9*r - 20. Let h be w(-4). Solve -6*y**3 + 7*y**3 + 16*y - h*y**2 + 3*y**3 = 0.
0, 2
Determine h, given that -14*h**3 + 3*h**4 + 17*h**2 + 21*h**2 + 71*h**3 - h**2 + 260*h**2 + 243*h = 0.
-9, -1, 0
Let r(k) be the second derivative of k**8/10080 + k**7/1260 + 5*k**3/6 + 10*k. Let f(o) be the second derivative of r(o). Suppose f(p) = 0. What is p?
-4, 0
Let w(m) be the third derivative of 0 - 1/240*m**6 + m**2 + 0*m**3 + 1/120*m**5 + 0*m + 1/24*m**4. Let w(q) = 0. Calculate q.
-1, 0, 2
Suppose 3*m = -4*a + 13, -2*m - 3*m - a + 16 = 0. Suppose 4*x + m = 5*x. Factor 0*g**3 + 4*g**2 - 2*g**3 - 3*g**3 + 2*g + 3*g**x - 4.
-2*(g - 2)*(g - 1)*(g + 1)
Let i = 217/33 - 65/11. Determine o so that 1/3 + 1/3*o**2 - i*o = 0.
1
Suppose -4*l + 9 - 1 = 0. Let v(s) = -s - 1. Let d(x) = 4*x**2 - 2*x - 6. Let n(y) = l*v(y) - d(y). Factor n(c).
-4*(c - 1)*(c + 1)
Let q(b) be the third derivative of 4*b**2 + 1/720*b**6 + 0*b**3 + 0 - 1/144*b**4 + 0*b + 0*b**5. Factor q(u).
u*(u - 1)*(u + 1)/6
Let y(l) = 21*l**3 + 16*l**2 - 7*l - 4. Let c(j) = j**2 + 2*j + 2. Let t(m) = -2*c(m) - y(m). Factor t(k).
-3*k*(k + 1)*(7*k - 1)
Factor -6*s**4 - 36*s**3 + 0*s + 0 - 1/4*s**5 + 0*s**2.
-s**3*(s + 12)**2/4
Let d(r) be the third derivative of -r**7/70 + r**6/2 - 59*r**5/10 + 45*r**4/2 - 81*r**3/2 + 7*r**2 - 4*r. Find a such that d(a) = 0.
1, 9
Let -342185 + 342185 - 3*j**2 + j**3 = 0. Calculate j.
0, 3
Suppose 2*s - 63 + 7 = 0. Let l be (-1 - 3) + 176/s. Factor -8/7 - l*m + 22/7*m**2 - 6/7*m**3.
-2*(m - 2)**2*(3*m + 1)/7
Let s(o) = -2*o**4 + 10*o**3 + 2*o**2 - 10*o + 6. Let i(q) = -2*q**4 + 9*q**3 + 3*q**2 - 9*q + 4. Let y(n) = 6*i(n) - 5*s(n). Factor y(r).
-2*(r - 3)*(r - 1)*(r + 1)**2
Let f(h) be the third derivative of h**6/600 - 7*h**5/100 + 13*h**4/40 - 19*h**3/30 + 273*h**2. Factor f(l).
(l - 19)*(l - 1)**2/5
Let q(t) be the first derivative of t**5/20 + t**4/2 - 5*t**3/2 - 11*t**2 + 19. Let w(u) be the second derivative of q(u). Factor w(s).
3*(s - 1)*(s + 5)
Let k(p) be the second derivative of 3/4*p**5 - 10/3*p**3 + 0*p**4 + 8*p - 1/6*p**6 + 0*p**2 + 0. Factor k(f).
-5*f*(f - 2)**2*(f + 1)
Let p be 1 + (28/308)/((-1)/(-11)). Let 1/3*m - 1/3 + 1/3*m**p - 1/3*m**3 = 0. What is m?
-1, 1
Let b = -100 - -74. Let s be 4/b + (-240)/(-715). Factor s*a**2 + 6/11*a + 4/11.
2*(a + 1)*(a + 2)/11
Let v(o) = -16*o - 11. Let a be v(-7). Let u = -98 + a. Find p, given that 0 - 5/2*p**4 - 1/2*p - 11/2*p**u - 7/2*p**2 = 0.
-1, -1/5, 0
Let y(x) = -x**3 + 7*x**2 - 6*x + 9. Let s be y(6). Suppose -2 + 5*t - s*t**4 - 3*t**3 - 11*t**3 - 7*t**3 + 4*t - t**2 = 0. Calculate t.
-2, -1, 1/3
Suppose -3*p - 25*q = -23*q - 17, 5*p + 5 = 5*q. Let d be 0 + 6/(1 + 1) + -1. Find r, given that 2/11*r**p + 0 + 0*r + 6/11*r**d = 0.
