
Let b = 73/150 - -1/75. Factor 1/2*i**3 - 1/4*i**4 + 1/4*i**2 - b*i + 0.
-i*(i - 2)*(i - 1)*(i + 1)/4
Let t(j) be the second derivative of -7*j + 1/30*j**6 - 1/12*j**4 - 1/20*j**5 + 0*j**2 + 0*j**3 + 0 + 1/42*j**7. Let t(p) = 0. What is p?
-1, 0, 1
Suppose 0 = -2*x + 88 - 82, -3*s = -5*x + 15. Suppose -1/6*f**3 + s + 0*f - 1/3*f**2 + 1/6*f**4 = 0. What is f?
-1, 0, 2
Suppose -9/4*b**4 + b**5 + 1/4 - 3/2*b + 1/2*b**3 + 2*b**2 = 0. Calculate b.
-1, 1/4, 1
Let l(w) be the third derivative of w**8/1680 - w**7/420 + w**6/360 - w**3/6 + 2*w**2. Let k(p) be the first derivative of l(p). Factor k(f).
f**2*(f - 1)**2
Find v, given that 8*v - 42*v**2 - 7*v**5 - 12*v**4 - 11*v**3 + 13*v**3 + 51*v**3 = 0.
-4, 0, 2/7, 1
Let a = -1 + 1. Let x(i) be the first derivative of -1/12*i**4 + 0*i + a*i**2 + 1/9*i**3 + 1. Determine j so that x(j) = 0.
0, 1
Let f(s) be the second derivative of s**6/30 + s**5/4 + 3*s**4/4 + 7*s**3/6 + s**2 - 7*s. Factor f(v).
(v + 1)**3*(v + 2)
Let d(x) = 3 - 10*x + 2*x**2 - 5 - 2. Let k(p) = p**2 - p. Let r(j) = d(j) - 4*k(j). What is b in r(b) = 0?
-2, -1
Let u = -19 - -20. Let j be u - 5/((-30)/(-4)). Suppose 0*z + 0 - 1/3*z**4 - j*z**3 + 0*z**2 = 0. Calculate z.
-1, 0
Let b be 5/(-18)*-3*3/5. Factor -1/2 + 1/2*j**3 + b*j**2 - 1/2*j.
(j - 1)*(j + 1)**2/2
Let h(r) be the first derivative of -r**4/14 - 2*r**3/7 - 3*r**2/7 - 2*r/7 + 18. Factor h(o).
-2*(o + 1)**3/7
Suppose -32*l = -22*l - 30. Factor 2 + t**l - 2*t - 3/2*t**2 + 1/2*t**4.
(t - 1)**2*(t + 2)**2/2
Suppose -1/3*l**3 + 0*l + 0 + 1/3*l**2 = 0. Calculate l.
0, 1
Let h be (-45)/60*(-196)/6. Let d = -24 + h. Determine a so that d + 1/2*a**2 - a = 0.
1
Let n = 2 - 4. Let w = n - -7. Find f such that 0 + 8*f**3 - f**w + 0 - 10*f**4 + 5*f**5 - 2*f**2 = 0.
0, 1/2, 1
Let i(l) be the first derivative of 5*l**5/6 + 5*l**4/24 - 8*l**3/9 + l**2/3 - 15. Let i(p) = 0. Calculate p.
-1, 0, 2/5
Factor -45/2*c**2 + 40*c + 10.
-5*(c - 2)*(9*c + 2)/2
Suppose -4*d**2 - 10/9*d**3 - 14/9*d + 4/3 = 0. What is d?
-3, -1, 2/5
Let w(k) be the first derivative of 4*k**3/9 - 4*k**2/3 + 4*k/3 + 12. Find z such that w(z) = 0.
1
Let b(r) = 3*r**2 - 12*r + 12. Let q(l) = l - 1. Let z(m) = b(m) + 12*q(m). Factor z(n).
3*n**2
Let j(c) be the first derivative of c**5/30 + c**4/27 - c**3/9 - 2*c**2/9 - 4*c - 3. Let z(p) be the first derivative of j(p). Let z(r) = 0. Calculate r.
-1, -2/3, 1
Factor -12*r**3 + 4*r**4 - 4*r**2 + 705 + 4*r**5 + 0*r - 705 + 8*r.
4*r*(r - 1)**2*(r + 1)*(r + 2)
Suppose 0 = 2*m - 0*m - 4. Suppose -4*q = -4*h - 2*q - m, -q + 1 = 5*h. Find o such that h + 2/3*o + 1/3*o**2 = 0.
-2, 0
Let l(o) be the first derivative of -o**3/3 - 3*o**2/2 - 2*o - 4. Factor l(p).
