*k - 2/5*k**3 - 246/5*k**2 = 0. What is k?
-123, -1, 1
Let r(h) be the second derivative of 9/7*h**2 - 2/7*h**3 + 34*h + 1/42*h**4 + 0. Factor r(f).
2*(f - 3)**2/7
Let u(z) be the second derivative of -z**5/25 - 19*z**4/30 - 18*z**3/5 - 9*z**2 + z - 111. Suppose u(k) = 0. What is k?
-5, -3, -3/2
Let j(f) = -101*f**2 - 292*f - 61. Let g(z) = -3*z + 1. Let i(u) = -6*g(u) - j(u). Let p(h) = 34*h**2 + 104*h + 18. Let t(c) = -6*i(c) + 17*p(c). Factor t(m).
-4*(m + 3)*(7*m + 2)
Let d(t) = 78*t - 29. Let x be d(3). Find j, given that -156*j + 3*j**2 + x - 382 + 1336 + 869 = 0.
26
Let z(h) = h**3 + 79*h**2 + 152*h + 77. Let r(q) = -6*q**3 - 474*q**2 - 911*q - 462. Let p(t) = 6*r(t) + 38*z(t). Determine c, given that p(c) = 0.
-77, -1
Let o(r) be the first derivative of -4/9*r**3 - 67 - 1/36*r**6 + 1/4*r**2 + 0*r**5 + 1/4*r**4 + 0*r. Factor o(k).
-k*(k - 1)**3*(k + 3)/6
Suppose -170*z**5 + 8000000 - 118801*z**3 - 7854833*z + 505*z**5 + 7760600*z**2 - 163*z**5 + 598*z**4 + 23734833*z - 173*z**5 = 0. What is z?
-1, 200
Let s(n) be the first derivative of n**7/280 + 3*n**6/40 + 3*n**5/5 + 5*n**4/2 - n**3/3 + 45*n + 52. Let l(f) be the third derivative of s(f). Factor l(m).
3*(m + 2)**2*(m + 5)
Let g = 149722/5 + -29944. Factor g*z**2 - 2/5*z - 4/5.
2*(z - 2)*(z + 1)/5
Let w be -5 + (15132/(-338))/(-6). Factor w*n**2 + 12/13*n**4 + 2/13*n**5 + 18/13*n + 28/13*n**3 + 4/13.
2*(n + 1)**4*(n + 2)/13
Let l = 237 + -164. Factor 70 - 714*a**2 - l*a + 28*a + 719*a**2.
5*(a - 7)*(a - 2)
Let w(v) be the second derivative of v**4/4 - 100*v**3 + 15000*v**2 - 19*v - 1. Solve w(m) = 0.
100
Factor -469*k**3 - 12*k**2 + 7*k**2 - 51*k**3 + 0*k**2 + 0*k**2.
-5*k**2*(104*k + 1)
Let m(p) be the first derivative of 13*p**3/3 + 30*p**2 - 25*p - 2873. Suppose m(d) = 0. Calculate d.
-5, 5/13
Let a(n) be the second derivative of -1/6*n**4 - 34*n - 2*n**3 + 2 + 16*n**2. Factor a(c).
-2*(c - 2)*(c + 8)
Factor 15*b**4 + 260*b**2 + 84*b**3 + 8366 - 320*b**3 - 164*b**3 - 8366.
5*b**2*(b - 26)*(3*b - 2)
Let t(v) = 4*v**5 + 12*v**4 - 6*v**3 - 6*v**2 - 6. Let w(h) = 3*h**5 + 13*h**4 - 5*h**3 - 5*h**2 - 5. Let j(x) = -5*t(x) + 6*w(x). Let j(q) = 0. What is q?
0, 9
Let z = 844 - 841. What is a in -123 + 16*a**2 + 3*a + 24*a**2 - 14*a**2 - z*a**3 + 97*a**2 = 0?
-1, 1, 41
Find w, given that -54 + 3328907*w**2 + 51*w + 0*w**4 - 3*w**4 - 3328850*w**2 - 51*w**3 = 0.
-18, -1, 1
Let p(n) be the second derivative of -n**5/70 - 10*n**4/21 - 53*n**3/21 - 34*n**2/7 - 174*n - 2. What is c in p(c) = 0?
-17, -2, -1
Let a(h) be the third derivative of h**5/390 + h**4/78 - 323*h**3/39 - 1479*h**2. Factor a(g).
2*(g - 17)*(g + 19)/13
Let c = 12 - 7. Factor 8*l + 2*l**3 - l - c*l - 4*l**2.
2*l*(l - 1)**2
Let f(x) be the second derivative of 5*x**4/4 - 203*x**3/9 + 3*x**2/2 - 20*x + 6. Let f(u) = 0. Calculate u.
