be 7 + 0 + ((-308)/(-55) - -9). Let v = -2/2391 + 86086/11955. Find i, given that -n - 3/5*i**2 - v*i = 0.
-6
Let m(x) be the first derivative of -35/4*x**4 + 5/6*x**6 + 0*x**2 + 2*x**5 + 0*x + 78 + 20/3*x**3. Suppose m(f) = 0. Calculate f.
-4, 0, 1
Factor -1840/13*b - 423200/13 - 2/13*b**2.
-2*(b + 460)**2/13
Determine t so that 128/3*t**4 + 1280 + 388*t**3 + 4/3*t**5 + 4432/3*t**2 + 7232/3*t = 0.
-20, -4, -3, -1
Solve 64/5 + 4/5*t**2 - 68/5*t = 0.
1, 16
Suppose -3*y = 56 - 65. Factor n**4 + 53*n**2 + 36 - 162*n**3 - 142*n**3 + 318*n**y + 76*n.
(n + 1)*(n + 2)**2*(n + 9)
Suppose -5*v = -5*c, v + 3*v - 306*c = -304*c. Let o(m) be the third derivative of 2*m**2 - 1/60*m**5 - 1/4*m**4 + 0 + 0*m + v*m**3. Solve o(z) = 0 for z.
-6, 0
Let 7*k**3 + 17*k**3 - 929878*k**4 - 22*k**2 + 929876*k**4 = 0. What is k?
0, 1, 11
Let s(h) = -h**3 + 19*h**2 + 106*h - 880. Let x be s(22). Factor -5/2*n**2 + x - 5/4*n**3 + 15/4*n.
-5*n*(n - 1)*(n + 3)/4
Let u(l) = -5*l**2 - 2*l + 6. Let a(v) = 9*v**2 + 5*v - 11. Let q(o) = 6*a(o) + 11*u(o). Let g be q(4). Factor -5 - g*r**2 - r**3 - 3 - 20*r - 3*r**3 + 0.
-4*(r + 1)**2*(r + 2)
Suppose 106*x**4 - 6538644*x - 50*x**4 - 44760*x**2 + 6434856 - 559*x**3 + 121317*x**2 + 27789*x**2 - 55*x**4 = 0. What is x?
1, 186
Let b = 1 + 2. Let x = -709 + 719. Let -18*c + 9*c - b*c**4 + 9*c**3 + 7*c**2 - x*c**2 + 6 = 0. Calculate c.
-1, 1, 2
Find p such that -p**3 - 1824 - 1716 + 20 - 3*p**3 - 896*p**2 + 3640*p - 7176*p = 0.
-220, -2
Let y(j) = -2*j**2 - 60*j + 21. Let x be y(-30). Suppose -4*a = -5*l - 0 + 2, 2*l + 3*a - 10 = 0. Suppose 8*k + 6*k**l + k - x*k - 2*k**2 + 8 = 0. Calculate k.
1, 2
Suppose -45 = -3*i - 36. Suppose -103 - o**2 + 207 - 102 - o**4 - 3*o + i*o**3 = 0. Calculate o.
-1, 1, 2
Let b = 1411889/25485 + -4/5097. Let t = 56 - b. Let 12/5*v**2 + 0 - t*v**5 - 4/5*v + 3/5*v**3 - 8/5*v**4 = 0. Calculate v.
-2, 0, 1/3, 1
Let m(d) be the third derivative of 13*d**6/30 - 1147*d**5/75 + 353*d**4/15 + 272*d**3/15 + 158*d**2 - 4. Let m(j) = 0. What is j?
-2/13, 4/5, 17
Factor -1/2*q**3 - 93/2*q**2 + 1/2*q + 93/2.
-(q - 1)*(q + 1)*(q + 93)/2
Let k = 43 - 555/13. Let o be 4/(-42) - (-2652)/10647. Suppose 0 + k*j**2 + o*j**3 + 0*j = 0. Calculate j.
-2, 0
Suppose -4*p + 3*n + 16 = 0, -4*p = 4*n - 7 - 9. Let a be (p + (-72)/21)*21/6. Factor -3/4*u**3 + 3/2*u**a - 3/2 + 3/4*u.
-3*(u - 2)*(u - 1)*(u + 1)/4
Let d(p) = -2*p**2 - p + 4. Let r = 5 - -1. Let a(k) = 3*k**2 - 46 + 0*k**2 + 3*k + 20 + 18. Let w(l) = r*a(l) + 10*d(l). Factor w(b).
-2*(b - 2)**2
Let a be 0*(-2)/(-6) - (-56)/8. Let y(l) be the third derivative of 2/735*l**a + 0 + 1/21*l**5 - 2/105*l**6 + 0*l - 1/21*l**4 + 8*l**2 + 0*l**3. Factor y(i).
