- 17*h**6/40 - 61*h**5/30 + 33*h**4/8 - 35*h**3/12 - 690*h**2. Solve o(k) = 0 for k.
-7, -5, 1/3
Let h(t) be the first derivative of 3*t**4/8 + 188*t**3/3 + 11655*t**2/4 - 3969*t + 342. Find r, given that h(r) = 0.
-63, 2/3
Factor 0 + 20*i - 56/3*i**2 - 4/3*i**3.
-4*i*(i - 1)*(i + 15)/3
Let z be -4*(-6 - 8/(-1 + -3)). Find c, given that -z + 3*c**4 - 12*c**3 - 30 + 48*c - 2 = 0.
-2, 2
Suppose -14 - 12 = -49*s + 72. Solve 0 + 7/2*b**3 + 8*b**s + 2*b = 0.
-2, -2/7, 0
Suppose 79 + 27 = -2*b + 4*t, 4*t = -4*b - 152. Let a = b - -43. Suppose 0 + 0*v + 0*v**4 + a*v**2 + 0*v**3 + 2/11*v**5 = 0. What is v?
0
Factor -61*z**2 + 189*z**2 + 286*z**2 - 54*z**2 + 3*z**4 + 63*z**3 + 6*z**3 - 432*z.
3*z*(z - 1)*(z + 12)**2
Let m(b) be the first derivative of -b**5/25 - 3*b**4/2 - 15*b**3 - 23. Factor m(l).
-l**2*(l + 15)**2/5
Let d = -13489 - -40468/3. Factor d*k**2 - 4*k + 12.
(k - 6)**2/3
Suppose 5*z = z - 2*u + 110, 3*z - 2*u = 86. Solve 53*g**3 + 6 + 15*g + 12*g**2 - 22*g**3 - z*g**3 = 0 for g.
-2, -1
Let u be ((-2)/9)/((-20)/180). Let c(i) be the third derivative of 8/15*i**5 + 0*i**4 - 1/3*i**3 - u*i**2 + 0*i + 0. Let c(q) = 0. Calculate q.
-1/4, 1/4
Suppose -8 = -2*o + 5*a + 16, 0 = -o + 5*a + 17. Let t = 18 - o. Determine m, given that -t*m**2 + 5*m**2 - 9*m**4 - 9*m**3 + 6*m**4 = 0.
-2, -1, 0
Let r(o) be the third derivative of 1/20*o**5 - 1/70*o**7 + 0 + 1/40*o**6 + 0*o + 0*o**4 + 0*o**3 - 1/112*o**8 - 19*o**2. Solve r(p) = 0.
-1, 0, 1
Let x(p) be the second derivative of 0 - 1/60*p**4 - 3*p + 3/5*p**2 + 1/6*p**3. Solve x(k) = 0.
-1, 6
Suppose v + 3*k - 7 = 0, -2*v - k + 6 = -3*k. Let p(w) = -w - 18. Let r be p(-20). Factor 5 + v*d**r - 10*d**2 - 3 + 1 + 3*d**4.
3*(d - 1)**2*(d + 1)**2
Let d(b) be the third derivative of b**5/15 + 5*b**4/6 - 28*b**3/3 - 18*b**2 - 4. Factor d(n).
4*(n - 2)*(n + 7)
Let m(q) be the first derivative of -15 + 5/6*q**2 - 4/3*q - 1/9*q**3. Solve m(c) = 0.
1, 4
Let z = -4 + 6. Suppose 3*k - z*w = 0, -k - 3*w = -7*w + 10. Find b, given that -4*b**3 - 3*b**5 + 9*b + 9*b**4 - 3*b**k - 3 - 3*b**2 - 2*b**3 = 0.
-1, 1
Let m(d) be the third derivative of d**10/50400 + d**9/25200 - d**8/5600 + 5*d**4/24 - 16*d**2. Let h(c) be the second derivative of m(c). Factor h(y).
3*y**3*(y - 1)*(y + 2)/5
Factor 3/2*l - 15/4*l**3 - 9/4*l**2 + 0.
-3*l*(l + 1)*(5*l - 2)/4
Suppose -n = -2*n + 10. Let f be 10/4*8/n. Find t such that 2 + 3*t**2 + 2 - 6*t - t**f = 0.
1, 2
Let v(x) be the first derivative of x**4/4 + 4*x**3/3 - x**2/2 - 4*x + 370. Solve v(c) = 0 for c.
-4, -1, 1
Let a = 2/19 + 13/57. Suppose 5*w = d - 2*d + 17, 0 = 3*d - 5*w + 9. Determine u, given that 7/6*u - 1/2 - a*u**d = 0.
1/2, 3
Let c(m) be the third derivative of -m**6/360 - m**5/45 + 29*m**4/72 - 4*m**3/3 - 353*m**2. Factor c(i).
