- 1/2*j**4 + 25*j**3.
-(j - 22)**2*(j - 3)**2/2
Find a, given that -8192 - 38024*a**2 - 2401/2*a**4 - 32256*a - 12348*a**3 = 0.
-32/7, -4/7
Let y(d) be the first derivative of 2*d**3/57 + 83*d**2/19 - 168*d/19 + 515. Let y(x) = 0. Calculate x.
-84, 1
Let k(h) be the second derivative of -h**5/150 - 11*h**4/90 - 26*h**3/45 - 16*h**2/15 + 320*h. Suppose k(u) = 0. Calculate u.
-8, -2, -1
Let l(x) = -x**2 + 5*x + 14. Let r be l(8). Let v = r + 43. Find w, given that -v*w**4 + 4*w**2 - 8*w**3 + 8*w**5 + 0*w**5 + 29*w**4 = 0.
-1, 0, 1/2, 1
Let c(n) be the second derivative of -n**6/35 + 39*n**5/70 - 25*n**4/7 + 32*n**3/7 + 288*n**2/7 - 3196*n. Suppose c(r) = 0. Calculate r.
-1, 4, 6
Let -1/4*h**2 - 13/12*h - 5/6 = 0. Calculate h.
-10/3, -1
Suppose -4*y - 3*w + 5 = 0, -14*w = 2*y - 13*w - 3. Let p(c) = 14*c**2 + 24*c + 8. Let z(h) = h**3 - h + 1. Let k(l) = y*z(l) + p(l). Factor k(x).
2*(x + 1)**2*(x + 5)
Suppose -117*m + 1584 = -129*m. Let d be m/(-110)*5/3. Factor d*w**3 - 4/3*w + 0 - 2/3*w**2.
2*w*(w - 1)*(3*w + 2)/3
Let p(o) be the second derivative of -8/15*o**2 + 17 - 1/150*o**5 - 1/9*o**4 + 3*o - 17/45*o**3. Factor p(m).
-2*(m + 1)**2*(m + 8)/15
Let w(m) = -m**4 - m**3 - m**2 + 4*m + 1. Let z(k) = 4*k**4 + 46*k**3 - 181*k**2 + 176*k - 3. Let a(q) = -12*w(q) - 4*z(q). Find v such that a(v) = 0.
-47, 0, 2
Factor -100/19 + 3030/19*l - 11858/19*l**3 - 22176/19*l**2.
-2*(l + 2)*(77*l - 5)**2/19
Let y be 1159/(-2145) - 750/(-1375). Let z(b) be the third derivative of y*b**5 + 0*b + 21*b**2 + 1/156*b**4 + 0*b**3 + 0 + 1/780*b**6. Factor z(a).
2*a*(a + 1)**2/13
Determine h so that 56*h**2 - 8*h + 12*h**3 - 4*h**4 - 22*h - 2*h**5 - 2*h**4 + 78*h = 0.
-2, 0, 3
Let j = -320844 + 320846. Factor -1/4*f**j + 21/4 + 5*f.
-(f - 21)*(f + 1)/4
Suppose 0 = -3*w + 3*a + 1114 + 647, -3*w = 3*a - 1791. Let f = w - 590. Factor 24/7*o**3 + 12/7*o**4 + 0 + 6/7*o + 2/7*o**5 + 20/7*o**f.
2*o*(o + 1)**3*(o + 3)/7
Let o(g) be the second derivative of -3*g - 1/4*g**5 + 0*g**3 - 1/3*g**6 - 22 + 5/6*g**4 + 5/42*g**7 + 0*g**2. Let o(p) = 0. What is p?
-1, 0, 1, 2
Let k(y) be the second derivative of y**7/28 + 2*y**6/5 - 69*y**5/40 - 13*y**4/4 + 11*y**3 + 30*y**2 - 8248*y. Determine a, given that k(a) = 0.
-10, -1, 2
Let m(a) be the first derivative of -a**6/21 + 2*a**5/35 + 31*a**4/7 - 152*a**3/7 + 216*a**2/7 + 3203. Solve m(k) = 0 for k.
-9, 0, 2, 6
Suppose 0 = 5*b - 2*p + 3, -4*p = 5*b - 8 - 13. Suppose -z - z + b = g, -2*z = 2*g + 2. Factor -25/3*n**z - 5/3*n**3 - 20/3 - 40/3*n.
-5*(n + 1)*(n + 2)**2/3
Let n(p) be the second derivative of -3*p**5/20 - 27*p**4/2 - 203*p**3/2 - 225*p**2 - 6*p - 73. Solve n(o) = 0 for o.
-50, -3, -1
Let r(n) be the first derivative of -34*n**3/15 + 9*n**2/5 + 161. Factor r(u).