-(p + 1)*(p + 2)
Let j(n) be the second derivative of -n**4/6 + 2*n**3/3 + 13*n. Factor j(d).
-2*d*(d - 2)
Factor -2/11*i**3 + 6/11*i**2 + 0*i - 8/11.
-2*(i - 2)**2*(i + 1)/11
Let b be ((-12)/(-15))/(16/40). Let m(c) be the third derivative of 4*c**b + 0*c**3 + 0*c + 0 - 1/8*c**4 + 1/20*c**5. Suppose m(y) = 0. What is y?
0, 1
Determine m so that 2/15*m**2 + 0 + 2/5*m = 0.
-3, 0
Let c(f) = -6*f**4 + 17*f**3 - 11*f**2 - 5*f. Let d(v) = 3*v**4 - 8*v**3 + 5*v**2 + 2*v. Let u(n) = -2*c(n) - 5*d(n). Factor u(k).
-3*k**2*(k - 1)**2
Let s(x) be the third derivative of -x**8/3360 - x**7/630 - x**6/360 - x**4/24 - 3*x**2. Let w(f) be the second derivative of s(f). Factor w(r).
-2*r*(r + 1)**2
Let w(v) be the second derivative of -1/2*v**3 + 0 + 0*v**2 - 3/40*v**5 + 3/8*v**4 + 2*v. Factor w(c).
-3*c*(c - 2)*(c - 1)/2
Factor -5*q + 168 - 168 - 5*q**2.
-5*q*(q + 1)
Let o(f) be the second derivative of f**6/75 - f**5/10 + 3*f**4/10 - 7*f**3/15 + 2*f**2/5 - 8*f. Factor o(c).
2*(c - 2)*(c - 1)**3/5
Let i(a) be the third derivative of -5*a**2 + 2/21*a**4 + 0*a - 1/210*a**5 + 0 - 16/21*a**3. What is f in i(f) = 0?
4
Let l = -4 - -7. Suppose -d + 6 - 2 = 0. Solve -y**5 + 2*y**4 + y**4 - y**l - y**d = 0.
0, 1
Let f be ((-51)/34)/(2/(-4)). Let a(q) be the first derivative of -2*q + 1 + 1/2*q**4 - q**2 + 2/3*q**f. Factor a(i).
2*(i - 1)*(i + 1)**2
Let i(a) be the second derivative of 1/5*a**6 + 0 - 5*a + 0*a**2 + 1/6*a**4 + 1/21*a**7 + 3/10*a**5 + 0*a**3. Factor i(c).
2*c**2*(c + 1)**3
Factor 1/3*k**3 - 5/3*k**2 + 8/3*k - 4/3.
(k - 2)**2*(k - 1)/3
Let u(f) be the third derivative of f**5/20 - 14*f**2. Factor u(v).
3*v**2
Let n(h) = -h**5 - 7*h**4 + 4*h**3 - 5*h**2. Let w(o) = -o**5 - 8*o**4 + 5*o**3 - 6*o**2. Let a(j) = -6*n(j) + 5*w(j). Factor a(g).
g**3*(g + 1)**2
Suppose -4*y - 2 = -18. Let 25/4*g**4 - 5/4*g**3 - g + 0 - y*g**2 = 0. Calculate g.
-2/5, 0, 1
Suppose -5 = -l - 2*s, -5*l + 1 + 4 = 5*s. Let g be 0/(0 + (-3)/l). Let g + 2/3*x**2 - 2/3*x**3 + 0*x = 0. Calculate x.
0, 1
Let h(z) be the third derivative of z**10/20160 - z**9/3360 + 3*z**8/4480 - z**7/1680 + z**4/8 - 3*z**2. Let a(b) be the second derivative of h(b). Factor a(p).
3*p**2*(p - 1)**3/2
Let m(d) be the second derivative of -1/2*d**2 + 0 + 7*d - 2/3*d**4 + d**3. Factor m(o).
-(2*o - 1)*(4*o - 1)
Let q = -1002 - -5024/5. Determine d so that 0 + 8/5*d - 16/5*d**2 - q*d**4 - 38/5*d**3 = 0.
-2, -1, 0, 2/7
Suppose -2*a - 2 = -3*a + 5*q, 0 = 4*a + 3*q + 38. Let s be (a/36)/((-1)/3). Suppose 0*u**4 + s*u + 0*u**2 - 4/3*u**3 + 2/3*u**5 + 0 = 0. What is u?
-1, 0, 1
Let c be 1/(-39) + 1/3. Let u be (-17)/(-68)*(1 - 1). Factor -14/13*a**2 - c*a - 10/13*a**3 + u.
