15. Let o be 3/(-2)*(-4 + 2). Let -s - 8/5*t + 2/5*t**2 + 8/5*t**o = 0. Calculate t.
-1, -1/4, 1
Let p(f) be the third derivative of -f**5/15 + f**4/6 + 4*f**3/3 + 7*f**2. Suppose p(y) = 0. What is y?
-1, 2
Suppose 3 - 23 = -5*w. Solve 2*x**3 - 3*x**w - x**3 - 3*x**3 + 1 + 2*x + 2*x**4 = 0.
-1, 1
Suppose -37 = -i - 35. Factor 9/2 + 3*q + 1/2*q**i.
(q + 3)**2/2
Let l(b) = 4*b**2 - 22. Let c(s) = 4*s**2 + 2*s - 21. Let j(o) = -2*c(o) + 3*l(o). Suppose j(q) = 0. Calculate q.
-2, 3
Factor 5/4*o**2 + 0 - 1/2*o**3 + 3/4*o.
-o*(o - 3)*(2*o + 1)/4
Let s = -11 - -20. Factor 12*c**2 - 4 - 2 - s*c**3 + 3*c + 0.
-3*(c - 1)**2*(3*c + 2)
Let r(b) = b**2 - 4*b. Let d be r(3). Let u be (0/d)/(-1*2). Find j, given that -j**3 + 0*j**2 + j**2 + u*j**2 = 0.
0, 1
Let l = -10 + 13. Let d = -1 + l. Factor 0*b + 2/5*b**d + 0 + 2/5*b**3.
2*b**2*(b + 1)/5
Suppose 7*x**2 - 5*x + 3 + 0 + 2*x**2 - 7*x = 0. What is x?
1/3, 1
Let q be (-9)/(-20) + (-16 - -17). Let i = q - 6/5. Factor -3/2*n - i*n**2 - 9/4.
-(n + 3)**2/4
Let 0*a - 2/5*a**4 - 2/5*a**2 + 0 + 4/5*a**3 = 0. What is a?
0, 1
Suppose 4*k = 4*z + 7 + 21, 0 = -3*k - 5*z - 3. Solve -10*n**2 + 9*n**2 - k + 5 = 0.
-1, 1
Factor -2/3*c + 0 + c**2 - 1/3*c**3.
-c*(c - 2)*(c - 1)/3
Suppose 14/13*o**2 - 22/13*o + 10/13 - 2/13*o**3 = 0. What is o?
1, 5
Let i(x) be the first derivative of 16/25*x**5 - 3 + 0*x + 3/5*x**3 + 6/5*x**4 + 1/10*x**2. Find h such that i(h) = 0.
-1, -1/4, 0
Suppose -2*v + 16 = -3*g, -2*v + g = -7*v + 6. Factor 1/2*f**3 + 1 + 0*f**v - 3/2*f.
(f - 1)**2*(f + 2)/2
Let d(g) be the third derivative of g**5/6 - 5*g**4/24 - 5*g**3/6 - 13*g**2. Determine w, given that d(w) = 0.
-1/2, 1
Let j = 110629/30 - 3687. Let b = j - 2/15. Factor 0 + b*z**2 + 1/2*z.
z*(z + 1)/2
Suppose -5*f - 5 = -10*f. Let n(a) = 16*a**3 + 8*a**2 - 12*a + 6. Let s(z) = z**3 - z + 1. Let q(k) = f*n(k) - 10*s(k). Suppose q(r) = 0. Calculate r.
-1, 2/3
Let i(o) = o**2 - 3*o - 5. Let l be i(5). Suppose -h + 3*h - y - 8 = 0, 2*h = -4*y - 12. Factor h*q**4 + 2*q**l - 2 + 2 - 4*q**5.
-2*q**4*(q - 1)
Let x(q) be the third derivative of -1/240*q**5 + 2*q**2 + 1/32*q**4 + 0 - 1/12*q**3 + 0*q. Factor x(u).
-(u - 2)*(u - 1)/4
Let r(z) = 13*z**2 - 25*z + 7. Let w(p) = 6*p**2 - 12*p + 3. Let c(n) = -3*r(n) + 5*w(n). Factor c(f).
-3*(f - 1)*(3*f - 2)
Let w(r) be the second derivative of -r**6/120 + r**5/40 + r**4/16 - r**3/3 + r**2/2 + 15*r - 1. Factor w(m).
-(m - 2)*(m - 1)**2*(m + 2)/4
Suppose 2*l - 34 = -3*l - 2*z, 4*l - 16 = 4*z. Suppose -l*m + 4*m = -8. Let -4*b**2 + 19*b**3 - 2*b**m - 3 - 13*b**3 + 3 = 0. Calculate b.
0, 1, 2
Suppose -3*w - m + 5 = 0, 6*m + 8 = 2*w + 2*m. Let q(t) be the first derivative of -1/2*t**4 + 1 - 2*t**3 - 2*t - 3*t**w. Find b such that q(b) = 0.