-2*u*(17*u - 9)/5
Let t = -420 + 418. Let h be t*2 - 748/(-170). Determine s, given that 0 + 2/15*s**5 - 4/15*s + h*s**4 + 2/15*s**3 - 2/5*s**2 = 0.
-2, -1, 0, 1
Let n(s) be the first derivative of -6*s**5/25 + 51*s**4/10 - 62*s**3/5 + 9*s**2 + 7563. Determine b so that n(b) = 0.
0, 1, 15
Let d(m) be the third derivative of -m**8/2184 - m**7/65 - 7*m**6/78 - m**5/13 + 71*m**4/156 + 17*m**3/13 - m**2 + 1863. Solve d(z) = 0.
-17, -3, -1, 1
Let b(g) = -46*g - 6 + 3*g**3 + 5*g**2 + 50*g**2 - 12 - 12*g**3. Let r(w) = -w**2 - w - 1. Let h(v) = b(v) - 6*r(v). What is f in h(f) = 0?
-2/9, 1, 6
Let h(g) be the first derivative of 2*g**6/7 + 116*g**5/35 + 87*g**4/7 + 52*g**3/3 + 60*g**2/7 + 74. Suppose h(i) = 0. What is i?
-5, -3, -1, -2/3, 0
Let i(n) = n**2 + 30*n - 31. Let m be i(-31). Suppose 34*a - 13 - 55 = m. Factor -2/3*q**4 + 0*q - 4/3*q**a + 0 + 2*q**3.
-2*q**2*(q - 2)*(q - 1)/3
Let v = 122105/98 + -1246. Let q = 20/147 - v. Find l such that 1/2 + 1/3*l - q*l**2 = 0.
-1, 3
Let d(x) be the second derivative of -x**6/1440 + x**5/96 + 7*x**4/48 + 15*x**3 + 5*x. Let w(s) be the second derivative of d(s). Factor w(i).
-(i - 7)*(i + 2)/4
Let r(p) be the third derivative of 1/6*p**4 + 38*p**2 + 4*p**3 - 1/15*p**5 + 0 + 0*p. Factor r(w).
-4*(w - 3)*(w + 2)
Suppose -14/15*q**2 + 0 - 2/3*q**5 + 82/15*q**3 + 0*q - 58/15*q**4 = 0. Calculate q.
-7, 0, 1/5, 1
Let a(n) be the first derivative of 5*n**6/6 - 11*n**5 + 95*n**4/4 - 15*n**3 - 58. What is h in a(h) = 0?
0, 1, 9
Let n(r) be the second derivative of -2*r - 13 - 5/12*r**4 + 0*r**2 + 55/2*r**3. Factor n(p).
-5*p*(p - 33)
Let u = -14917 - -46597/3. Let f = u + -615. Let 2/3*n + 1/3*n**2 + f = 0. What is n?
-1
Let n(f) be the first derivative of 1/3*f**4 + 0*f - 1/2*f**2 + 0*f**3 + 1/15*f**5 + 10. Let a(c) be the second derivative of n(c). Factor a(p).
4*p*(p + 2)
Solve -7*y**3 - y**3 + 156*y**2 - 60*y**4 - 58*y**4 + 608*y + 114*y**4 + 448 = 0.
-4, -1, 7
Let t(n) be the third derivative of 1/6*n**3 - 184*n**2 + 1/16*n**4 + 0 + 1/120*n**5 + 0*n. Suppose t(g) = 0. What is g?
-2, -1
Let h be (13/2)/((-11)/(-22)). Suppose -h*v + v = -36. Factor -10*b**2 - 25 + 45*b + 13*b**4 + 5*b**5 + 5 - 40*b**v + 17*b**4 - 10*b**5.
-5*(b - 4)*(b - 1)**3*(b + 1)
Let n(z) = -z**2 - 141*z + 177786. Let u be n(357). Let 7/6*t**3 + 5/3*t**2 + 0*t + u = 0. What is t?
-10/7, 0
Let j = 1018581 + -5092899/5. Let -3/5*h**4 + 0 - 6/5*h**3 + j*h + 3/5*h**2 = 0. What is h?
-2, -1, 0, 1
Let a(x) = 25*x**2 - 155*x - 160. Let j(l) = 7*l**2 - 52*l - 53. Let i(v) = -3*a(v) + 10*j(v). Factor i(n).
-5*(n + 1)*(n + 10)
Let i = 220/7801 - -13622/70209. Solve 64/9 - 4*m + i*m**2 = 0 for m.
2, 16
Let x(j) be the second derivative of j**7/63 + 8*j**6/9 + 65*j**5/6 + 125*j**4/3 + 1077*j. Determine q, given that x(q) = 0.
