3
Factor -1/3*f**5 + 2/3*f**4 + 32/3*f**2 + 2 + 6*f**3 + 23/3*f.
-(f - 6)*(f + 1)**4/3
Let l = -1/12 + 7/48. Let w(a) be the third derivative of 0 - 1/120*a**6 + 3/80*a**5 + 0*a - l*a**4 - 2*a**2 + 1/24*a**3. Factor w(n).
-(n - 1)**2*(4*n - 1)/4
Let p be -2 + -57*4/(-112). Let m(h) be the third derivative of -p*h**4 + 0*h + 2/21*h**3 + 1/420*h**6 + 0*h**5 + 0 + h**2. Find c, given that m(c) = 0.
-2, 1
Let g(m) be the first derivative of 2*m**5/5 + m**4/2 - 2*m**3/3 - m**2 - 7. What is u in g(u) = 0?
-1, 0, 1
Let n = -5 - -3. Let h = 4 + n. Solve -5 + h*l + 3*l**3 + 5*l**2 + 5 = 0 for l.
-1, -2/3, 0
Let j(s) be the second derivative of -s**8/2240 + s**7/840 + s**4/6 + s. Let t(m) be the third derivative of j(m). Factor t(d).
-3*d**2*(d - 1)
Let h = 42 - 39. Find j such that 0 + 2/5*j**h + 2/5*j - 4/5*j**2 = 0.
0, 1
Let q(i) be the second derivative of i**7/420 + i**6/75 + i**5/50 - i**4/60 - i**3/12 - i**2/10 - 13*i. Factor q(m).
(m - 1)*(m + 1)**3*(m + 2)/10
Let c = 42 + -37. Let q(a) be the second derivative of 0*a**3 + 0 + 0*a**c - a**2 + 1/3*a**4 - 2*a - 1/15*a**6. Suppose q(n) = 0. Calculate n.
-1, 1
Factor -8*d**2 + 16*d - 13 + 13 - 6*d**3 - 8*d + 4*d**4 + 2*d**5.
2*d*(d - 1)**2*(d + 2)**2
Let t(i) be the second derivative of -i**4/42 - i**3/7 - 7*i. Factor t(l).
-2*l*(l + 3)/7
Let d be ((-5)/(-4) - 1)*(-800)/(-1500). Let q(m) be the second derivative of 0 + 1/5*m**2 + 3*m - 2/15*m**4 - 4/25*m**5 + d*m**3. Factor q(a).
-2*(2*a - 1)*(2*a + 1)**2/5
Let r(d) = d**2 + 13*d + 32. Let c be r(-10). Let 1/2*q + 0 - 1/2*q**c = 0. Calculate q.
0, 1
Solve 4*r**3 + 9/7 + 51/7*r - 80/7*r**2 = 0.
-1/7, 3/2
Suppose 0 = 5*j + 35 - 95. Let n be j/7 + (-4)/14. Factor -2/7 - n*r**2 - 8/7*r - 4/7*r**3.
-2*(r + 1)**2*(2*r + 1)/7
Suppose -k + 4*v = 2*k - 8, -v - 2 = -3*k. Suppose -15 = 2*y - 5*d - 41, 2*y + 4*d + 10 = k. Factor -3/4*p**y - 2*p - 1 + 11/4*p**2.
-(p - 2)**2*(3*p + 1)/4
What is b in -3*b + 9 - 3*b**3 + b**2 + 6*b**3 + 0*b - 10*b**2 = 0?
-1, 1, 3
Let z(n) be the third derivative of n**5/480 + n**4/64 - n**3/12 - 41*n**2. What is r in z(r) = 0?
-4, 1
Let u = -4 - -8. Find w, given that -3*w**u + 6*w**4 + 3*w + 3*w**4 + w**2 - 3*w**5 - 7*w**2 = 0.
-1, 0, 1
Suppose -1/5*p**2 + 1/5 + 0*p = 0. Calculate p.
-1, 1
Let w(r) be the second derivative of r**5/120 - r**4/36 + 9*r. Factor w(t).
t**2*(t - 2)/6
Let s = -9 + 19/2. Solve 1/2*l**2 - s + 0*l = 0 for l.
-1, 1
Let i(s) = s + 15. Let n be i(-9). Solve n*p**2 + 6*p + 3/2 = 0.
-1/2
Suppose 12 = -4*g - 0*g + 5*k, 4*k - 16 = 0. Solve -4*l - 3*l**g - l**3 + 2*l + 3*l**4 + 3*l = 0 for l.
-1, 0, 1/3, 1
Let a(t) = 2*t**3 - 11*t**2 + 5*t + 8. Let q be a(7). Let c = q + -946/5. Suppose c*r**3 + 0*r + 0 - 2/5*r**2 - 2/5*r**4 = 0. Calculate r.
