34*f**3 + 10*f**2 - 38*f**3 - 4*f**4 + 2*f**4 - m*f**2 = 0. What is f?
-3, 0, 1
Suppose 13*r - 13*r = 59*r - 118. Let h be (1/(-3))/(2/(-8)). Find t such that -1/3*t**r + h*t - 1 = 0.
1, 3
Let n(r) be the first derivative of -2*r**3/57 - 12*r**2/19 + 14*r + 647. Factor n(b).
-2*(b - 7)*(b + 19)/19
Suppose -3*n = 4*v - 11, -2*v + 17 = 4*n + v. Suppose -3*m**n + 3*m**3 + 2*m**2 - 536*m**4 + 533*m**4 + m**2 = 0. What is m?
-1, 0, 1
Let c(g) be the third derivative of g**8/672 + 11*g**7/210 + g**6/12 - 11*g**5/60 - 7*g**4/16 + 28*g**2 - 2*g. Find d, given that c(d) = 0.
-21, -1, 0, 1
Factor -6*y**3 - 34*y**5 + 4*y**3 + 21*y**5 + y + 14*y**5.
y*(y - 1)**2*(y + 1)**2
Find v, given that -2/3*v**2 + 0 - 214/3*v = 0.
-107, 0
Let h(t) be the first derivative of -t**7/840 + t**6/480 - 3*t**2 + 12. Let k(x) be the second derivative of h(x). Factor k(q).
-q**3*(q - 1)/4
Let s(t) be the third derivative of t**5/40 + t**4/2 - 14*t**2 - 4*t. Factor s(n).
3*n*(n + 8)/2
Find d, given that -2/9*d**3 + 0 + 8/9*d + 0*d**2 = 0.
-2, 0, 2
Let g be 3*1/((-9)/(-78)). Let o = g + -11. Factor -4 - 5*s + o*s**2 - 4*s - 2.
3*(s - 1)*(5*s + 2)
Let l(x) = 5*x**4 - 15*x**3 + 59*x**2 - 78*x + 29. Let y(d) = -6*d**4 + 14*d**3 - 60*d**2 + 80*d - 28. Let t(n) = -4*l(n) - 3*y(n). Factor t(z).
-2*(z - 4)*(z - 2)**2*(z - 1)
Let o(t) be the second derivative of -1/2*t**4 + 0*t**2 + 1/5*t**6 + 0 + 1/10*t**5 + 42*t + 0*t**3 - 1/21*t**7. Suppose o(y) = 0. Calculate y.
-1, 0, 1, 3
Let g(o) be the third derivative of -o**5/20 + 19*o**4/8 + 10*o**3 - 265*o**2. Factor g(c).
-3*(c - 20)*(c + 1)
Determine s, given that -14/9*s - 8/9 - 4/9*s**2 + 2/9*s**3 = 0.
-1, 4
Let b(h) be the second derivative of -h**8/20160 + 7*h**6/2160 - h**5/60 - 3*h**4/4 - 40*h. Let z(m) be the third derivative of b(m). Let z(s) = 0. What is s?
-3, 1, 2
Let s(p) be the second derivative of -p**5/5 + 3*p**4 - 10*p**3 - 50*p**2 + 2*p - 16. Find f such that s(f) = 0.
-1, 5
Let o(i) = i - 22. Let b be o(22). Let a(d) be the second derivative of 0*d**3 + 0*d**2 + 1/105*d**7 + 6*d + b*d**4 + 0*d**5 + 0*d**6 + 0. Factor a(v).
2*v**5/5
Let p(b) be the third derivative of b**7/735 + b**6/60 + 8*b**5/105 + b**4/7 + 18*b**2 + 4*b. Determine m so that p(m) = 0.
-3, -2, 0
Let i(c) be the third derivative of -1/20*c**5 - 34*c**2 + 0 + 0*c - 121/2*c**3 - 11/4*c**4. Find s, given that i(s) = 0.
-11
Let f = 221 + -219. Let q(p) be the second derivative of 0*p**2 - p**4 - 3/20*p**5 - 2*p**3 + 0 - f*p. Find m such that q(m) = 0.
-2, 0
Factor 0 + 10/9*l**3 - 2/9*l**4 - 4/3*l**2 + 0*l.
-2*l**2*(l - 3)*(l - 2)/9
Factor -100/3*a**4 + 0 - 332/3*a**2 - 4/3*a**5 + 108*a**3 + 112/3*a.
-4*a*(a - 1)**3*(a + 28)/3
Let w = -1424 + 1424. What is f in 8/7*f + 4/7*f**3 + w - 12/7*f**2 = 0?