-2*a*(a + 1)*(5*a + 2)/13
Factor -2/13*p**2 + 4/13*p + 6/13.
-2*(p - 3)*(p + 1)/13
Let r = -1 - -5. Let a(w) be the third derivative of 1/60*w**r + 0 + 0*w**3 - 2*w**2 + 1/150*w**5 + 0*w. Find v such that a(v) = 0.
-1, 0
Let b(z) be the first derivative of 1/6*z**3 + 0*z**2 + 2 - 1/24*z**4 + z. Let f(g) be the first derivative of b(g). Factor f(o).
-o*(o - 2)/2
Let v(j) be the third derivative of -j**7/8820 - j**4/8 - j**2. Let z(p) be the second derivative of v(p). Factor z(s).
-2*s**2/7
Let i = 553 + -551. Factor -2/7*s**i - 2/7*s + 0 + 4/7*s**3.
2*s*(s - 1)*(2*s + 1)/7
Factor -2*w - 2/3 + 2/3*w**2 + 2*w**3.
2*(w - 1)*(w + 1)*(3*w + 1)/3
Let c(o) be the first derivative of 1 + 1/24*o**6 + 0*o**2 - 1/16*o**4 + 0*o**5 + 0*o**3 + 0*o. Factor c(x).
x**3*(x - 1)*(x + 1)/4
Let k(g) be the third derivative of g**7/1890 - g**6/540 - g**5/180 + g**4/27 - 2*g**3/27 - 23*g**2. Solve k(r) = 0.
-2, 1, 2
Let s(b) be the third derivative of b**7/840 - b**6/1440 + b**3/2 + b**2. Let z(o) be the first derivative of s(o). Factor z(d).
d**2*(4*d - 1)/4
Let p be (-2)/7 - (-30)/7. Let t = p - 2. Find k such that k**3 - 2*k**4 - k + 2*k**4 + k**t - k**4 = 0.
-1, 0, 1
Let n(g) be the third derivative of -g**9/10080 + g**8/960 - g**7/240 + g**6/120 - g**5/20 - 4*g**2. Let h(f) be the third derivative of n(f). Factor h(b).
-3*(b - 2)*(b - 1)*(2*b - 1)
Let j(f) be the third derivative of f**6/420 + f**5/210 - 9*f**2. Solve j(w) = 0 for w.
-1, 0
Suppose -10 = 3*d - 2*w, -2*w - 10 = -4*d - 4*w. Let i = 4 - d. Suppose -2*f**2 + 4*f**3 + 6*f**i - 4*f**4 - 3*f + 4*f - 5*f = 0. Calculate f.
-2, -1, 0, 1
Let g(l) be the third derivative of l**7/420 - l**6/40 + 13*l**5/120 - l**4/4 + l**3/3 + 22*l**2. Factor g(x).
(x - 2)**2*(x - 1)**2/2
Let h(x) be the second derivative of 0*x**4 + 0*x**2 + 1/70*x**5 + 3*x + 0 - 1/21*x**3. What is g in h(g) = 0?
-1, 0, 1
Let t be -5 + (2/1 - 0). Let k be (-1 - t) + -2 + 0. Find r such that 1/4*r**5 + 0*r**2 + k*r**4 + 0 - 1/2*r**3 + 1/4*r = 0.
-1, 0, 1
Let s(n) be the third derivative of 7*n**5/360 + n**4/2 + 5*n**3/9 - 34*n**2. Let s(a) = 0. What is a?
-10, -2/7
Let g(d) be the first derivative of 5*d**2 - 4*d - 2*d**3 - 3 - 1/2*d**4 + 2/5*d**5. Factor g(f).
2*(f - 1)**3*(f + 2)
Let v(r) be the first derivative of -r**6/240 + r**5/40 + r**4/48 - r**3/4 + 4*r**2 + 1. Let l(g) be the second derivative of v(g). Solve l(p) = 0 for p.
-1, 1, 3
Let j(m) be the second derivative of -1/12*m**3 + 2*m - 1/12*m**4 - 1/40*m**5 + 0 + 0*m**2. Determine g so that j(g) = 0.
-1, 0
Let n(x) be the second derivative of -x**7/6300 - x**6/600 - x**5/150 + x**4/12 + x. Let z(f) be the third derivative of n(f). Suppose z(h) = 0. Calculate h.
-2, -1
Suppose -6 = -2*w - 2. Factor 13*u**2 + 32*u - w*u**2 + 24*u**3 + 4*u**4 + 37*u**2.
4*u*(u + 2)**3
Let q = 16 + -13. Suppose q*t = -t. Solve 0*b**2 - 2/5*b + 2/5*b**3 + t = 0.
-1, 0, 1
Suppose -3*r + 2*