-3, 0
Let j(p) be the first derivative of 1/33*p**3 + 13/11*p**2 + 169/11*p + 37. Suppose j(a) = 0. Calculate a.
-13
Solve -40/7*r**2 - 30/7*r - 8/7 - 20/7*r**3 + 2/7*r**5 + 0*r**4 = 0.
-1, 4
Let g(x) be the second derivative of -x**6/72 - x**5/6 - 5*x**4/6 + 22*x**3/3 + 14*x - 1. Let d(n) be the second derivative of g(n). Solve d(j) = 0 for j.
-2
Let b(g) be the second derivative of 1/18*g**3 + 0*g**2 + 40*g + 1/36*g**4 + 0. Factor b(r).
r*(r + 1)/3
Let r be ((-3)/(-8))/((-36)/48)*-6. Let c(p) be the third derivative of 2/3*p**r + 1/12*p**5 + 0 - 1/2*p**4 - 6*p**2 + 0*p. Determine i so that c(i) = 0.
2/5, 2
Let x = 239 - 237. Factor 0 - 13/5*j**x + 2/5*j.
-j*(13*j - 2)/5
Let 6*s - 20/3 + 2/3*s**2 = 0. Calculate s.
-10, 1
Find x, given that -18/17*x - 2/17*x**2 + 20/17 = 0.
-10, 1
Let i(o) be the first derivative of 7*o**2 - 22 - 16*o + 2/3*o**3. Factor i(s).
2*(s - 1)*(s + 8)
Factor 0 + 8*n**2 + 2/3*n**3 + 22/3*n.
2*n*(n + 1)*(n + 11)/3
Let g(u) be the third derivative of 0*u - 1/108*u**4 + 0 - 4*u**2 - 2/27*u**3 + 1/270*u**5. Solve g(w) = 0.
-1, 2
Let l(h) be the third derivative of h**6/160 + 3*h**5/20 - 27*h**4/32 + 7*h**3/4 - 49*h**2. Factor l(o).
3*(o - 1)**2*(o + 14)/4
Suppose -3*w - 48 = -0*w. Let b(g) = -g - 14. Let z be b(w). Solve -a**z - 2*a - a**2 - 2*a**3 - 2*a**2 = 0.
-1, 0
Let o = -12444/7 - -1778. Determine q so that 0*q - o*q**3 + 4/7*q**2 + 0 = 0.
0, 2
Find b such that -101848 + 101848 + 5*b**5 + 10*b**3 - 15*b**4 = 0.
0, 1, 2
Let g(a) = -11*a**3 + 2*a**2 + 3*a + 2. Let c be g(-1). Suppose -18*i + 14*i = -c. Suppose -1 - 9*d**2 + i*d + 4*d + d - 2*d = 0. What is d?
1/3
Let r(l) = -l**2 - l + 2. Let n(j) = -2*j**5 + 11*j**4 - 11*j**3 - 12*j**2 + 8*j + 6. Let b(w) = -2*n(w) + 10*r(w). Let b(y) = 0. What is y?
-1, 1/2, 1, 4
Let f(s) = 3*s**4 + 4*s**3 + 9*s**2 + 4*s - 4. Let h(n) = 5*n**4 + 7*n**3 + 17*n**2 + 7*n - 8. Let j(x) = 7*f(x) - 4*h(x). What is q in j(q) = 0?
-2, -1, 1, 2
Let f(i) be the second derivative of -i**6/480 - i**5/80 - i**4/48 - 6*i**2 - 10*i. Let j(k) be the first derivative of f(k). Determine o, given that j(o) = 0.
-2, -1, 0
Let d = -139 + 139. Let p(i) be the third derivative of 1/48*i**4 - 1/6*i**3 + 1/60*i**5 + d*i - 1/240*i**6 - i**2 + 0. Factor p(q).
-(q - 2)*(q - 1)*(q + 1)/2
Let t be (1 - -5)/(-5 + 7). Suppose -a = -t*a + 6. Solve 2 - 4*j**2 - 2 + 1 + a = 0 for j.
-1, 1
Let t(h) = 21*h**2 - 63*h + 60. Let g = 5 + -6. Let k be (0 - 5)*g/(-1). Let w(o) = -6*o**2 + 18*o - 17. Let v(s) = k*t(s) - 18*w(s). Factor v(a).
3*(a - 2)*(a - 1)
Find p such that 2*p + 31/2*p**2 - 19/2*p**4 - 3/2*p**5 - 1/2*p**3 - 6 = 0.
-6, -1, 2/3, 1
Let b be 114/42 + (-2)/(-7). Suppose 12*q - 8 = 16. Solve -1/3 - g + 2/3*g**b + 1/3*g**5 + g**4 - 2/3*g**q = 0 for g.