0, 1
Let w(t) be the third derivative of -t**6/660 - t**5/110 + 4*t**3/33 - 25*t**2. Factor w(j).
-2*(j - 1)*(j + 2)**2/11
Let f = -59 - -297/5. Factor -12/5*s**3 - 18/5*s**2 - f*s**4 + 0 + 0*s.
-2*s**2*(s + 3)**2/5
Let w = -5 + 11. Let b(l) be the third derivative of -7/360*l**w - 1/9*l**3 + 0*l + 7/72*l**4 + 1/90*l**5 + 0 - l**2. What is c in b(c) = 0?
-1, 2/7, 1
Let n(z) be the first derivative of 3/4*z**2 + 1/2*z**3 + 1/8*z**4 + 1/2*z + 3. Factor n(l).
(l + 1)**3/2
Factor -8/5 - 2/5*d**3 + 0*d + 6/5*d**2.
-2*(d - 2)**2*(d + 1)/5
Let x(c) be the third derivative of c**5/12 - 5*c**4/8 - 10*c**3/3 + 18*c**2. Solve x(a) = 0.
-1, 4
Let a(j) be the second derivative of -1/21*j**3 + 0*j**2 - 1/70*j**5 + 1/21*j**4 + 0 + j. Solve a(x) = 0 for x.
0, 1
Determine n, given that 6/5*n**3 - 6/5*n + 2*n**2 + 0 - 2*n**4 = 0.
-1, 0, 3/5, 1
Let i(s) = -s**2. Let t(o) = o**3 - 8*o**2 + 5*o - 2. Let v(q) = 4*i(q) - t(q). Factor v(r).
-(r - 2)*(r - 1)**2
Suppose 0*p - 4*p + 5*l + 13 = 0, 8 = 2*p - 4*l. Suppose p*c - 9 = -3*w, 4*w - 2 = -2*c + 8*w. Factor 2/7*v**c + 0*v + 2/7*v**2 + 0.
2*v**2*(v + 1)/7
Let d(s) = 8*s**2 + 4*s - 8. Let g(u) = u. Let w(r) = -d(r) + 6*g(r). Let x(a) = -a**3 + 17*a**2 - 5*a - 16. Let c(k) = -5*w(k) - 2*x(k). Factor c(t).
2*(t - 1)*(t + 2)**2
Factor -24/5*j**2 + 4/5*j**3 - 32/5 + 48/5*j.
4*(j - 2)**3/5
Let h = -2/55 - -24/55. Suppose -2*u + 7 = -2*t - 3, 3*u + 5*t = 7. Find d such that -2/5*d + 2/5*d**u + 0 + h*d**3 - 2/5*d**2 = 0.
-1, 0, 1
Let x(z) = -8*z**4 + 4*z**3 + 4*z**2 + 4*z. Let o(f) = -f**5 + 9*f**4 - 5*f**3 - 3*f**2 - 3*f. Let g(a) = 4*o(a) + 3*x(a). Let g(v) = 0. Calculate v.
0, 1, 2
Suppose -5*h + 14 = -z + 2*z, 4*z - 16 = 0. Suppose 0 + 2/3*a**5 + 0*a + 2/3*a**4 + 0*a**h + 0*a**3 = 0. What is a?
-1, 0
What is n in 10/7*n**3 - 6/7*n**2 - 2/7*n + 6/7*n**4 - 8/7*n**5 + 0 = 0?
-1, -1/4, 0, 1
Let i = 127 + -122. Factor 14/5*c**2 + 2/5*c**i + 0 + 2*c**4 + 18/5*c**3 + 4/5*c.
2*c*(c + 1)**3*(c + 2)/5
Let 0*u**2 + 1/6*u**5 + 1/6*u**3 + 0*u - 1/3*u**4 + 0 = 0. What is u?
0, 1
Let k(a) be the second derivative of 5*a**7/6 - 5*a**6/6 - 9*a**5/4 + 25*a**4/12 + 5*a**3/3 - 6*a. Let k(b) = 0. Calculate b.
-1, -2/7, 0, 1
Let j(w) be the second derivative of 2*w**7/21 - 3*w**5/5 + 2*w**4/3 - 19*w. What is i in j(i) = 0?
-2, 0, 1
Let f(o) be the second derivative of 1/189*o**7 - o + 1/135*o**6 + 0*o**5 + 0*o**4 + 0*o**3 + 0*o**2 + 0. Factor f(p).
2*p**4*(p + 1)/9
Suppose -3*g - 143 = 4*w + 78, 2*g - 10 = 0. Let d = -175/3 - w. Let 0*a + 4/3*a**2 + 0 - d*a**3 = 0. What is a?
0, 2
Suppose -3 = p - 2*p. Let y be (-1 - 0/p)*-3. Determine j, given that 3 + 0 + 2*j**2 - 2*j**3 - 2 + 3*j - j**5 - y*j**4 = 0.
