h**2 + 145*h + 2. Let z(u) = 0. Calculate u.
-2, -1, 1, 2
Let w be (-28)/40*-6 - (-5)/(-25). Let d(v) be the second derivative of 0 + 2*v**2 + 2/3*v**w + 3*v - 2*v**3. Factor d(s).
4*(s - 1)*(2*s - 1)
Let d(s) be the first derivative of 0*s + 1/4*s**4 + 1/3*s**3 - 1/2*s**2 - 1/5*s**5 + 36. Factor d(p).
-p*(p - 1)**2*(p + 1)
Let i = 491/42 + -235/21. Factor -1/6*m**3 - 1/3*m + i*m**2 + 0.
-m*(m - 2)*(m - 1)/6
Let x(h) be the third derivative of -h**8/141120 - h**7/5040 - h**6/840 + 7*h**5/60 + 11*h**2. Let n(k) be the third derivative of x(k). Solve n(y) = 0.
-6, -1
Let p = 7544 - 22628/3. Suppose -4/3*v + 4/3*v**3 + p - 4/3*v**2 = 0. What is v?
-1, 1
Let b(p) be the second derivative of 3*p**5/100 - 21*p**4/10 + 41*p**3/10 - 209*p. Suppose b(f) = 0. What is f?
0, 1, 41
Let x be (-7 + 7)*(-8)/16. Suppose -2*h - 2*h = -8. Find d, given that 4/17*d + 2/17*d**h + x = 0.
-2, 0
Let m(g) be the third derivative of -25*g**8/112 + 3*g**7/7 + 11*g**6/40 - 3*g**5/5 - g**4/2 + g**2 - 25. Find i such that m(i) = 0.
-2/5, 0, 1
Let i = -577 + 577. Let o(v) be the second derivative of i - 4*v**2 + 2/3*v**3 + v + 1/3*v**4. Let o(w) = 0. Calculate w.
-2, 1
Let t be 1659/(-609) - 1*-3. Let v = 214/145 - t. Determine i, given that 36/5*i**3 - 14/5*i**4 - v + 26/5*i + 2/5*i**5 - 44/5*i**2 = 0.
1, 3
Let u(y) be the first derivative of 0*y**4 + 3/5*y**5 + 3*y + 46 - 2*y**3 + 0*y**2. Factor u(i).
3*(i - 1)**2*(i + 1)**2
Determine s, given that 0 + 6/19*s**5 - 58/19*s**2 - 12/19*s - 22/19*s**4 - 74/19*s**3 = 0.
-1, -1/3, 0, 6
Suppose 15*n = -42 + 117. Let r(w) be the third derivative of -1/40*w**n + 0*w**3 + 0*w - 1/16*w**4 + 0 - w**2. Determine m so that r(m) = 0.
-1, 0
Suppose 0 = 4*s - 4 + 28. Let t = s + 8. Suppose 6 + t + m**2 + m**2 + 10*m - 2*m = 0. Calculate m.
-2
Let x be (-3)/(2 - 1/2). Let o = x + 4. What is v in -2 - 73*v**4 + 75*v**4 + o - 2*v**3 = 0?
0, 1
Let b(a) = 18*a**3 - 54*a**2 + 60*a - 24. Let g(x) = x**4 + 17*x**3 - 54*x**2 + 60*x - 24. Let s(o) = -4*b(o) + 3*g(o). Factor s(c).
3*(c - 2)**3*(c - 1)
Factor 27 + 0*u - 3/4*u**2.
-3*(u - 6)*(u + 6)/4
Let s(n) = -n**3 - n**2 + n. Suppose 7 = w + 1. Suppose 3*f - w = 2*f. Let o(m) = -4*m**3 + 10*m**2 - 6*m. Let b(i) = f*s(i) + o(i). Factor b(l).
-2*l**2*(5*l - 2)
Let b be (-1)/(10 - (-62)/(-6)). Suppose 1/9*o**4 - 4/3*o + 13/9*o**2 - 2/3*o**b + 4/9 = 0. What is o?
1, 2
Let y(x) be the third derivative of -x**6/90 + x**5/30 + x**4 - 41*x**3/6 - 18*x**2. Let o(d) be the first derivative of y(d). Factor o(m).
-4*(m - 3)*(m + 2)
Suppose 5*u + 80 = 9*u. Factor 75*h - 52*h**2 - u - 14*h**3 + 12*h**2 + 16*h**3 - 17*h**3.
-5*(h - 1)*(h + 4)*(3*h - 1)
Let f be 48/456 - 93/(-19). Let p(v) be the third derivative of 0*v + 1/18*v**4 - 1/90*v**f - 10*v**2 + 0 - 1/9*v**3. Factor p(g).