-30, -5, 0
Let r(z) be the third derivative of -z**8/112 + 73*z**7/840 + 29*z**6/160 - 59*z**5/240 - 25*z**4/32 - 7*z**3/12 - 42*z**2. Find o, given that r(o) = 0.
-1, -2/3, -1/4, 1, 7
Let p = -18 - -21. Solve 3*f**2 + 2*f**2 - 21 - f**p - 140*f + 5*f**3 - 3*f**3 + 123*f = 0.
-7, -1, 3
Suppose 0 = 10*r - f + 10, 2*r - 89 = 4*r - 3*f - 3. Let v = -55/4 - -14. Factor 1/2*d - v*d**r + 3/4.
-(d - 3)*(d + 1)/4
Let u = -4290 - -4290. Let k(s) be the third derivative of 0*s + 0 + 14*s**2 + u*s**3 - 1/480*s**6 + 1/96*s**4 + 1/840*s**7 - 1/240*s**5. Factor k(j).
j*(j - 1)**2*(j + 1)/4
Let o = -31189 + 405889/13. Factor 972/13*q + 4*q**3 - o*q**2 - 2/13*q**4 + 1458/13.
-2*(q - 9)**3*(q + 1)/13
Let m(l) = 4*l**3 + 5*l**2 - 17*l + 27. Let c be m(8). Let o be 1 - -1 - (-9 + c/207). Factor 6/23*d**3 + 2/23*d**4 + o*d + 0 + 6/23*d**2.
2*d*(d + 1)**3/23
Let v(n) = 2068*n + 20680. Let m be v(-10). Let b = 94 - 468/5. Factor -1/10*t**2 + b*t + m.
-t*(t - 4)/10
Let i(r) = -r**3 - 21*r**2 - 21*r - 18. Let k be (-441)/14 + 13 - (-3)/(-2). Let m be i(k). Solve m*t + 8/3 + 1/3*t**2 = 0.
-4, -2
Let d(x) be the first derivative of -x**3/6 + 45*x**2/4 + 23*x - 3698. Let d(a) = 0. Calculate a.
-1, 46
Suppose -19*c + 76 = 0, 27 = 5*r - 2*c + 13*c - 8*c. Factor 2/7*m**r + 10*m - 22/7*m**2 - 50/7.
2*(m - 5)**2*(m - 1)/7
Let -2/3*x**5 - 6*x + 16/3*x**4 - 44/3*x**3 + 16*x**2 + 0 = 0. Calculate x.
0, 1, 3
Factor 5*w - 14*w**2 + 5*w**3 + 0*w**3 + 3*w**2 - 2*w**2 + 3*w**2.
5*w*(w - 1)**2
Let m(r) be the first derivative of -3*r**4/4 - 6120*r**3 - 18727200*r**2 - 25468992000*r + 2819. Factor m(n).
-3*(n + 2040)**3
Suppose -1581*d = 4104*d. Let 188/7*h - 4/7*h**2 + d = 0. What is h?
0, 47
Suppose -260*o + 50 + 593 + 230 = 93. Factor 1144/3*i + 2704/3 - 100/3*i**2 + 2/3*i**o.
2*(i - 26)**2*(i + 2)/3
Suppose 0 = -2*i - 5*g + 119, g - 2 = 1. Factor 10*o**3 - 198 - i*o**2 - 105*o - o**5 + 6*o**4 + 384 - 236.
-(o - 5)**2*(o + 1)**2*(o + 2)
Let g = 56 - 158. Let s = g + 102. Suppose -x**2 - 8*x + s*x**4 - 4*x**4 + 8*x**3 + 5*x**2 = 0. Calculate x.
-1, 0, 1, 2
Let o be 1 - (4 - (-7)/(-1)). Factor -18*w**2 + 21*w**4 + 70*w**3 - 70*w**o - 67*w**2 + 34*w**4 + 30*w.
-5*w*(w - 3)*(w - 1)*(3*w - 2)
Factor 17*r**2 - 177*r - 86*r**2 + 432 - 39*r**3 + 36*r**3 - 183*r.
-3*(r - 1)*(r + 12)**2
Let x(p) be the first derivative of -p**7/1365 - p**6/780 + 13*p**2/2 + 51. Let u(n) be the second derivative of x(n). Factor u(t).
-2*t**3*(t + 1)/13
Let v(j) be the second derivative of -j**5/15 + 2*j**4/9 + 2*j**3/3 - 4555*j. What is b in v(b) = 0?
-1, 0, 3
Let z(j) = 6*j - 4*j**2 + 10 + 0*j**3 + 0*j**3 + j**3 - 67*j. Let g be z(10). Solve -6/5*m + g + 9/5*m**2 - 3/5*m**3 = 0.
0, 1, 2
Let n(g) = -9*g**3 - 1913*g**2