-1
Suppose -5*j + 30 - 5 = 0. Let v = -1 + 5. Factor 3*n**2 - j*n - 2*n**v - 3*n**3 + 4*n + 3*n**4.
n*(n - 1)**3
Let g(x) be the first derivative of x**5/5 + x**4/2 + 2*x**3/3 - x + 4. Let r(u) = -3*u**4 - 6*u**3 - 7*u**2 - u + 3. Let b(i) = -21*g(i) - 6*r(i). Factor b(m).
-3*(m - 1)*(m + 1)**3
Let f be 8 + (-45)/(-25) + -7. Factor f*o**2 + 0 - 18/5*o**3 - 2/5*o**5 - 4/5*o + 2*o**4.
-2*o*(o - 2)*(o - 1)**3/5
Suppose 2*m + 5*c - 18 = 0, -5*c = -2 - 8. Suppose 0 - 2/3*r**m + 0*r - 2/3*r**2 - 4/3*r**3 = 0. What is r?
-1, 0
Let m be ((-22)/6)/(2/6). Let o = -7 - m. Factor -q - 2*q**o + 0*q - q**5 + 2*q**2 + 2*q**5.
q*(q - 1)**3*(q + 1)
Let c(f) be the third derivative of -1/96*f**4 + 0*f + 1/12*f**3 - 2*f**2 + 0 - 1/240*f**5. Determine t so that c(t) = 0.
-2, 1
Suppose -3*w + 8 = -w. Suppose -2*z + 12 = -0*z + 3*f, 0 = w*z - 2*f + 8. Solve -1/3*d**2 + 2/3*d + d**5 + z + 1/3*d**4 - 5/3*d**3 = 0.
-1, 0, 2/3, 1
Let v = 1111/930 + -36/31. Let m(c) be the third derivative of 0*c**3 - 1/12*c**4 + 0 - v*c**5 + 0*c + c**2. Factor m(p).
-2*p*(p + 1)
Let z(r) be the first derivative of 1/9*r**2 + 1/18*r**4 + 0*r + 3 - 4/27*r**3. Factor z(q).
2*q*(q - 1)**2/9
Let z(v) = -v**2 - 5*v + 9. Let r be z(-6). Let d(q) be the second derivative of 1/30*q**4 + 0 - 4/15*q**r + 4/5*q**2 + 2*q. Factor d(s).
2*(s - 2)**2/5
Let j be (-6)/10*(-18)/54. Factor -3/5*b**2 + 2/5*b + j*b**3 + 0.
b*(b - 2)*(b - 1)/5
Let m = 14 - 14. Solve 5*b**2 - 5*b**2 + b**3 - b + m*b = 0.
-1, 0, 1
Let a(m) be the second derivative of m**7/3780 + m**6/810 + m**5/540 - 2*m**3/3 - 5*m. Let k(v) be the second derivative of a(v). Factor k(p).
2*p*(p + 1)**2/9
Let d be 8 + -1 + 4/(-4). Let a(x) = -2*x**2 + 3*x**2 - x**3 - 6*x**3. Let h(v) = -8*v**3 + v**2. Let z(c) = d*h(c) - 7*a(c). Factor z(n).
n**2*(n - 1)
Let a be 456/96 + 3/(-4). Let -4/7*p**2 - 2/7*p**a + 0*p + 0 + 6/7*p**3 = 0. What is p?
0, 1, 2
Let p = 9/7 + 3/14. Solve p*w**2 - 1 - 1/2*w**4 - 1/2*w**3 + 1/2*w = 0.
-2, -1, 1
Let p(q) be the first derivative of -3*q**5/10 + q**4/6 - 4*q - 1. Let m(t) be the first derivative of p(t). Factor m(o).
-2*o**2*(3*o - 1)
Let j(r) = -63*r**2 - 27*r + 9. Suppose 4*p - 1 + 21 = 0. Let s(u) = 126*u**2 + 53*u - 19. Let v(n) = p*j(n) - 3*s(n). Find g such that v(g) = 0.
-2/3, 2/7
Solve 0 - 1/4*z**5 - 3/2*z**3 + 1/2*z**2 + 0*z + 9/8*z**4 = 0 for z.
0, 1/2, 2
Factor -4*v**4 - 24*v**2 - 2 + 17*v**3 + 2*v**4 - 2*v**4 + 13*v.
-(v - 2)*(v - 1)**2*(4*v - 1)
Suppose -2/9*u**2 - 4/9 + 2/3*u = 0. Calculate u.
1, 2
Let q(b) = 3*b - 3. Let l be q(5). Suppose 10 - 9*o**3 + l*o**5 - 10 - 3*o**2 = 0. Calculate o.
-1/2, 0, 1
Let n be (14/(-147))/((12/(-14))/2). Suppose 0*y + 0 + 0*y**2 - n*y**3 + 2/9*y**4 = 0. Calculate y.
