
Let c(h) be the third derivative of 1/100*h**6 + 8/15*h**3 + 0 + 7/75*h**5 + 1/3*h**4 + 0*h - 2*h**2. Factor c(m).
2*(m + 2)**2*(3*m + 2)/5
Factor 2*y**3 + 2*y**2 + 4*y**5 - y + 0*y - y**4 - 1 - 5*y**5.
-(y - 1)**2*(y + 1)**3
Let z be ((-3)/1)/((-1)/1). Suppose y = -z*y. Factor 0 - 2/3*u**5 + 2/3*u**3 + 0*u + 0*u**4 + y*u**2.
-2*u**3*(u - 1)*(u + 1)/3
Let c = -26/7 - -144/35. Factor 4/5 - 2/5*r - c*r**2.
-2*(r - 1)*(r + 2)/5
Let p(j) be the first derivative of -1/6*j**4 - 1/3*j**2 + 1 + 0*j + 4/9*j**3. Suppose p(k) = 0. Calculate k.
0, 1
Suppose -4*j + 5 = -3. Suppose 0 = -j*n + k + 14, -28 = -5*n + n - 5*k. Suppose -n*s**2 - 13*s**3 + 5*s**2 - 6*s**2 - 5*s**4 - s**2 + 2 + s = 0. What is s?
-1, 2/5
Let f(c) = c. Let p be f(4). Let m be (-3)/(-6)*p/6. Factor -1/3*u**3 - 1/3 + m*u + 1/3*u**2.
-(u - 1)**2*(u + 1)/3
Let p(o) = -3*o**3 + 6*o**2 - 4. Let a(i) = 2*i**3 - 5*i**2 + 3. Let q be ((-9)/(-6))/(1/2). Let k(y) = q*p(y) + 4*a(y). Determine v so that k(v) = 0.
-2, 0
Let f be -5*(0 - 2/10). Factor -2 + f + u**2 - u + u**2.
(u - 1)*(2*u + 1)
Let l = 20 - 8. Suppose 3*m - 2*x - 6 = 0, 5*x - 3 - l = 0. Solve 1/6*b**m - 1/2*b**3 - 1/6*b + 1/2*b**2 + 0 = 0.
0, 1
Factor 1/2*x + 1/2*x**2 + 1/8*x**3 + 0.
x*(x + 2)**2/8
Find i such that 2/9*i**4 - 2/3*i**5 + 10/9*i**3 - 2/9*i**2 - 4/9*i + 0 = 0.
-1, -2/3, 0, 1
Let n(k) be the third derivative of -k**8/840 + k**6/100 - k**5/75 - 8*k**2. Let n(o) = 0. What is o?
-2, 0, 1
Let g be (-3)/(-12) - (-85)/(-4). Let z = g - -23. Let -1/2*w**4 - z*w**3 + 0 - 2*w**2 + 0*w = 0. Calculate w.
-2, 0
Suppose x + 0*x - 5 = 0. Determine k, given that 4 - 4 + 2*k**3 - 2*k**x + 2*k**4 - 2*k**2 = 0.
-1, 0, 1
Determine y, given that 0*y - 2/13*y**2 - 2/13*y**3 + 2/13*y**5 + 0 + 2/13*y**4 = 0.
-1, 0, 1
Suppose 0 = -3*b + 1 + 11, 5*n - 24 = -b. Suppose 0 = n*x - 3*x - 2. What is f in f - 2 - 2*f**3 + 0*f**2 + f + x*f**2 = 0?
-1, 1
Let f(l) be the first derivative of 0*l**2 - 4 + 1/3*l**3 - l. Find w, given that f(w) = 0.
-1, 1
Let b(q) = 3*q**3 - 5*q**2 + 2*q + 4. Let y(n) = -5*n - 5*n**3 - 9 - n**3 + 0 + 0 + 10*n**2. Let i(k) = -9*b(k) - 4*y(k). Suppose i(g) = 0. Calculate g.
-1/3, 0, 2
Let s(b) = 1. Let h(c) = -c**2 + 3. Let o(x) = -h(x) + 3*s(x). Let v(k) = -5*k**2. Let p(l) = 6*o(l) + v(l). Let p(w) = 0. Calculate w.
0
Let n = 120/31 - 104/155. Factor 2*p**2 + 2/5*p**3 + n*p + 8/5.
2*(p + 1)*(p + 2)**2/5
Let o(r) be the third derivative of -r**8/1008 + r**7/210 - r**5/45 - 5*r**2. What is x in o(x) = 0?
-1, 0, 2
Let y(o) be the second derivative of -o**8/2688 + o**7/1680 + o**6/720 - o**4/12 - 2*o. Let s(f) be the third derivative of y(f). Let s(p) = 0. Calculate p.
-2/5, 0, 1
Factor 8/7*p - 2/7*p**2 - 6/7.