-(i - 3)*(i - 1)*(i + 8)/3
Suppose u - 5 = -2*l + 2*u, 2 = 5*l + u. Let v be ((-35)/(-21) - (l + 2)) + 2. Solve 2/3*r - v - 1/6*r**2 = 0 for r.
2
Let h(s) be the third derivative of -s**8/2520 - s**7/1575 + s**6/180 + s**5/450 - 2*s**4/45 + 4*s**3/45 - 25*s**2. Factor h(a).
-2*(a - 1)**3*(a + 2)**2/15
Suppose 4 = -0*i + 2*i. Suppose i + 10 = 3*r. Factor 7*m + r*m**2 - 3*m**2 - 4*m + 2.
(m + 1)*(m + 2)
Suppose w + 0 = 6. Let s be 4/22 + w/33. Solve 0 - 4/11*m + s*m**3 + 2/11*m**2 - 2/11*m**4 = 0.
-1, 0, 1, 2
Let a(c) be the second derivative of c**6/90 - c**5/30 - c**4/36 + c**3/9 + 472*c. Factor a(p).
p*(p - 2)*(p - 1)*(p + 1)/3
Solve 42*h - 3/2*h**2 - 225/2 = 0.
3, 25
Suppose -66 + 10 = -4*i. Let h = i + -9. Let t(j) = -4*j**3 + 7*j**2 + 6*j - 5. Let n(b) = 3*b**3 - 6*b**2 - 5*b + 4. Let s(v) = h*n(v) + 4*t(v). Factor s(y).
-y*(y + 1)**2
Let c = 14 - -6. Let b = c - 19. Factor -8*i**3 - 4*i - 7 + i**2 + 5*i**2 + 12*i - b + 2*i**4.
2*(i - 2)**2*(i - 1)*(i + 1)
Solve 1/4*k**4 + 7/4*k**3 - 4*k + 0 + 2*k**2 = 0.
-4, 0, 1
Let i(o) = 2*o**2 - o - 3. Let b be i(-1). Let j(l) be the second derivative of l + 2/9*l**3 + 0 + 1/18*l**4 + b*l**2. Factor j(z).
2*z*(z + 2)/3
Let k(b) = b**2 - 374*b + 375. Let h be k(1). Suppose p**4 + 1/2*p**3 + 0*p + 0*p**h + 1/2*p**5 + 0 = 0. What is p?
-1, 0
Let s = 7 - 3. Determine w, given that -34*w**4 - 470*w**2 - 343*w**5 - 7 - 1 - 819*w**s - 100*w - 1015*w**3 - 127*w**4 = 0.
-1, -2/7
What is u in -2/19*u + 28/19 - 28/19*u**2 + 2/19*u**3 = 0?
-1, 1, 14
Let c(z) be the second derivative of z**3/6 + 5*z**2 + 3*z. Let t be c(-7). Factor -2*s**4 + 0*s**3 + 3*s**5 - 6*s**3 + t*s**4 + 2*s**4.
3*s**3*(s - 1)*(s + 2)
Let r be (18/(-27))/((-3)/18). Let o be 8 + -4 + -2 - 6/r. Suppose -1/4*j + 0 - o*j**2 + 1/4*j**5 + 0*j**3 + 1/2*j**4 = 0. What is j?
-1, 0, 1
Let j(n) be the first derivative of -2/33*n**3 - 20/11*n**2 - 200/11*n - 22. Solve j(r) = 0 for r.
-10
Suppose -42/5 - 3/5*g**2 + 9*g = 0. What is g?
1, 14
Let y = -12/35 - -26/35. Let d(v) = -v**3 + 12*v**2 + 27*v + 16. Let i be d(14). Factor 6/5*s**4 - 4/5*s**i + 2/5*s**5 - y + 4/5*s**3 - 6/5*s.
2*(s - 1)*(s + 1)**4/5
Let r(p) be the first derivative of p**5/40 - 3*p**4/32 - p**3/8 + 7*p**2/16 + 3*p/4 - 86. Find i such that r(i) = 0.
-1, 2, 3
Let f(r) be the second derivative of r**5/10 - 7*r**4/12 + 7*r**3/6 - r**2 + 135*r. Factor f(l).
(l - 2)*(l - 1)*(2*l - 1)
Suppose -13*w + 64 = 3*w. Suppose -64*z - 32 - 16*z**3 + 252*z**4 - 123*z**w - 48*z**2 - 131*z**4 = 0. Calculate z.
-2
Let h = 253 - 758/3. Let c(m) be the second derivative of -5*m - h*m**2 + 7/9*m**3 + 0 - 2/3*m**4. Suppose c(t) = 0. Calculate t.
1/4, 1/3
Let y be -1*3 + -9 + 14. Factor y - 7*n**2 - 2 + 9*n**2 - 8.