0, 1, 2
Let f(b) be the third derivative of b**7/210 + 113*b**6/600 + 809*b**5/300 + 561*b**4/40 - 27*b**3 - 13*b**2 + b. Factor f(g).
(g + 5)*(g + 9)**2*(5*g - 2)/5
Suppose 3*f = -3*b + 18, 12 = 3*b - f - 2*f. Suppose 5*x - n = 415, -2*x + b*n + 107 = -x. Determine y, given that x*y + 0 + 10 - 97*y + 5*y**2 = 0.
1, 2
Suppose -108*q = -98*q - 20. Let p(s) be the first derivative of 16/3*s - 4 + 4/3*s**q + 1/9*s**3. Factor p(w).
(w + 4)**2/3
Suppose 50*s = -13*s. Let -20/3*d**3 + 0*d**2 + 0*d**4 + 0*d + s + 5/3*d**5 = 0. What is d?
-2, 0, 2
Let p(g) be the first derivative of -g**7/840 + g**5/120 + 26*g**3/3 + 3. Let q(o) be the third derivative of p(o). Solve q(u) = 0.
-1, 0, 1
Let k be 18/(-24)*-4 - 6/(-2). Factor z + 3*z + 1 - 2*z**2 + k - 1.
-2*(z - 3)*(z + 1)
Let o be (-41)/(-10) + 15/(-150). Let l(i) be the second derivative of -4*i + 1/18*i**3 + 1/3*i**2 + 0 - 1/36*i**o. Factor l(r).
-(r - 2)*(r + 1)/3
Determine s so that 21980*s**3 + 42*s - 196 - 11*s**2 - 21978*s**3 + 35*s**2 = 0.
-7, 2
Let m(a) = -a**3 - 7*a**2 + a - 1. Let g(q) = -5*q**3 + 130*q**2 + 395*q + 180. Let l(r) = g(r) - 10*m(r). Suppose l(i) = 0. Calculate i.
-38, -1
Let z be 66/24 + (-2)/(-8). Let 22*q**3 - 5*q - 18*q**3 - 7*q - z - 5 = 0. Calculate q.
-1, 2
Factor -8*s - s**2 + 3*s + 137 - 2*s - 129.
-(s - 1)*(s + 8)
Let l(i) = -i**3 - 5*i**2 - 4*i - 12. Let u be l(-6). Suppose t = -2*r - r + 48, 0 = 3*t - 3*r - 144. Factor t + 17*g - 45*g**2 + 7*g + u*g**2.
3*(g + 4)**2
Let m be 2015/6825 - 1/5. Let -2/21*z**2 - 2/21*z + 2/21 + m*z**3 = 0. What is z?
-1, 1
Let p be (-10*1/(-5))/(-1 - -2). Suppose 0*y - 8 = -2*y. Determine x so that -y*x**2 + 4*x**2 - 3*x**p - 12 - 15*x = 0.
-4, -1
Let h(x) = x**5 - 4*x**4 - 3*x**3 + 8*x**2 - 2*x. Let j(f) = f**5 - 5*f**4 - 3*f**3 + 8*f**2 - f. Let o(t) = 3*h(t) - 2*j(t). Let o(w) = 0. Calculate w.
-2, 0, 1, 2
Let x(s) = -20*s**2 - 304*s - 134. Let o(t) = -t**2 + t - 1. Let n(p) = -10*o(p) + x(p). Determine c so that n(c) = 0.
-31, -2/5
Suppose 10*w - 15 = 5. Let g(b) be the second derivative of 2*b + 0 - 1/2*b**3 - b**w - 1/12*b**4. Factor g(o).
-(o + 1)*(o + 2)
Let m(z) be the first derivative of -z**5 - 5*z**4/2 - 5*z**3/3 - 115. Factor m(y).
-5*y**2*(y + 1)**2
Let s be ((-3)/8)/(63/(-378)). Determine d, given that 3/2*d + 0 + 3/4*d**4 + 0*d**3 - s*d**2 = 0.
-2, 0, 1
Suppose 0*r + 3*r - 7 = -4*d, 2*d - 21 = -5*r. Let b be (d - -1)*(0 - 3). Find q, given that 18*q**2 + 3*q + 8*q**b + 4 - 6 + 0 = 0.
-2, -1/2, 1/4
Let g(k) be the first derivative of -3/16*k**4 - 5/12*k**3 - 1/8*k**2 + 9/20*k**5 + 2 + 0*k. Factor g(f).
f*(f - 1)*(3*f + 1)**2/4
Suppose -14 = -39*z + 32*z. Suppose -4*p = 4*g - 4, g = 3*p - 0*g + 1. Factor -15/4*k**3 - k**5 + p - 1/4*k - 13/4*k**4 - 7/4*k**z.