-1, 1
Let s(c) be the second derivative of -c**8/30240 + c**6/1080 - c**5/270 + c**4/6 + 3*c. Let g(b) be the third derivative of s(b). Solve g(i) = 0 for i.
-2, 1
Suppose 0 = 27*g - 21*g - 12. Let w(t) be the second derivative of 0 + 0*t**g - 1/30*t**4 + 1/75*t**6 + 2*t + 0*t**5 + 0*t**3. Factor w(x).
2*x**2*(x - 1)*(x + 1)/5
Suppose u**2 - 2*u**4 + 2*u**4 + u**4 - 2*u**4 = 0. What is u?
-1, 0, 1
Let m(i) = i**2 + 4*i. Let u be m(-5). Suppose -u*r = z + 2 - 7, -r - z - 3 = 0. Find k, given that -2*k**3 + 3*k**r - 3*k**2 - k**2 = 0.
-1/2, 0
Let t(r) be the first derivative of 0*r**2 - 1/360*r**6 + 0*r**5 + 0*r + 0*r**4 - 2 + 4/3*r**3. Let i(j) be the third derivative of t(j). Factor i(s).
-s**2
Let w(s) be the second derivative of -s**7/315 + s**6/90 - s**4/18 + s**3/9 - s**2 + 4*s. Let n(f) be the first derivative of w(f). Factor n(y).
-2*(y - 1)**3*(y + 1)/3
Let g(i) be the third derivative of -i**6/16 + 7*i**5/40 + i**4/2 - i**3 + 18*i**2. Let g(n) = 0. Calculate n.
-1, 2/5, 2
What is n in 0*n**4 + 2/7*n + 0*n**2 - 4/7*n**3 + 0 + 2/7*n**5 = 0?
-1, 0, 1
Suppose z - c = 1, 2*z = -17*c + 20*c - 1. Determine m, given that 0*m + 4*m**2 + 52/3*m**3 + 0 + 61/3*m**z + 5*m**5 = 0.
-3, -2/3, -2/5, 0
Let m = 1077/5 - 215. What is g in m*g**3 + 0*g**2 - 2/5*g + 0 = 0?
-1, 0, 1
Let a(z) be the first derivative of -1/2*z**2 - 2/3*z**3 + 4 + 2/5*z**5 + 0*z**4 + 1/6*z**6 + 0*z. Factor a(j).
j*(j - 1)*(j + 1)**3
Let a(v) = -13*v**4 - 10*v**3 + 13*v**2 + 10*v + 4. Let f(c) = -c**4 - c**3 + c**2 + c + 1. Let t(x) = -a(x) + 4*f(x). Let t(y) = 0. Calculate y.
-1, -2/3, 0, 1
What is z in 16/15*z**2 + 0 + 2/5*z**3 + 8/15*z = 0?
-2, -2/3, 0
Let c(s) be the third derivative of -s**7/1785 + s**6/255 - s**5/102 + s**4/102 + 10*s**2. Factor c(h).
-2*h*(h - 2)*(h - 1)**2/17
Let m(z) be the third derivative of -z**6/180 + z**5/45 + z**4/36 - 2*z**3/9 + 5*z**2. Let m(v) = 0. Calculate v.
-1, 1, 2
Let w(a) be the second derivative of -25*a**4/72 + 3*a**3/4 - a**2/6 - 33*a. Factor w(u).
-(u - 1)*(25*u - 2)/6
Let q(o) = -o - 4. Let u be q(-7). Suppose -n + 16 = 4*z + 3*n, 2 = -u*z + 4*n. Find f, given that f**4 + 3*f**2 - f + f**3 - f**z - 3*f**2 = 0.
-1, 0, 1
Suppose 4 = -4*h - u, h - 6*h + 4*u = -16. Solve -6*o**5 + 10*o**3 + h*o**5 + 4*o**4 - 4*o**2 - 3*o**5 - o**5 = 0 for o.
-1, 0, 2/5, 1
Let u(p) = p**2 + 5*p - 12. Let i be u(-7). Suppose 6 + 6*z**4 - 6*z**i + 12*z**3 - 9*z - 6*z**4 - 3*z**5 = 0. Calculate z.
-2, -1, 1
Let y(s) be the second derivative of 0*s**2 - 1/24*s**3 - 1/24*s**4 + 0 - 5*s - 1/80*s**5. What is i in y(i) = 0?
-1, 0
Let d(g) be the first derivative of g**5/20 - g**4/6 + g**3/6 - 4*g + 3. Let o(w) be the first derivative of d(w). Suppose o(i) = 0. Calculate i.
0, 1
Let f(l) = 3*l + 1. Let r(c) = -c. Let g(o) = f(o) + 5*r(o). Let z be g(-1). Suppose -y**3 + 0*y**3 - 3*y - 6*