-1, 1
Let n(j) be the first derivative of 7 + 4/3*j**3 + j**2 + 0*j + 1/2*j**4. Factor n(t).
2*t*(t + 1)**2
Let o(a) = 9*a - 3. Let k(d) = -4*d + 2. Let y(r) = -7*k(r) - 3*o(r). Let j be y(5). Determine w so that -2/3*w**2 + 0 + w**3 + j*w - 1/3*w**4 = 0.
0, 1, 2
Let g = 3347/10068 - -3/3356. Factor 0*t**4 + 0*t**2 + g*t**5 + 0 + 1/3*t - 2/3*t**3.
t*(t - 1)**2*(t + 1)**2/3
Let z(l) be the third derivative of l**8/224 - l**7/105 - l**6/30 + l**5/20 + 5*l**4/48 - l**3/6 + 120*l**2. Let z(n) = 0. Calculate n.
-1, 1/3, 1, 2
Let q(s) be the second derivative of 1/30*s**6 + 0*s**4 + 0 + 0*s**2 - 26*s - 1/84*s**7 + 0*s**3 + 0*s**5. Factor q(x).
-x**4*(x - 2)/2
Let h(f) be the second derivative of 3*f**5/20 + 4*f**4 + 29*f**3/2 + 21*f**2 + f + 17. Factor h(k).
3*(k + 1)**2*(k + 14)
Let l be 5 + -2 + 0 - -1. Suppose 0 = 4*d - 4*d + 4*d. Factor d*m + 0 - 2/13*m**2 + 2/13*m**5 - 2/13*m**3 + 2/13*m**l.
2*m**2*(m - 1)*(m + 1)**2/13
Let p(g) be the first derivative of -4 + 4/3*g**3 + g**4 + 0*g**2 + 0*g. Suppose p(b) = 0. What is b?
-1, 0
Let d(l) be the second derivative of l**7/14 + 6*l**6/5 + 27*l**5/5 + 8*l**4 - 22*l. Let d(j) = 0. Calculate j.
-8, -2, 0
Solve -4/5*p - 2/5*p**4 + 0 + 4/5*p**3 + 2/5*p**2 = 0 for p.
-1, 0, 1, 2
Suppose -10 = -6*m + 8. Let s be 0 + m + 1/((-2)/6). Factor -2/3*g**3 + s*g + 0 - 2/3*g**4 + 0*g**2.
-2*g**3*(g + 1)/3
Determine x, given that -112*x + 15*x**3 + 16*x**3 + 17 - 53*x**3 + 26*x**3 - 97 - 28*x**2 = 0.
-2, -1, 10
Find t such that 4/5*t**2 - 4/5 + 2*t - 2*t**3 = 0.
-1, 2/5, 1
Let y be 22630/(-5)*(2 + (-34)/20). Let x = 1365 + y. Suppose -24/5*v**2 + 0 - 16/5*v - 2*v**4 + x*v**3 = 0. What is v?
-2/5, 0, 2
Let i(p) be the first derivative of p**3/18 - p**2/6 + p/6 - 231. Suppose i(d) = 0. What is d?
1
Let b(x) = -x**2 + 4*x. Let j be b(0). Factor 0*h + 0*h**3 + j - 1/5*h**2 + 1/5*h**4.
h**2*(h - 1)*(h + 1)/5
Let y(x) be the third derivative of 0*x - 1/30*x**3 + 1/100*x**5 - 5*x**2 + 0 + 1/60*x**4. Solve y(c) = 0 for c.
-1, 1/3
Let k(n) be the third derivative of 0 - 1/10*n**5 + 0*n**4 + 0*n**3 + 1/40*n**6 + 10*n**2 + 0*n. Factor k(d).
3*d**2*(d - 2)
Let y be ((-29)/(-58))/((-182)/4). Let l = y - -187/455. Solve -2/5 + l*c**2 + 0*c = 0.
-1, 1
Let m be (-30)/(-16)*1176/1470. Factor m*r + 3*r**2 - 3/2*r**3 - 3.
-3*(r - 2)*(r - 1)*(r + 1)/2
Let l be 10 - 8/(-5 - -7) - 0. Let -l*m**2 - 18/11*m**3 - 48/11*m + 24/11 = 0. Calculate m.
-2, 1/3
Let u be 3/((-2124)/(-3968)) - 0. Let k = u - 16/59. Factor -2/3 + 3*b**3 + k*b**2 + 5/3*b.
(b + 1)**2*(9*b - 2)/3
Factor -3*b**3 + 21 + 16*b**2 + 9*b - 37*b**2 - 6*b.
-3*(b - 1)*(b + 1)*(b + 7)
Let q(d) be the third derivative of d**9/211680 + d**8/70560 - d**7/17640 - d**6/2520 + d**5/5 + 2*d**2. Let g(x) be the third derivative of q(x). Factor