-2*(p - 3)*(p - 1)/7
Let j be 28/7 - (0 + 2). Let x(b) be the first derivative of 0*b + 1/2*b**6 - 1/5*b**5 + 1/3*b**3 + 2 + 0*b**j - 3/4*b**4. Factor x(w).
w**2*(w - 1)*(w + 1)*(3*w - 1)
Let f = 27 + -24. Factor 3*a**2 + 0*a**2 - 3*a**f + 3*a**5 - 3*a**4 - 8*a + 8*a.
3*a**2*(a - 1)**2*(a + 1)
Let p(u) be the first derivative of u**4/16 - u**3/6 + u**2/8 + 3*u - 1. Let s(h) be the first derivative of p(h). Factor s(b).
(b - 1)*(3*b - 1)/4
Solve -1/4*w**2 + 0 + 0*w = 0.
0
Suppose -3*l + 3*r = 30 + 48, 2*r = -8. Let q be ((-1)/(-21))/((-5)/l). Factor 6/7*y**2 + q + 2/7*y**3 + 6/7*y.
2*(y + 1)**3/7
Let c be 4 - (196/60 + 6/15). What is a in 0*a**2 + 1/3*a + 0 - c*a**3 = 0?
-1, 0, 1
Let r(l) be the second derivative of -1/14*l**7 - 3*l + 0*l**2 - l**4 - 1/2*l**3 + 0 - 9/10*l**5 - 2/5*l**6. Factor r(z).
-3*z*(z + 1)**4
Let o(q) be the first derivative of -q**5/25 + q**3/15 + 11. Find h, given that o(h) = 0.
-1, 0, 1
Let o(n) be the first derivative of -n**6/120 + n**4/24 - 3*n**2/2 - 2. Let d(g) be the second derivative of o(g). Determine m so that d(m) = 0.
-1, 0, 1
Let w(d) = -15*d**4 - 2*d**3 + 19*d**2 + 15*d + 9. Let s(n) = -7*n**4 - n**3 + 9*n**2 + 7*n + 4. Let k(p) = -13*s(p) + 6*w(p). Factor k(o).
(o - 1)**2*(o + 1)*(o + 2)
Let p(i) = 3*i**3 - 3*i**2 - 6*i + 6. Suppose 2 = h - 4. Let q(r) = 5*r**3 - 6*r**2 - 11*r + 11. Let c(a) = h*q(a) - 11*p(a). Solve c(t) = 0.
-1, 0
Determine y so that 1/6*y**3 - 1/6*y**2 + 0 + 1/2*y**5 + 5/6*y**4 + 0*y = 0.
-1, 0, 1/3
Find x, given that -150*x**3 + 100*x**2 + 97*x**4 + 45*x**4 - 58*x**4 - 4 - 28*x**3 - 2*x = 0.
-1/6, 2/7, 1
Suppose -o - 1 - 4 = 3*m, 5*o - m = -9. Let h = o + 5. Suppose -a**3 + 4*a**2 + a**3 - 2*a - 2*a**h = 0. What is a?
0, 1
Let l(w) be the third derivative of -1/72*w**4 + 1/360*w**6 + 0 + 0*w**5 - 5*w**2 + 0*w**3 + 0*w. Let l(a) = 0. What is a?
-1, 0, 1
Let r(q) be the third derivative of q**8/1008 - q**7/210 + q**6/120 - q**5/180 + 8*q**2. Find w such that r(w) = 0.
0, 1
Suppose -q + 4*q = 0. Suppose -3*u = -q*u - 9. What is y in -15*y**2 + 0 - 2*y**u - y**4 + 15*y**2 + 1 + 2*y = 0?
-1, 1
Let k(u) be the second derivative of 0*u**2 + 0 + 0*u**4 + 0*u**3 + 2/15*u**6 - 1/5*u**5 - 4*u. Solve k(p) = 0 for p.
0, 1
Suppose -16 = -11*o + 7*o. Let t(i) be the first derivative of 1/24*i**6 + 0*i**o + 0*i**3 + 0*i - 1/20*i**5 - 1 + 0*i**2. Factor t(b).
b**4*(b - 1)/4
Let z(v) be the second derivative of 0 - 1/10*v**5 + v - v**2 + 1/3*v**3 + 1/6*v**4. Let z(f) = 0. Calculate f.
-1, 1
Suppose -5*m + 18 = 4*f, -6*m + 3*m - 2 = -4*f. Let w(z) be the first derivative of 0*z**m - 1/3*z**3 + z + 1. Determine r so that w(r) = 0.
-1, 1
Let p(c) be the second derivative of -c**4/12 + 2*c**2 + 5*c - 2. Let p(q) = 0. What is q?
-2, 2
Suppose -2*r - 4*f + 36 = 0, 0*f + 12 = 2*r - 2*f. Let d be (-48)/(-15) + (-2)/r. Determine z so that 3*z - d*z**2 + 0 + z**3 + 0*z**2 - 1 = 0.
