1/8*k**6 + 1/42*k**7 + 0 - 5/12*k**4 - 5/12*k**5. Determine j so that g(j) = 0.
-1, 0, 2
Factor 12*j + 1/4*j**2 + 144.
(j + 24)**2/4
Suppose -70 = 2*n - 16*n. Let z(v) be the second derivative of 0 - 1/10*v**5 + n*v + 1/3*v**4 - 2*v**2 + 1/3*v**3. Factor z(w).
-2*(w - 2)*(w - 1)*(w + 1)
Let p(r) = -r**3 - 5*r**2 + 3*r - 12. Let o be p(-6). Let z be ((-2)/8)/(o/(-120)). Factor 2/5*q + 0 + 2/5*q**z - 4/5*q**3 + 0*q**4 + 0*q**2.
2*q*(q - 1)**2*(q + 1)**2/5
Let j(o) be the first derivative of -3*o**2 + 0*o + 3*o**3 + 16 + 63/4*o**4 + 9/2*o**6 + 15*o**5. Factor j(q).
3*q*(q + 1)**3*(9*q - 2)
Suppose 0 = 9*w - 2*w - 21. Let -15*s**3 - 2*s**2 - 13*s**3 + 29*s**w - s + 2 = 0. Calculate s.
-1, 1, 2
Let h(d) = -3*d**2 - 8*d. Let c be h(-4). Let z = 18 + c. Let 5/6*n + 1/3 - 1/2*n**z = 0. Calculate n.
-1/3, 2
Determine d so that d**2 - 6*d**2 - 100*d - 94*d + 209*d - 10 = 0.
1, 2
Let s(o) = 3*o**5 - 4*o**4 - 24*o**3 - 12*o**2 + 4*o + 4. Let c(x) = -5*x**5 + 9*x**4 + 47*x**3 + 25*x**2 - 7*x - 7. Let z(a) = -4*c(a) - 7*s(a). Factor z(d).
-d**2*(d + 2)**2*(d + 4)
Let k(j) be the first derivative of -j**7/42 - j**6/30 - 45*j - 1. Let d(r) be the first derivative of k(r). Factor d(t).
-t**4*(t + 1)
Let m = -12332 - -49729/4. Let h = m + -100. Factor -3/4*v**4 + h*v**3 + 1/4*v**5 + 3/4*v**2 - 1/2*v + 0.
v*(v - 2)*(v - 1)**2*(v + 1)/4
Let g be ((-2)/4)/(4/(-560)). Let l be (-2 + 212/g)/(2/7). Factor 14/5*o**4 + 0*o + 0 + l*o**3 + 4/5*o**2.
2*o**2*(o + 1)*(7*o + 2)/5
Let f(n) be the first derivative of -3/25*n**5 - 3/5*n + 6/5*n**2 - 6/5*n**3 + 3/5*n**4 - 7. Let f(i) = 0. What is i?
1
Factor -3/4*v**3 + 0*v + 0 - 6*v**2.
-3*v**2*(v + 8)/4
Let b(g) be the second derivative of -g**6/6 + 35*g**4/12 + 5*g**3 + 25*g. Factor b(i).
-5*i*(i - 3)*(i + 1)*(i + 2)
Let h(f) be the first derivative of 12/5*f**2 + 19/5*f**3 + 21 + 21/20*f**4 - 12/5*f. Let h(w) = 0. Calculate w.
-2, -1, 2/7
Determine i, given that -20/7*i - 24/7*i**2 - 4/7 = 0.
-1/2, -1/3
Suppose -21*l - 24*l + 44*l = 0. Factor 2/7*o**3 + 4/7 + l*o**2 - 6/7*o.
2*(o - 1)**2*(o + 2)/7
Let h(q) be the first derivative of 8*q**3/3 + 9*q**2/2 - 7*q - 7. Let f(s) = 7*s**2 + 8*s - 6. Let n(k) = 7*f(k) - 6*h(k). Determine v, given that n(v) = 0.
-2, 0
Let j = 1266 + -8850/7. Factor j*n**2 + 0 + 2/7*n**3 + 18/7*n.
2*n*(n + 3)**2/7
Let r(t) be the first derivative of -4*t**3/3 + 6*t**2 - 8*t + 93. Factor r(p).
-4*(p - 2)*(p - 1)
Suppose 30*b - 31*b - 5*s + 12 = 0, 4*b - 10 = -s. Let y(k) be the third derivative of 0 + 5*k**b + 0*k + 1/140*k**5 + 0*k**4 + 0*k**3. Solve y(x) = 0.
0
Let g(h) = 8*h**2 - 2*h + 2. Let z(u) = 3*u**2 + u. Let q(y) = -g(y) + 2*z(y). Factor q(p).