-k*(k + 1)**3*(4*k + 1)/4
Suppose 0 = -4*y - 2*z + 26, -y = 2*y + 4*z - 32. Determine k so that 25 - 105*k - 40*k**y - 18*k**2 + 3*k**2 + 100*k**3 - 35*k**2 + 5*k**5 + 65 = 0.
-1, 1, 2, 3
Factor 0 + 5/3*v**2 - 25/6*v**3 + 0*v.
-5*v**2*(5*v - 2)/6
Solve -4*i**2 - 7 + 7*i**2 - i**2 - 7 + 40*i + 4*i**2 = 0.
-7, 1/3
Let g(i) be the second derivative of -i**5 + 328*i**4/3 + 934*i**3/3 + 268*i**2 + 22*i + 7. Factor g(c).
-4*(c - 67)*(c + 1)*(5*c + 2)
Let o(d) be the first derivative of 5*d**7/42 - d**6/6 + 41*d - 3. Let u(i) be the first derivative of o(i). Factor u(g).
5*g**4*(g - 1)
Let b(f) be the first derivative of 91/12*f**3 + 7/12*f**6 + 4*f**2 + f + 67/20*f**5 - 21 + 29/4*f**4. Let b(l) = 0. Calculate l.
-2, -1, -1/2, -2/7
Let c(v) = -v**3 + 4*v**2 + 6*v - 17. Let r be c(6). Let s be r/(-30) - 13/78. Factor 4/5*k**3 - s - 12/5*k + 0*k**2.
4*(k - 2)*(k + 1)**2/5
Let v(a) = -a + 1. Let m(k) = -4*k**2 - 42*k - 98. Suppose -5*c = -4*g + 25, 5*g - 9 - 16 = 0. Let r(s) = c*m(s) + 2*v(s). Determine j so that r(j) = 0.
-5
Let v be 2/(-5) - 144/(-40). What is q in 2/5*q + 9/5*q**4 + 0 - v*q**3 + q**2 = 0?
-2/9, 0, 1
Let q be (-3)/(-18) - (-138)/36. Find h such that -q*h**3 + 14*h**4 + 2*h**4 + 2*h - 2*h - 12*h**5 = 0.
0, 1/3, 1
Let u = 3 + 2. Suppose -u*n - 3 = -2*y - 9, 3*y = -3*n + 33. Factor -7*w**3 + y*w**3 + 5*w**5 - 2*w**5.
3*w**5
Suppose b = -4*j + 16, -2 = b + 2. Factor 3*w**4 - 19*w**2 + 36 + 29 - 17 - j*w**2.
3*(w - 2)**2*(w + 2)**2
Let g(u) be the third derivative of u**7/1260 + u**6/72 + 5*u**5/72 + 77*u**2. Suppose g(a) = 0. Calculate a.
-5, 0
Let b(p) = -p + 16. Let w be b(7). Let g(a) = 25*a**2 - 297*a + 1287. Let k(t) = 6*t**2 - 74*t + 322. Let n(i) = w*k(i) - 2*g(i). What is h in n(h) = 0?
9
Let s(j) be the third derivative of j**8/1344 - j**7/210 - j**6/80 + 2*j**5/15 - 35*j**4/96 + j**3/2 + 72*j**2. Factor s(a).
(a - 4)*(a - 1)**3*(a + 3)/4
Let b(j) be the first derivative of -2/9*j**3 - 4/3*j - j**2 + 10. Solve b(n) = 0.
-2, -1
Let h(n) be the first derivative of 10*n + 4*n**2 - 2/3*n**3 - 14. Factor h(u).
-2*(u - 5)*(u + 1)
Find w, given that -2/7*w - 2/7*w**3 + 0 + 4/7*w**2 = 0.
0, 1
Let j(s) be the second derivative of -1/2*s**3 + 1/28*s**4 + 0 - 12/7*s**2 - 20*s. Factor j(z).
3*(z - 8)*(z + 1)/7
Let x(z) be the second derivative of -7/900*z**6 - 1/2*z**3 - 1/15*z**4 + 0 + 0*z**2 - 4*z - 4/75*z**5. Let s(m) be the second derivative of x(m). Factor s(t).
-2*(t + 2)*(7*t + 2)/5
Factor 10125/4 + 5/4*r**2 - 225/2*r.
5*(r - 45)**2/4
Factor 0 + 9/4*t**2 + 3/8*t**4 + 15/8*t**3 + 0*t.
3*t**2*(t + 2)*(t + 3)/8
Let h(d) be the second derivative of 12*d + 0 - 1/18*d**3 - 1/12*d**2 - 1/72*d**4. Determine f, given that h(f) = 0.
-1
Let b(w) = 2*w**3 - 6*w**2 + 7*w - 18. Let z be b(3