et t(u) = -68*m(u) - 6*w(u). Find s such that t(s) = 0.
-861
Let n = -10 + 15. Suppose n*h - h + 7 = -3*w, -3*w + 3*h + 21 = 0. Suppose -35*t**4 + 23*t**4 - 20*t**w - 3*t**5 + 8*t**3 = 0. Calculate t.
-2, 0
Suppose 46*b + 46*b = 30*b. Let h(i) be the third derivative of 1/210*i**7 + b*i**3 - 1/24*i**6 - 1/8*i**4 + 0*i + 0 + 7/60*i**5 - 10*i**2. Factor h(p).
p*(p - 3)*(p - 1)**2
Let v be (3/6*-6)/(72/(-760)). Let k(w) be the first derivative of -40*w**2 - 22 - 25/4*w**4 - v*w**3 + 20*w. Find s such that k(s) = 0.
-2, 1/5
Suppose -4*i + x = 126 - 139, -3*x = 3. Let n(s) be the first derivative of 0*s - 3/16*s**4 - 1/20*s**5 - 10 + 0*s**i + 1/2*s**2. Suppose n(b) = 0. What is b?
-2, 0, 1
Let f(i) be the third derivative of -i**8/15120 - i**7/1680 - i**6/1080 - 17*i**5/12 + 2*i**2 - 81*i. Let n(l) be the third derivative of f(l). Factor n(o).
-(o + 2)*(4*o + 1)/3
Let i(x) be the first derivative of -x**4/16 + 4*x**3/3 - 49*x**2/8 - 33*x/2 + 2847. Let i(q) = 0. What is q?
-1, 6, 11
Let l(u) be the third derivative of u**6/360 - 91*u**5/90 - 373*u**4/24 - 94*u**3 - 5369*u**2. Find v, given that l(v) = 0.
-3, 188
Let y(x) be the first derivative of -x**3 - 288*x**2 - 1140*x + 8134. Suppose y(d) = 0. Calculate d.
-190, -2
Let u(w) = -6*w + 1. Let b be u(0). Suppose t - 5*s - b = 16, 0 = 2*s + 6. Factor 12/5 + 16/5*x**t + 26/5*x + 2/5*x**3.
2*(x + 1)**2*(x + 6)/5
Let v = 12 - 10. Let q be 2*(21/6 - v). Suppose -34*f**2 - q*f**3 + 3*f - 27*f**2 + f**4 + 60*f**2 = 0. What is f?
-1, 0, 1, 3
Let n(z) = 2*z**3 - z**2 - 3*z - 1. Let k(a) = 10*a**3 + 56*a**2 - 626*a + 1914. Let t(w) = -k(w) + 6*n(w). Suppose t(i) = 0. What is i?
8, 15
Let n(p) be the first derivative of -p**5/10 + 19*p**4/2 - 253*p**3 + 703*p**2 - 1369*p/2 - 272. Let n(a) = 0. What is a?
1, 37
Let q = 24361 - 24361. Factor q + 1/8*n**2 - 5/4*n.
n*(n - 10)/8
Suppose 2186*s**2 + 6241/3 + 12640/3*s + 160/3*s**3 + 1/3*s**4 = 0. Calculate s.
-79, -1
Let t be (-79)/9 + (-26)/117. Let a(o) = -o**3 - 10*o**2 - 7*o + 21. Let l be a(t). Let 2*q**5 - 38*q + 2*q**3 - 4*q**l + 38*q = 0. Calculate q.
-1, 0, 1
Let o(c) be the first derivative of c**8/2520 + 2*c**7/315 + 4*c**6/135 - 32*c**3/3 - 63. Let j(b) be the third derivative of o(b). Suppose j(g) = 0. What is g?
-4, 0
Let r(o) be the third derivative of -o**7/10080 - o**6/576 - o**5/120 - 19*o**4/6 - 11*o**2 - 1. Let z(u) be the second derivative of r(u). Factor z(g).
-(g + 1)*(g + 4)/4
Let q(a) = -a**3 - 253*a**2 - 10624*a + 336. Let h be q(-200). Factor 1296 - h*c - 16/9*c**3 - 1724/9*c**2.
-4*(c + 54)**2*(4*c - 1)/9
Suppose -5*l - 21 = -4*p, 15*p - 16*p + 2 = 2*l. Solve 5*c**3 - 14*c**3 + 3*c**2 - 14*c**4 + 15*c**p + 2*c + 3*c**5 = 0 for c.
-2, -1/3, 0, 1
Let s(b) be the first derivative of b**6/18 + 83*b**5/15 - 7*b**4 - 2365. Determine h, given that s(h) = 0.