-2*(p - 1)**2
Determine m, given that 8 + 35*m + 35 - 1 + 0*m + 5*m**2 + 18 = 0.
-4, -3
Determine h so that -28 - 105*h**3 - 45*h**2 + 43*h**4 + 43*h**4 - 20 + 210*h - 98*h**4 = 0.
-8, -2, 1/4, 1
Let o(v) be the third derivative of -1/7*v**7 + 0*v + 0*v**4 + 1/2*v**6 - 2/3*v**5 + 5/336*v**8 + 0*v**3 + 0 - 17*v**2. What is q in o(q) = 0?
0, 2
Let w(q) be the first derivative of q**6/72 + 5*q**5/12 + 125*q**4/24 + 17*q**3/3 - 11. Let x(c) be the third derivative of w(c). Factor x(o).
5*(o + 5)**2
Factor 156*f + 9*f**2 - 14*f**3 + 127959*f**4 - 127962*f**4 + 180 - 4*f**3.
-3*(f - 3)*(f + 2)**2*(f + 5)
Let h(d) = 470*d - 3287. Let f be h(7). What is q in 1/2*q**4 + 0*q - 1/4*q**5 + 7/4*q**f + 0 + q**2 = 0?
-1, 0, 4
Let j = 26/7 - 7/2. Let l = j - -1/14. Factor 2/7 + 6/7*w**3 - 10/7*w**2 + l*w.
2*(w - 1)**2*(3*w + 1)/7
Let h(z) be the first derivative of -z**8/168 + z**7/84 - z**6/240 + 25*z**2/2 - 9. Let x(r) be the second derivative of h(r). Determine a so that x(a) = 0.
0, 1/4, 1
Let g = 1/2169 - -23107/62901. Let o = g + -1/29. Determine w so that o*w**2 - 1/3*w + 0 = 0.
0, 1
Let h = 23722 + -4080149/172. Let q = 2/43 + h. Find v, given that 1/4*v**3 - q*v - 1/4 + 1/4*v**2 = 0.
-1, 1
Let b(n) = -9*n**2 + 27*n - 49. Let z(r) = 4*r**2 - 13*r + 24. Let p(u) = 3*b(u) + 7*z(u). Factor p(g).
(g - 7)*(g - 3)
Let x(t) be the second derivative of t**4/57 - t**3/3 + 9*t**2/19 - 64*t + 2. Factor x(z).
2*(z - 9)*(2*z - 1)/19
Let x(z) be the third derivative of 4/9*z**3 + 5/36*z**4 + 0 + 1/90*z**5 + 0*z + 14*z**2. Determine o so that x(o) = 0.
-4, -1
Let m(z) = -z**2 - z + 3. Let a be m(0). Suppose 5*n = f + 20, 4*n + a*f - 25 = 2*f. Factor d - n*d**2 + 0*d**2 + 2*d**2 + 2*d**2 - d**3 + 1.
-(d - 1)*(d + 1)**2
Let u(j) be the first derivative of j**4/108 - 17*j + 25. Let s(k) be the first derivative of u(k). Determine a, given that s(a) = 0.
0
Find d such that -d + 2*d**4 - 9*d - 6*d**3 - 2*d**3 + 2*d**3 - 18*d**2 = 0.
-1, 0, 5
Let p(g) be the first derivative of -3*g**5/5 + 21*g**4/2 + g**3 - 21*g**2 + 166. Find s, given that p(s) = 0.
-1, 0, 1, 14
Let b(f) be the second derivative of 0 - 9/22*f**2 + 28*f + 1/11*f**3 - 1/132*f**4. Factor b(q).
-(q - 3)**2/11
Let u(p) = 24*p**3 + 4216*p**2 + 184396*p - 61965. Let q(v) = -6*v**3 - 1054*v**2 - 46100*v + 15491. Let j(d) = 26*q(d) + 6*u(d). Factor j(n).
-4*(n + 88)**2*(3*n - 1)
Suppose -27 - 5 = -8*h. Factor -d + 4*d**2 - 18*d**4 + 14*d**4 - 3*d + h*d**3.
-4*d*(d - 1)**2*(d + 1)
Let t(q) = -3*q**2 + 3*q - 6. Let n(g) = 3*g**2 - 2*g + 7. Suppose -123 = -4*c + 25. Let k = 31 - c. Let l(z) = k*n(z) - 7*t(z). Find d, given that l(d) = 0.
0, 3
Let s = -11/26 + 731/130. Let p = -328/65 + s. Find x, given that -p*x**3 + 2/13*x + 0 + 0*x**2 = 0.