1/45, 9
Let n(h) be the third derivative of 17 + 56/3*h**4 - 43/5*h**5 - 2/7*h**7 + 1/84*h**8 + 67/30*h**6 + 0*h + 10*h**2 - 24*h**3. Determine w so that n(w) = 0.
1, 2, 9
Factor 26 + 144*r + 11/2*r**2.
(r + 26)*(11*r + 2)/2
Find d such that 8963378/5 + 2/5*d**2 - 8468/5*d = 0.
2117
Let q(l) be the first derivative of 4*l**5/35 + 2*l**4/7 - 76*l**3/7 - 340*l**2/7 - 64*l + 26. Let q(x) = 0. Calculate x.
-7, -2, -1, 8
Let g(k) be the third derivative of -3*k + 27/80*k**6 - 55*k**2 - 1/140*k**7 - 243/40*k**5 + 0 + 729/16*k**4 + 0*k**3. Factor g(d).
-3*d*(d - 9)**3/2
Suppose -172*k**4 + 0 - 8/3*k**3 + 688*k**2 + 0*k + 2/3*k**5 = 0. Calculate k.
-2, 0, 2, 258
Factor 87/8*d**2 - 3/8*d - 87/8 + 3/8*d**3.
3*(d - 1)*(d + 1)*(d + 29)/8
Let w(l) = -4*l - 13. Let n be w(-11). Find r, given that -16*r + 7*r**2 + 16 + 28*r**2 - n*r**2 = 0.
2
Let j(z) be the first derivative of -z**5/5 + 13*z**4/4 + 52*z**3/3 - 26*z**2 - 192*z - 352. Determine b, given that j(b) = 0.
-3, -2, 2, 16
Let o = -9199/150 + 184/3. Let m(t) be the third derivative of 3*t**2 + 0*t + 0*t**3 + 0*t**4 - o*t**5 + 0. Find d such that m(d) = 0.
0
Let c(t) be the second derivative of -t**4/90 + 19*t**3/15 + 58*t**2/15 - t - 17. Find h such that c(h) = 0.
-1, 58
Factor 128000 + 800*w + 5/4*w**2.
5*(w + 320)**2/4
Let i(x) be the first derivative of -3*x**4/4 + 148*x**3 - 15975*x**2/2 - 33750*x - 2787. Let i(p) = 0. What is p?
-2, 75
Let a = 961811 + -961808. What is f in 2/11*f**4 + 10/11*f**a + 6/11*f**2 - 10/11*f - 8/11 = 0?
-4, -1, 1
Let u(v) = 48*v**4 + 26*v**3 - 46*v**2 - 118*v - 80. Let n(f) = 10*f**4 + 5*f**3 - 9*f**2 - 23*f - 16. Let s(m) = -14*n(m) + 3*u(m). Factor s(p).
4*(p - 2)*(p + 1)**2*(p + 2)
Find p, given that -14*p + 84*p**2 - 39*p - 2*p**3 - p + 12*p**3 = 0.
-9, 0, 3/5
Let w(s) be the second derivative of -8*s**7/21 - 46*s**6/15 - 481*s**5/80 + 23*s**4/8 - 3*s**3/8 + 190*s - 1. Solve w(z) = 0 for z.
-3, 0, 1/8
Suppose -g + o = -3 - 8, 0 = 3*g - 5*o - 35. Suppose 0 = -5*y + g - 0. Solve -p**2 - 3*p**5 + p + 4*p**5 + p**2 - y*p**3 = 0 for p.
-1, 0, 1
Let j(c) be the second derivative of -c**4/12 + c**2/2 - 92*c. Let m(p) = -4*p**2 + 160*p - 3198. Let t(s) = -2*j(s) + m(s). Find f, given that t(f) = 0.
40
Let j(q) = -2*q**3 - 5*q**2 + q + 4. Let b be j(0). Let h = -68 + 68. Factor -3/2*w**5 + 0*w**3 + 0*w**b + 0*w**2 + 0*w + h.
-3*w**5/2
Let i(n) = n**2 - 23. Let u be i(5). Suppose -14*s**2 + 22*s - 10 + 20*s**u - 8*s**2 - 10 = 0. Calculate s.
1, 10
Let d be -16 + 7/(7/6) - 294/(-24). Factor 1 - d*v**2 - 4*v.
-(v + 2)*(9*v - 2)/4
Let i = -117 - -119. Find h, given that 118*h**2 - 4*h**4 - 32*h**3 + 49*h**2 - 40*h - 210*h**i + 119*h**2 = 0.
-10, 0, 1
Let f(c) = -59*c + 75. Let q be f(-9). Suppose 63*j + 481*j + 28*j**2 + q*j + 190*j - 200*j - 328 = 0. What is j?