-84, 0, 1
Let v(s) be the second derivative of 5*s**7/21 - 52*s**6/15 + 14*s**5 + s**4/3 - 145*s**3/3 + 50*s**2 - 29*s. Solve v(f) = 0.
-1, 2/5, 1, 5
Let i(r) be the second derivative of r**7/98 + 3*r**6/70 - 33*r**5/28 - 115*r**4/28 + 27*r**3/7 + 24*r**2 - 5649*r. Suppose i(f) = 0. What is f?
-8, -2, -1, 1, 7
Factor 9016 + 2/23*t**2 - 56*t.
2*(t - 322)**2/23
Let j = -266 + 269. Suppose -j*k + 25 = 5*u, 3*u + 12 = 3*k + 3. Find v such that -31/3*v - 3*v**k + 40/3*v**3 - 2 - 10/3*v**2 + 16/3*v**4 = 0.
-1, -2/9, 1, 3
Let b be 4/16 - 54/(-8). Factor 24*i + 24 - b*i**2 + 14*i**2 + 21*i**2 - 92*i.
4*(i - 2)*(7*i - 3)
Let a(r) = 2*r**3 - 13*r**2 + 9*r - 9. Let d be a(6). Solve -23*x + 15*x + 3*x**2 + d*x**2 - x**3 - 2*x - x**3 = 0.
0, 1, 5
Solve 27897769*i**2 - 464817*i**3 + 301280854 - 52024955 + 66620835*i**2 - 4*i**5 + 3412*i**4 + 113387093 - 366487264*i - 509851*i**3 = 0 for i.
2, 283
Let d(j) = j**4 + 13*j**3 - 5*j**2 - 5*j + 5. Suppose 0 = 8*x - 47 + 7. Let n(l) = 2*l**4 + 20*l**3 - 8*l**2 - 8*l + 8. Let o(f) = x*n(f) - 8*d(f). Factor o(p).
2*p**3*(p - 2)
Let l(g) be the third derivative of 14 + 0*g + 2/3*g**5 + 6*g**4 + 3/28*g**8 - g**2 - 16/3*g**3 - 3/2*g**6 - 4/105*g**7. Suppose l(u) = 0. What is u?
-2, -1, 2/9, 1, 2
Let u be 3 + ((-24)/8 - -4). Factor -5*o**3 - 20 - o**3 - 60*o - u*o**3 - 27*o**2 + 8*o**2 - 26*o**2.
-5*(o + 2)**2*(2*o + 1)
Let m(h) be the second derivative of 8/3*h**6 + 38/5*h**5 + 7 + 0*h**2 - 7*h - 6*h**3 + 4*h**4 + 2/7*h**7. Solve m(t) = 0.
-3, -1, 0, 1/3
Let x(j) = -2*j**2 + 60*j - 157. Let q(p) = -p**2 + 32*p - 78. Let o(g) = 5*q(g) - 2*x(g). Factor o(a).
-(a - 38)*(a - 2)
Suppose -2*s - 8262 + 8294 = 4*y, 4*s + 24 = 3*y. Factor s - 82/5*f - 2/5*f**2.
-2*f*(f + 41)/5
Let r(z) be the second derivative of 0 + 31*z + 1/3*z**4 + 88/3*z**3 + 968*z**2. Factor r(k).
4*(k + 22)**2
Suppose 5*m - m = 3*r - 6, -10 = m - 5*r. Suppose -7*a + 41 - 20 = m. Factor 53*z**3 + 30 + 18*z**2 + a*z**4 - 77*z**3 + 45 + 120*z.
3*(z - 5)**2*(z + 1)**2
Suppose 3*q**3 - 38*q**2 + 4357889*q**4 - q**5 + 16*q + 12*q**2 - 4357881*q**4 = 0. What is q?
-2, 0, 1, 8
Suppose -236 + 198 = -2*l, 0 = -3*p + 7*l - 9*l + 74. Factor 4/3*g**2 + 4/3*g**3 - p - 12*g.
4*(g - 3)*(g + 1)*(g + 3)/3
Let x(y) = 6*y**4 - 4*y**3 - 6*y**2 + 8*y. Let o(z) = 2*z - 3*z**4 - 94 + 94 - 26*z - 16*z**4 + 19*z**2 + 10*z**3. Let m(i) = 2*o(i) + 7*x(i). Factor m(b).
4*b*(b - 2)*(b - 1)*(b + 1)
Suppose -3*y - 27 = -3*i - 8*y, -4*y = -2*i + 18. Suppose 3*k + p + 2 = 8, 3*p = -i. Find f, given that 0*f**4 + 3/5*f**5 + 3/5*f + 0 + 0*f**2 - 6/5*f**k = 0.
-1, 0, 1
Let o be (-64)/672 + 176/84. Let i(g) be the third derivative of 1/240*g**6 + 0 - 4/3*g**3 + 13*g**o - 3/40*g**5 + 0*g + 1/2*g**4. Find x, given that i(x) = 0.