1
Let d(g) be the first derivative of -4/3*g**2 - 8 + 0*g - 1/6*g**4 - 8/9*g**3. Factor d(y).
-2*y*(y + 2)**2/3
Let o(b) be the second derivative of b**5/10 + b**4/24 + 3*b. Factor o(z).
z**2*(4*z + 1)/2
Let z(h) be the first derivative of -h**6/3 + 4*h**5/5 - h**4/2 + 3. Factor z(f).
-2*f**3*(f - 1)**2
Let f(k) be the first derivative of -2*k**5/11 + 17*k**4/22 - 14*k**3/11 + k**2 - 4*k/11 + 10. Factor f(q).
-2*(q - 1)**3*(5*q - 2)/11
Let z(f) = -5*f**5 - 9*f**4 + f**3 + 6*f**2 + 7*f - 3. Let p(q) = -6*q**5 - 10*q**4 + 2*q**3 + 6*q**2 + 8*q - 4. Let s(k) = 3*p(k) - 4*z(k). Factor s(b).
2*b*(b - 1)*(b + 1)**2*(b + 2)
Let s be 426/315 - 4/10. Let w = s - 2/7. Factor -w - 2*y**2 + 2/3*y**3 + 2*y.
2*(y - 1)**3/3
Let k - 4*k**2 + 4*k**3 - 2*k - 5*k + 4 + 2*k = 0. What is k?
-1, 1
Let p(j) be the first derivative of j**6/27 + 4*j**5/45 - j**4/18 - 4*j**3/27 + 3. Solve p(c) = 0 for c.
-2, -1, 0, 1
Let a(s) = -2*s**4 + 5*s**3 + 3*s**2 + s - 1. Let h(j) = j**4 - 4*j**3 - 2*j**2 + 1. Let t(x) = 2*a(x) + 3*h(x). Factor t(i).
-(i - 1)*(i + 1)**3
Let u(j) be the third derivative of j**6/180 + j**5/27 + j**4/108 - 2*j**3/9 - 4*j**2. Determine a, given that u(a) = 0.
-3, -1, 2/3
Suppose -10 = -4*b + 14. Determine c, given that -2*c**2 + 10*c + 0 - b*c**2 - 2 = 0.
1/4, 1
Let v(x) be the second derivative of -x + 1/42*x**7 + 0 + 0*x**2 + 1/10*x**6 + 13/80*x**5 + 1/24*x**3 + 1/8*x**4. Solve v(d) = 0 for d.
-1, -1/2, 0
Let g(h) be the first derivative of 7 + 0*h + h**3 - 1/2*h**4 - 3/5*h**5 + h**2. Factor g(u).
-u*(u - 1)*(u + 1)*(3*u + 2)
Let p(g) = -20*g**5 - 6*g**4 + 6*g**3 - 8*g**2 + 14*g - 14. Let m(z) = -7*z**5 - 2*z**4 + 2*z**3 - 3*z**2 + 5*z - 5. Let v(l) = 14*m(l) - 5*p(l). Factor v(o).
2*o**2*(o - 1)*(o + 1)**2
Let -1/6*t**2 - 1/6*t + 1 = 0. Calculate t.
-3, 2
Let q(y) be the first derivative of -5*y**6/2 - 9*y**5/5 + 3*y**4/2 + 6. Factor q(j).
-3*j**3*(j + 1)*(5*j - 2)
Suppose 3*v - 10 = -4. Determine z, given that -1 + z**2 + 3*z**v + z**2 - z - 3*z**2 = 0.
-1/2, 1
Find b, given that b - 2 + 2 + 16*b**2 - 20*b**2 = 0.
0, 1/4
Suppose -c + 3 = 0, 3*p - 3*c + 39 = -0*p. Let v be (-2)/p + 1/45. Suppose 8/9*u**4 + 8/9*u**2 - 4/3*u**3 - 2/9*u + 0 - v*u**5 = 0. What is u?
0, 1
Let u(x) be the second derivative of 1/40*x**5 - 2*x + 0*x**2 + 0*x**3 + 1/24*x**4 + 0. Find t such that u(t) = 0.
-1, 0
Factor -1/2 - g**2 + 1/4*g**3 + 5/4*g.
(g - 2)*(g - 1)**2/4
Let u(z) = -z**2 - z + 1. Let x(c) = 2*c**2 + 5*c - 3. Let s(f) = 6*u(f) + 2*x(f). Solve s(o) = 0 for o.
0, 2
Let o be -6 + 8/2 + 6. Let f(n) be the second derivative of -1/25*n**5 + 0*n**2 + 1/75*n**6 + 3*n + 0 - 1/30*n**o + 2/15*n**3. Factor f(p).
2*p*(p - 2)*(p - 1)*