-41, 2/7
Find h such that 60/13*h**3 - 574/13*h + 294/13 + 244/13*h**2 + 2/13*h**5 - 2*h**4 = 0.
-3, 1, 7
Determine u so that -14/5*u**2 + 6/5*u**4 + 0*u + 8/5 + 2/5*u**3 - 2/5*u**5 = 0.
-1, 1, 2
Suppose -17*n + 156 = 9*n. Suppose 2*c = -3*v - 5, -2*c + n*v = 4*v - 10. Let 16/5 + 4*y**c - 20*y**3 + 64/5*y = 0. Calculate y.
-2/5, 1
Let r(u) = -35*u**2 + 89*u - 44. Let v(p) = 351*p**2 - 891*p + 441. Let k(d) = 21*r(d) + 2*v(d). Factor k(a).
-3*(a - 2)*(11*a - 7)
Let f(l) be the second derivative of 11*l**6/30 + 82*l**5/15 + 226*l**4/9 + 368*l**3/9 - 8*l**2 - 1269*l. Solve f(z) = 0.
-6, -2, 2/33
Let g(r) = -1405*r - 2825. Let c(u) = u**2 + 703*u + 1411. Let o(l) = -5*c(l) - 3*g(l). Find d, given that o(d) = 0.
-2, 142
Let y be (21/(-3)*1/(-7))/(12/3). Factor 11/4*s**3 - y*s**4 + 0 - 8*s**2 + 7*s.
-s*(s - 7)*(s - 2)**2/4
Let i(r) be the first derivative of 17 + 13/2*r**2 - 14/15*r**3 - 20*r + 1/20*r**4. Factor i(l).
(l - 5)**2*(l - 4)/5
Let i(x) = -2*x**5 + 2*x**4 - 4*x**3 - 8*x**2 + 16. Let p(q) = 2*q**5 - q**4 + 4*q**3 + 7*q**2 - 14. Let g(w) = -7*i(w) - 8*p(w). Factor g(n).
-2*n**3*(n + 1)*(n + 2)
Let t(o) be the first derivative of -o**7/21 - 3*o**6/5 - 3*o**5/2 - 7*o**4/6 + 54*o + 3. Let l(f) be the first derivative of t(f). Factor l(g).
-2*g**2*(g + 1)**2*(g + 7)
Let t = 282682 + -565353/2. Determine n, given that 1/4*n**2 + 9/4*n - t = 0.
-11, 2
Suppose 182*z - 330 = 167*z. Suppose -2*k = z*k. Factor 0*g + 2/7*g**2 + 4/7*g**3 + k + 2/7*g**4.
2*g**2*(g + 1)**2/7
Determine h, given that -248*h**4 - 12249*h**2 + 9913*h**2 - 2048*h - 512 - 1227*h**3 + 91*h**3 - 20*h**5 = 0.
-4, -2, -2/5
Let m(x) be the second derivative of x**6/10 - 3*x**5/10 - 4*x**4 + x**3 + 45*x**2/2 + 3*x - 4. Suppose m(b) = 0. Calculate b.
-3, -1, 1, 5
Suppose 4*a + 4*s + 372 = 0, 3*a - 2*s + 44 + 220 = 0. Let t be 590/a + 1 + 6. Factor t*r**2 + 0 + 8/9*r - 2/9*r**3 - 1/9*r**4.
-r*(r - 2)*(r + 2)**2/9
Let p = 6780 - 4346. Let k = p + -2431. Factor -3/4*m**2 + 0 + 3/4*m**k - 3/2*m.
3*m*(m - 2)*(m + 1)/4
Let b(m) be the second derivative of m**8/2520 + m**7/1260 - m**6/135 - m**5/45 - m**3 + m**2 - 34*m. Let o(t) be the second derivative of b(t). Factor o(c).
2*c*(c - 2)*(c + 1)*(c + 2)/3
Let y(a) = 131*a**3 + 266*a**2 + 4*a - 6. Let g be y(-2). Factor -3/4*q**g - 3/2*q**4 + 0 + 3/8*q - 21/8*q**3.
-3*q*(q + 1)**2*(4*q - 1)/8
Solve 3*v - 1/4*v**3 + 0 - 1/4*v**2 = 0.
-4, 0, 3
Let k = 549538/13 - 42272. Determine g, given that -22/13*g + 64/13*g**2 + 16/13*g**4 + k*g**5 - 60/13*g**3 + 0 = 0.
-11, 0, 1
Suppose 1600863 + 533315 - 2344*m + 2*m**2 - 1788*m = 0. What is m?
1033
Factor 8 + 4*g - 2/9*g**2 - 1/9*g*