1, 4
Factor -224/5*b - 464/5 + 4/5*b**2.
4*(b - 58)*(b + 2)/5
Let s be -1 - (27 - (-5 - -1)). Let u = -30 - s. Factor -12*i**3 - 12*i**2 + 46*i - 50*i + u*i**4 - 6*i**4.
-4*i*(i + 1)**3
Let t be 118/286 - 2313/10023. Solve 4/11*c**3 - 4/11*c**4 - 2/11*c**5 - t*c + 8/11*c**2 - 4/11 = 0 for c.
-2, -1, 1
Let i(j) be the first derivative of -j**3/9 + 155*j**2/2 - 926*j/3 + 1794. Factor i(q).
-(q - 463)*(q - 2)/3
Let p(l) be the third derivative of l**8/1344 + l**7/168 - 43*l**6/480 + 67*l**5/240 - 5*l**4/16 - 3624*l**2. What is n in p(n) = 0?
-10, 0, 1, 3
Suppose -45 = 4*n + 3*c + 14, -n - 15 = c. Let q be (-1 - 7/n) + 3/6. What is w in q - 1/6*w**5 + 0*w**2 + 0*w - 1/6*w**3 + 1/3*w**4 = 0?
0, 1
Let d(j) be the first derivative of -2*j**3/21 - 79*j**2/7 - 288*j - 4888. Let d(x) = 0. Calculate x.
-63, -16
Let l(z) be the third derivative of -z**5/60 + 17*z**4/6 + 23*z**3/2 - 1847*z**2 + 2*z. Find y, given that l(y) = 0.
-1, 69
Solve -2/3*v**3 - 8 + 16/3*v + 10/3*v**2 = 0 for v.
-2, 1, 6
Let 0 + 2/11*i**5 - 50/11*i**2 - 48/11*i + 50/11*i**4 + 46/11*i**3 = 0. What is i?
-24, -1, 0, 1
Factor -52*h**2 + 48*h**2 + 5362*h - 11354*h - 2244004.
-4*(h + 749)**2
Determine g, given that -132/7 + 93/7*g**4 + 384/7*g - 93/7*g**3 + 9/7*g**5 - 261/7*g**2 = 0.
-11, -2, 2/3, 1
Let o = -71 - -66. Let k(i) = 2*i**3 - i. Let w(v) = -v**5 - 7*v**4 - 30*v**3 - 22*v**2 - 7*v - 3. Let m(z) = o*w(z) - 30*k(z). Solve m(x) = 0.
-3, -1
Let i = -28 + 31. Let q = -137999/5 - -27605. Suppose 0 + 12/5*k**4 + 24/5*k**2 - q*k**i - 2/5*k**5 - 8/5*k = 0. What is k?
0, 1, 2
Let x(c) be the third derivative of 0 + 1/60*c**6 - 1/12*c**4 + 0*c**3 - 7/60*c**5 + 1/30*c**7 - 7*c**2 + 0*c. Solve x(s) = 0.
-1, -2/7, 0, 1
Suppose -y + 121 = 4*u, y - 41 = -u + 80. Suppose -y*g = -102*g. Factor g + 3/8*w**2 - 3/4*w.
3*w*(w - 2)/8
Let y = -1565 - -1565. Let g be (y/((24/(-4))/(-3)))/(-1). Determine k so that -240*k**3 + g - 250/3*k**5 - 32/3*k + 800/3*k**4 + 256/3*k**2 = 0.
0, 2/5, 2
Let c(u) be the third derivative of -u**6/8 - u**5/6 + 245*u**4/8 + 245*u**3/3 - 173*u**2 - 2*u. Let c(y) = 0. Calculate y.
-7, -2/3, 7
Let w(z) be the second derivative of 5*z**7/84 + z**6/6 - 9*z**5/2 - 395*z**4/12 - 1025*z**3/12 - 105*z**2 + 4138*z. Let w(a) = 0. Calculate a.
-4, -3, -1, 7
Let u(s) be the second derivative of 12*s**2 + s + 42/5*s**5 + 29 + 9/10*s**6 + 93/4*s**4 + 27*s**3. Factor u(p).
3*(p + 1)**2*(p + 4)*(9*p + 2)
Let o(x) be the first derivative of 164*x**3/3 + 3*x**2 - 1986. Solve o(s) = 0.
-3/82, 0
Suppose -26 = -30*u + 64. Factor -20*l + 6*l**2 - 12*l**2 + 13*l**3 - 9*l**2 + 15 + 7*l**u.
5*(l - 1)*(l + 1)*(4*l - 3)
Suppose l + 10 = 13. Determine c, given that -1