4*i*(i - 2)*(i - 1)**2/7
Suppose -6426 = -1728*y - 1242. Factor -3/7*n**y - 51/7*n**2 - 93/7*n - 45/7.
-3*(n + 1)**2*(n + 15)/7
Let z(y) = -y**3 + 9*y**2 + 2*y + 22. Let v be z(10). Let m = -29 - v. Find f such that 0*f**3 + 28*f**4 + 0*f**3 - f**5 - m*f**4 = 0.
-1, 0
Let f = -1216 + 1234. Let r be (1*(-243)/f)/(-1). Let -r*c**5 + 21/2*c**2 - 9/2*c**4 + 51/2*c**3 - 12*c - 6 = 0. What is c?
-1, -2/3, 1
Let v(l) be the first derivative of l**4/2 + 1114*l**3/21 - 807*l**2/7 + 486*l/7 - 4545. Factor v(n).
2*(n - 1)*(n + 81)*(7*n - 3)/7
Factor 9 + 9755*g - 9632*g - 63*g**2 + 5*g**2 + 16*g**2.
-3*(g - 3)*(14*g + 1)
Suppose -y - w + 4 = 0, y - 24*w - 19 = -20*w. Factor -i**3 + 2*i**2 + 4*i**3 - i**4 - 181*i + 170*i + 5 + y*i**3 - 6*i**4 + i**5.
(i - 5)*(i - 1)**3*(i + 1)
Factor 3 - 377968*j**2 + 13*j + 377967*j**2 - 3 + 28 + 14*j.
-(j - 28)*(j + 1)
Let i = 4689/11735 - -1/2347. Let m(u) be the second derivative of 8*u**2 + 0 + i*u**6 + 14/5*u**5 + 32/3*u**3 + 28*u + 23/3*u**4. Determine z so that m(z) = 0.
-2, -1, -2/3
Let u be (-13020)/1395*18/(-8). Let t(x) = -x**3 + 3*x**2 + 5*x - 2. Let j be t(4). Let 0*b**2 + 3*b**j + 6 + 16*b + 2*b + u = 0. What is b?
-3
Suppose -15/2*r**4 + 35/2*r**2 + 200 + 5/2*r**5 - 215/2*r**3 + 315*r = 0. What is r?
-5, -1, 2, 8
Let u(q) be the first derivative of -5*q**2 + 8/3*q**3 - 1/2*q**4 + 18 + 4*q. Solve u(c) = 0 for c.
1, 2
Let q(s) be the first derivative of -3*s**4/20 - 6*s**3 - 243*s**2/10 + 753. Find l, given that q(l) = 0.
-27, -3, 0
Let j(d) be the third derivative of d**5/80 - d**4 + 39*d**3/2 - 224*d**2. Factor j(h).
3*(h - 26)*(h - 6)/4
Let o(i) be the third derivative of -4*i**2 - 1/336*i**8 - 1/6*i**4 + 1/105*i**7 - 1/15*i**5 + 5 + 0*i**3 + 1/40*i**6 + 0*i. Factor o(n).
-n*(n - 2)**2*(n + 1)**2
Let x = 7 + 74. Suppose -x + 17 = -4*o. Solve 15*c**2 + 6*c**2 - 23*c**2 + o*c = 0 for c.
0, 8
Let i = -45 + 68. Let v = 266 + -255. Determine r, given that 21*r - 2*r**2 + v - i*r + 1 = 0.
-3, 2
Let r(t) be the third derivative of t**5/120 - 33*t**4/16 + 24*t**3 + 58*t**2 + 21. Factor r(i).
(i - 96)*(i - 3)/2
Let -8/7 + 6/7*w**4 + 24/7*w - 22/7*w**2 - 2/7*w**5 + 2/7*w**3 = 0. Calculate w.
-2, 1, 2
Let m(q) be the second derivative of -3/140*q**5 + 0*q**3 - 1/14*q**4 + 0 + 0*q**2 - 49*q. Suppose m(s) = 0. What is s?
-2, 0
Let n(s) = 8*s**2 - 430*s - 842. Let t(i) = i**2 - 32*i - 1. Let h(m) = -n(m) + 5*t(m). Factor h(d).
-3*(d - 93)*(d + 3)
Let r be 1*(-16)/12*(-9)/3. Factor 4076*b**3 - 3659*b**4 + 6812*b - 2232*b - 561*b**4 + 280 + 38879*b**3 + 24750*b**2 - 2435*b**r.
-5*(b - 7)*(11*b + 2)**3
Let j be 99/27 + 4/3 + 0. Let 15*r**4 + 30*r**2 + 3 + 30*r**3 + 84*r + 75*r - 144*r + 3*r**j = 0. Calculate r.
-1
Let g(a) be the third derivative of -2*a**7/105 + 11*a**6/15 + 52*a**5/15 - 44*a**4/3 - 128*a**3 + 2003*a**2. F