0, 1
Let a(b) be the third derivative of -5*b**8/1008 + b**7/63 - b**5/18 + 5*b**4/72 - 2*b**2 + 14*b. Find m, given that a(m) = 0.
-1, 0, 1
Factor -4/9 - 2*w - 10/3*w**2 - 22/9*w**3 - 2/3*w**4.
-2*(w + 1)**3*(3*w + 2)/9
Suppose w - 6 = -2*o, 0 = 4*w - 5*w + 5*o - 8. Suppose 2*l - 3*l**w + 4*l**2 + 2 - 1 = 0. Calculate l.
-1
Suppose -4*a - 3 = 5*k - 13, 2*k + 4*a + 8 = 0. Solve -7*u**4 + 0*u**4 + 1 + k*u**2 - 3*u**5 - 6*u**3 + 5*u + 4*u**3 = 0 for u.
-1, -1/3, 1
Suppose 0 = -2*c + c. Factor c*v**3 + 0*v**2 + 2/13*v**5 + 0*v - 2/13*v**4 + 0.
2*v**4*(v - 1)/13
Let n(z) be the second derivative of -2*z - 3/100*z**5 + 2/15*z**3 + 0*z**4 - 1/150*z**6 + 0 + 0*z**2. Find g such that n(g) = 0.
-2, 0, 1
Suppose -5 + 5 + c**4 + c**4 = 0. Calculate c.
0
Let y be 138/189 - (57/(-21) + 3). Let h(z) be the first derivative of 2/27*z**3 + 1/9*z**2 - y*z + 2. What is v in h(v) = 0?
-2, 1
Let g(f) = -f. Let u = 27 + -18. Suppose -2*i - i - u = 0. Let w(k) = -2*k**2 + 3*k - 4. Let o(t) = i*g(t) + w(t). Factor o(a).
-2*(a - 2)*(a - 1)
Let n(j) = j**2. Let f(g) = 5*g**3 - 15*g**3 + 14*g**2 - 8*g + 6*g**3. Let w(u) = -f(u) + 2*n(u). Let w(h) = 0. Calculate h.
0, 1, 2
Suppose -u = -3*p, 2*u - 7 = -0*u - p. Find y such that 4/7 + 16*y**u - 10/7*y - 52/7*y**2 = 0.
-2/7, 1/4, 1/2
Let r(c) be the second derivative of c**7/168 - c**6/48 + 3*c**5/160 + c**4/96 - c**3/48 + 2*c. Factor r(g).
g*(g - 1)**3*(2*g + 1)/8
Let p = -95 + 381/4. Let t = 0 + 4. Determine j so that 0*j**2 - p*j**t + 0*j**3 + 0 + 0*j = 0.
0
Let n(o) be the second derivative of -o**8/1344 + o**7/840 + o**2 + 4*o. Let i(m) be the first derivative of n(m). Find k such that i(k) = 0.
0, 1
Let p = -12 + 14. Let 18 - 27*j**4 + 6*j**4 + 111*j**p - 14*j**3 - 2*j**3 + j**3 - 93*j = 0. What is j?
-3, 2/7, 1
Let f(j) be the first derivative of -j**2 - 8*j + 2. Let o be f(-6). Factor u**2 + 2*u + 5*u**2 + 0*u - o*u**2.
2*u*(u + 1)
Solve 1 - 7/2*v - 2*v**2 = 0.
-2, 1/4
Let o(t) be the third derivative of -t**8/23520 - t**7/8820 + t**6/2520 + t**5/420 + 5*t**4/24 - 2*t**2. Let p(h) be the second derivative of o(h). Factor p(n).
-2*(n - 1)*(n + 1)**2/7
Let n(i) be the second derivative of -i**6/420 + i**4/84 + 3*i**2/2 + 5*i. Let m(z) be the first derivative of n(z). Factor m(l).
-2*l*(l - 1)*(l + 1)/7
Suppose -3*v - 25 = 5*n, 0 = v - n + 6*n + 25. Factor v + 0*b + 0*b**2 + 3/4*b**4 + 3/2*b**3 - 3/4*b**5.
-3*b**3*(b - 2)*(b + 1)/4
Let f(h) be the third derivative of -h**6/30 - h**5/6 - h**4/3 - h**3/3 - 21*h**2. Suppose f(q) = 0. What is q?
-1, -1/2
Factor 2*j + 15*j**3 + 5*j**4 - 5*j**2 - 10*j + 2*j - 9*j.
5*j*(j - 1)*(j + 1)*(j + 3)
Let u(a) = 11*a**2 - a**3 + a**3 - 9 - a**3 + 13*a. Let m be u(12). Factor -44 + m*o + 3*o**2 + 44.
3*o*(o + 1)
Let 45*f**2 - 5*f**3 - 33*f - 52*f + 135 - 50*f = 0. What is 