-2*(g - 1)**2/3
Let o(j) be the second derivative of -j**7/630 - j**6/180 + j**5/15 - j**4/4 - 6*j. Let b(h) be the third derivative of o(h). Solve b(k) = 0 for k.
-2, 1
Let d be (-4)/(0 + (1 + 0)*-4). Let n(a) be the first derivative of -d - 1/6*a**4 + 0*a + 1/3*a**2 + 0*a**3. Factor n(q).
-2*q*(q - 1)*(q + 1)/3
Let c(x) be the second derivative of x**8/2240 - x**7/840 + 11*x**4/12 + 11*x. Let u(h) be the third derivative of c(h). Factor u(z).
3*z**2*(z - 1)
Let l(y) = 2*y**2 + 20*y - 13. Let b be l(-11). Suppose 4*x - 5*c = -12, -3*c + 13 + b = 5*x. Solve 2/17*t**x - 8/17*t + 8/17 = 0.
2
Let l(n) = -10*n**3 - 10*n**2 - 15*n - 5. Let v(t) = 11*t**3 + 9*t**2 + 15*t + 5. Let q(o) = 6*l(o) + 5*v(o). Solve q(a) = 0.
-1
Suppose -s - 2*s + 12 = 0. Suppose -s*i - 53 = -153. Determine a, given that -i*a**2 - 16*a + 4 - 4 + 6*a = 0.
-2/5, 0
Let a(j) be the third derivative of j**7/840 - j**6/80 + 23*j**4/24 - 23*j**2. Let i(n) be the second derivative of a(n). Factor i(d).
3*d*(d - 3)
Let g(k) = k**2 - 21*k + 36. Let h(o) = -o**2. Let v(p) = -g(p) + 2*h(p). Solve v(r) = 0.
3, 4
Suppose 5*i + 45 = 5*a, 0*i - 3*i - 42 = 2*a. Let d = i - -15. Factor -3*k**4 + 4*k - 3*k**3 - 5*k + k**5 + 2*k**4 + k**2 + d*k.
k*(k - 2)*(k - 1)*(k + 1)**2
Let y = -516 - -516. Let l(d) be the second derivative of -1/105*d**6 + 0*d**4 + y*d**5 + 0 - 1/147*d**7 - 3*d + 0*d**3 + 0*d**2. Factor l(z).
-2*z**4*(z + 1)/7
Factor 2 + 150*o**2 + 14*o**3 + 38 + 180*o - 59*o**3 - 80*o**3.
-5*(o - 2)*(5*o + 2)**2
Let -55/2*r + 1/2*r**2 + 27 = 0. What is r?
1, 54
Let j(f) = -2*f**3 - 5*f**2 - 3*f + 3. Let g be j(-3). Find i, given that 12*i**2 - 16*i**2 + 3*i**2 + 7*i**2 + 9*i**4 + g*i**3 = 0.
-2, -1/3, 0
Let n(v) be the second derivative of 0 + 6*v**2 + 1/4*v**4 - 5/2*v**3 + 13*v. Let n(c) = 0. Calculate c.
1, 4
Let j(o) = o**2 - 11*o + 14. Let m be j(10). Find x, given that -m*x**2 - 20*x + 0*x**2 + 41*x + 2 - 19*x = 0.
-1/2, 1
Let u(m) be the first derivative of -2*m**5/5 - m**4 + 2*m**3/3 + 2*m**2 - 38. Factor u(y).
-2*y*(y - 1)*(y + 1)*(y + 2)
Let m be (-7 + 10 - 3)/2. Let h(k) be the first derivative of 1/2*k**6 + 0*k**2 + 0*k**5 + 2 + m*k**3 - 3/4*k**4 + 0*k. Factor h(a).
3*a**3*(a - 1)*(a + 1)
Determine f so that -1/2*f**3 - 311/3*f + 377/6*f**2 + 124/3 = 0.
2/3, 1, 124
Let l(d) be the second derivative of d**9/25200 - d**8/5600 + d**6/600 - d**5/200 - 3*d**4/4 + 5*d. Let m(f) be the third derivative of l(f). Factor m(p).
3*(p - 1)**3*(p + 1)/5
Let a(g) be the first derivative of g**3/2 - 25*g**2/4 + 11*g + 75. Determine m, given that a(m) = 0.
1, 22/3
Let o(p) be the second derivative of -1/8*p**4 + 0 + 3/4*p**2 + 1/40*p**5 - 1/12*p**3 - 5*p. Find w, given that o(w) = 0.
-1, 1, 3
Factor 11/4*q + 3/2 - q**4 - 3*q**3 - 1/2*q**2 + 1/4*q**5.