2*(n - 2)*(n + 2)
Let m be (20/8)/((-3)/(-6)). Suppose 3*l - m*i = 22, i = -2*l + 2*i + 10. What is q in q**4 - 46*q**2 + 34*q**2 + 3*q**l + 8*q = 0?
-2, 0, 1
Let x = -44 - -46. Let 4*d**x + 22*d**4 - 8*d**5 - 3*d**5 - 21*d**5 - 28*d**3 + 34*d**4 = 0. What is d?
0, 1/4, 1/2, 1
Suppose 45 = -4*j + 133. Let t = 24 - j. Suppose 1/2*w - 1/2 + 1/2*w**t - 1/2*w**3 = 0. What is w?
-1, 1
Factor -2/5*w**2 - 1/5*w**3 - 1/5*w + 0.
-w*(w + 1)**2/5
Let j(f) = -3*f**2 + 130*f - 4098. Let r(h) = -4*h**2 + 131*h - 4099. Let s(y) = 3*j(y) - 2*r(y). Factor s(o).
-(o - 64)**2
Let s = -221 + 885/4. Let k(g) be the third derivative of 0*g + 3*g**2 - 1/2*g**3 + 0 - 1/20*g**5 - s*g**4. Solve k(d) = 0.
-1
Let u(v) be the second derivative of 0 - 2/45*v**6 + 1/9*v**4 + 2/15*v**5 + 0*v**2 - 6*v - 4/9*v**3. Find q such that u(q) = 0.
-1, 0, 1, 2
Factor 13*c - 3*c + 32 + 9*c - c**4 - 4*c**2 + 2*c + 3*c - 6*c**3.
-(c - 2)*(c + 2)**2*(c + 4)
Let y = -353 - -353. Let q(l) be the second derivative of 0*l**2 - 1/120*l**5 - 1/180*l**6 + y + 5*l + 0*l**3 + 1/252*l**7 + 1/72*l**4. Factor q(s).
s**2*(s - 1)**2*(s + 1)/6
Let d(l) be the second derivative of l**8/1344 - l**7/168 - 11*l**4/6 - l. Let u(s) be the third derivative of d(s). Factor u(b).
5*b**2*(b - 3)
Let v(c) = c**4 + 2*c**3 - 2*c**2 - 18. Let a(m) = 1. Let x(t) = 6*a(t) - v(t). Let s(d) be the first derivative of x(d). What is b in s(b) = 0?
-2, 0, 1/2
Let s(x) be the second derivative of -2*x**6/75 - 6*x**5/25 + 8*x**4/15 + 4*x**3/5 - 14*x**2/5 - 6*x - 2. Determine h so that s(h) = 0.
-7, -1, 1
Factor 45*h**3 + 2*h + 5*h**5 + 5*h - 25*h**4 + 3030 - 3030 + 3*h - 35*h**2.
5*h*(h - 2)*(h - 1)**3
Let t(r) = -9*r + 3*r + 33 - r**2 - 40. Let o be t(-3). Solve -1 - 23*s**o + 0*s + 24*s**2 + 3 + 3*s = 0 for s.
-2, -1
Let k(u) = -2*u**3 + u**2. Let t be k(-1). Suppose 0 = t*h + 3*z + 9, 5*z - 7 + 40 = 4*h. Factor 3*m**3 + 3*m**h - 3*m**4 - m**2 - 3*m**2 - 3*m + 4*m**2.
-3*m*(m - 1)**2*(m + 1)
Let r(f) be the first derivative of f**6/42 - f**5/35 - 57*f**4/28 + 145*f**3/21 + 100*f**2/7 + 468. Factor r(q).
q*(q - 5)**2*(q + 1)*(q + 8)/7
Let o(q) be the first derivative of -1/10*q**6 - 7/12*q**4 + 0*q**2 + 1/3*q**3 + q - 5 + 2/5*q**5. Let m(j) be the first derivative of o(j). Factor m(l).
-l*(l - 1)**2*(3*l - 2)
Suppose b = -4*b. Let d = -713/13 + 55. Find l, given that b + d*l**2 - 4/13*l = 0.
0, 2
Let k = -9 - -29. Let b be k/(-35) + (-100)/(-126). Factor 2/9*f**4 + b*f + 0 + 2/3*f**2 + 2/3*f**3.
2*f*(f + 1)**3/9
Suppose b + 88 = -g + 91, 5*g = -4*b + 13. Solve -6/13*d - 2/13*d**3 - 2/13 - 6/13*d**b = 0.
-1
Suppose -2*b - 72 = -4*n + 2*b, -3*n = -b - 50. Suppose -5*r + 40 = 5*h, 5*r - 2*h - 22 = 11. Factor -2*x - x**5 + n*x**4 + r*x**5 - 54*x**3 + 66*x**3.
2*x*(x + 1)**3*(3*x - 1)