-1, 0, 1
Factor 11*s**2 + 1 + 7*s**2 + 24 - 1 - 3*s**3 + 45*s + 0*s**2.
-3*(s - 8)*(s + 1)**2
Let p = -16/209 + 884/627. Factor 0*y - p + 4/3*y**2.
4*(y - 1)*(y + 1)/3
Let i(o) = 2*o**4 - 44*o**3 + 232*o**2 + 628*o + 334. Let k(l) = 6*l**4 - 133*l**3 + 697*l**2 + 1883*l + 1003. Let u(z) = -11*i(z) + 4*k(z). Factor u(d).
2*(d - 13)**2*(d + 1)**2
Suppose 11 + 17 = 3*r - f, -2*r + f + 17 = 0. Let i(n) = -n + 13. Let x be i(r). Solve 0*o**2 - 4*o**x + o**3 + o**2 + 4*o**2 = 0.
-1, 0
Let i(s) be the first derivative of -s**6/135 + s**5/90 + s**4/27 - 2*s - 12. Let a(n) be the first derivative of i(n). Solve a(d) = 0.
-1, 0, 2
Determine t, given that 2/13*t**3 + 43904/13 + 168/13*t**2 + 4704/13*t = 0.
-28
Let a(q) be the third derivative of q**7/630 - q**6/180 + 5*q**4/24 + 3*q**2. Let d(r) be the second derivative of a(r). Solve d(s) = 0.
0, 1
Let l(j) = -2*j**2 - 20*j - 18. Let o be -28 - -18 - 2/(-2). Let u be l(o). Factor u - 1/4*i**4 - 1/4*i - 3/4*i**2 - 3/4*i**3.
-i*(i + 1)**3/4
Let p(k) be the first derivative of k**5/20 - k**4/12 - k**3/6 + k**2/2 + 17*k + 8. Let o(t) be the first derivative of p(t). What is z in o(z) = 0?
-1, 1
Let h(d) be the second derivative of 3/5*d**5 - 2/3*d**4 + 14*d + 0 + 1/21*d**7 + 0*d**2 - 4/15*d**6 + 1/3*d**3. Suppose h(g) = 0. What is g?
0, 1
Let d(t) be the second derivative of -t**7/840 - t**6/120 - t**5/60 - 3*t**3/2 - 14*t. Let o(q) be the second derivative of d(q). Factor o(r).
-r*(r + 1)*(r + 2)
Let o(w) = 3*w**2 + 5*w - 3. Let g be o(1). Let j(z) be the second derivative of -27/20*z**g + 6*z**2 - 3/4*z**4 + z + 0 + 4*z**3. Determine k so that j(k) = 0.
-2/3, 1
Suppose 4*u + 4*q + 13 = -31, q + 5 = 0. Let g be 35/15*(0 + u/(-21)). What is j in -2/3*j + 1/3*j**2 - 1/3*j**4 + g*j**3 + 0 = 0?
-1, 0, 1, 2
Suppose 59 - 89 = -5*a, -5*a = -2*o - 26. Factor -12/5 - 14/5*u + 36/5*u**o - 2*u**3.
-2*(u - 3)*(u - 1)*(5*u + 2)/5
Suppose 0 = -2404*f + 2449*f. Let 1/6*y**3 + f*y**2 - 1/2*y + 1/3 = 0. Calculate y.
-2, 1
Factor -9/4*d**3 + 9/4*d**4 + 3/4*d**2 + 0*d - 3/4*d**5 + 0.
-3*d**2*(d - 1)**3/4
Let j(o) be the second derivative of -o**6/105 + 2*o**5/35 + 19*o**4/42 - 46*o**3/21 + 24*o**2/7 - 336*o. Determine n, given that j(n) = 0.
-4, 1, 6
Let z(h) be the first derivative of h**5/120 + 3*h**4/32 + h**3/6 + 13*h**2/2 + 25. Let q(y) be the second derivative of z(y). Factor q(d).
(d + 4)*(2*d + 1)/4
Let f = 1286 + -1286. Let i = 186 + -926/5. Factor f*j - i*j**2 + 2/5*j**3 + 0.
2*j**2*(j - 2)/5
Let a(q) be the first derivative of -q**6/360 - q**5/30 + 5*q**4/24 + 11*q**3/3 + 8. Let m(f) be the third derivative of a(f). Solve m(c) = 0 for c.
-5, 1
Let l(x) be the third derivative of x**6/15 + 43*x**5/150 + 13*x**4/30 + x**3/5 - x**2 - 157*x. Find v such that l(v) = 0.
-1, -3/20
Determine n so that 136*n + 268*n**2 + 128*n**3 - 4*n**4 - 34907 + 34907 = 0.
-1, 