(q - 6)*(q - 1)*(q + 1)**3/4
Let h(k) = 12*k + 58. Let w be h(-4). Let s be (-3)/24 - (-33)/336*w. Factor -s*a**2 + 4/7 - 2/7*a.
-2*(a + 1)*(3*a - 2)/7
Let m(q) be the first derivative of -q**5/10 + 13*q**4/9 + q**3 + 39*q + 34. Let y(d) be the first derivative of m(d). Factor y(n).
-2*n*(n - 9)*(3*n + 1)/3
Let z = 134/3 - 929/21. Solve 0 + z*x**5 - 6/7*x + 9/7*x**4 + 3/7*x**3 - 9/7*x**2 = 0 for x.
-2, -1, 0, 1
Let u(a) be the second derivative of -a**6/70 + 9*a**5/140 + a**4/28 - 3*a**3/14 + a - 55. Factor u(r).
-3*r*(r - 3)*(r - 1)*(r + 1)/7
Factor -2*d**3 + d**3 - 2*d**3 - 3*d**2 - d + 6*d**2 + d**4.
d*(d - 1)**3
Let x(c) be the third derivative of -c**5/30 - 5*c**4/2 + 31*c**3/3 + 103*c**2. Let x(n) = 0. What is n?
-31, 1
Let f(s) be the first derivative of 3*s**6/280 - s**5/21 + 13*s**4/168 - s**3/21 + 9*s**2/2 + 17. Let c(p) be the second derivative of f(p). Factor c(o).
(o - 1)**2*(9*o - 2)/7
Let j(q) be the second derivative of -q**5/30 - 557*q**4/18 - 8587*q**3 + 25947*q**2 + 600*q. Find u, given that j(u) = 0.
-279, 1
Let q be 3 - (-6)/(-2) - -4. Suppose i + 16 = -4*t, -3*t - 2 = q*i + 10. Factor i*j + j**2 - 4*j + 3*j.
j*(j - 1)
Let z be (-1)/3 + 84*39/1404. Factor 0 - 2/3*r**4 - 4/3*r + 2/3*r**z + 4/3*r**3.
-2*r*(r - 2)*(r - 1)*(r + 1)/3
Let s(y) = -18*y**4 + 55*y**3 - 36*y**2 - 88*y - 7. Let a(n) = -8*n**4 + 27*n**3 - 18*n**2 - 44*n - 3. Let d(v) = 7*a(v) - 3*s(v). Let d(c) = 0. What is c?
-1, 0, 2, 11
Suppose -4*g + g + 37 = 4*l, -3*g + 28 = -5*l. Let k(b) = 3*b**3 - b**2 - 32*b + 8. Let i(f) = -f**3 + f**2 + 16*f - 4. Let t(p) = g*i(p) + 6*k(p). Factor t(y).
(y - 1)*(y + 2)*(7*y - 2)
Let k = 1782 + -1778. Let s(a) be the third derivative of 2/3*a**3 + 0 + 3/5*a**5 - 3*a**2 + a**k + 0*a. Find t, given that s(t) = 0.
-1/3
Suppose g = 5*o - 16, 0 = -4*g - g + 20. Let z(b) be the first derivative of 0*b**2 + 1/4*b**o + 0*b**3 + 4 - 2/5*b**5 + 1/6*b**6 + 0*b. Factor z(a).
a**3*(a - 1)**2
Let u(l) be the first derivative of 5*l**3/3 - 55*l**2/2 + 38. Factor u(y).
5*y*(y - 11)
Let q(x) = -x**3 + 30*x**2 + 101*x - 63. Let w be q(33). Let s + 0 - 1/4*s**4 + s**2 - 1/4*s**w = 0. What is s?
-2, -1, 0, 2
Suppose m = -2*m. Suppose m = 4*z - 4*h - 12, 3 = 3*z + 3*h - 0*h. Solve 2/3*f**2 + z*f + 4/3 = 0.
-2, -1
Let h = -1906/9 - -9548/45. Solve 0 - 2/5*o**4 + h*o**2 - 2/5*o**3 + 2/5*o**5 + 0*o = 0.
-1, 0, 1
Determine v so that -12/7*v + 16/7 + 2/7*v**2 = 0.
2, 4
Let n be -3*(1 - 5) - 7. Suppose 20 = 5*q - 2*s, q - n*s = 2*q + 23. Factor 1/10*g**q + 0*g + 0 - 1/10*g**3.
-g**2*(g - 1)/10
Factor 3/4*c**2 + 27/2*c + 231/4.
3*(c + 7)*(c + 11)/4
Let d(b) = 9*b**4 + 29*b**3 + 12*b**2 - 40*b + 10. Let i(u) = 8*u**4 + 28*u**3 + 12*u**2 - 40*u