
0, 1
Let z(p) = 6*p**5 - p**4 - 8*p**3 + 2*p + 1. Let w(t) = -13*t**5 + 3*t**4 + 16*t**3 - t**2 - 3*t - 2. Let c(i) = 6*w(i) + 15*z(i). Find q, given that c(q) = 0.
-1, -1/4, 1
Let g(m) be the second derivative of -m**4/24 - m**3/4 - m**2/2 - 3*m. Suppose g(o) = 0. Calculate o.
-2, -1
Suppose -8 = -2*k - 4*p, k + k = -3*p + 8. Let x(y) = 2 + y**2 - 6*y + y + k*y. Let z(o) = -o**2 + o - 3. Let q(m) = 6*x(m) + 4*z(m). Factor q(r).
2*r*(r - 1)
Let c(h) be the first derivative of -25/4*h**4 + 1 + h - 11/2*h**2 + 35/3*h**3. Solve c(x) = 0 for x.
1/5, 1
Let g = -123 - -126. Factor -3/4*c**2 - 1/2 + 5/4*c - 1/4*c**g + 1/4*c**4.
(c - 1)**3*(c + 2)/4
Let -15/7*y - 3/7*y**3 + 12/7*y**2 + 6/7 = 0. What is y?
1, 2
Let t be -5 + 2 + (-404)/(-12). Let h = t + -30. Determine z so that 2/9*z + 0 - h*z**4 + 2/3*z**2 - 2/9*z**3 = 0.
-1, -1/3, 0, 1
Let f(r) be the third derivative of -5*r**8/12096 + r**6/540 - r**5/15 - r**2. Let a(k) be the third derivative of f(k). Determine z, given that a(z) = 0.
-2/5, 2/5
Let h(x) = 13*x - 78. Let c be h(6). Let 0*d**3 + 2/3*d + 4/3*d**4 - 4/3*d**2 + c - 2/3*d**5 = 0. Calculate d.
-1, 0, 1
Suppose 0 = -0*k + 2*k - 10. Let -v**5 + 0*v**k + 5*v**3 - 4*v**3 = 0. Calculate v.
-1, 0, 1
Let b(x) be the first derivative of 0*x**2 - 3 - 3*x + 1/6*x**3 - 1/6*x**4 + 3/80*x**5. Let f(g) be the first derivative of b(g). Factor f(s).
s*(s - 2)*(3*s - 2)/4
Let k be -1*3 + 833/(-840) + 4. Let c(l) be the third derivative of -k*l**5 + 0 + 1/24*l**3 - l**2 + 1/840*l**7 + 0*l**6 + 0*l**4 + 0*l. Factor c(y).
(y - 1)**2*(y + 1)**2/4
Let s be 1*(4 - (-1 + 2)). Determine t, given that 3/2*t + 1/2*t**5 + 0*t**4 - 1 + t**2 - 2*t**s = 0.
-2, -1, 1
Let w(q) = 2*q + 2. Let o be w(3). Suppose -o = -4*f + 4*s, -4*f + 5*s + 7 = -1. Factor m**2 + f*m**2 - m**3 - 1 - 3*m + 2.
-(m - 1)**3
Suppose 2*g = 5*g - 15. Suppose 3*p**3 - g*p**3 - 2*p**2 + p**4 + p + p**5 + 1 + 0*p**5 + 0*p**3 = 0. What is p?
-1, 1
Let z(t) be the third derivative of t**5/20 + 3*t**4/8 - 7*t**3/6 - 8*t**2. Let j(s) = 4*s - 1 + s**2 - 1 - 1. Let n(m) = -10*j(m) + 4*z(m). Factor n(l).
2*(l - 1)**2
Suppose 0*p - 3 = -p. Let j(m) be the second derivative of -1/3*m**3 + 0 + 1/6*m**4 + p*m + 0*m**2. Factor j(x).
2*x*(x - 1)
Factor s**2 - 1/3*s - 2/3.
(s - 1)*(3*s + 2)/3
Let j(w) = w**2 + 16*w - 15. Let o be j(-14). Let h = o + 131/3. Let h*z + 1/3*z**2 + 0 = 0. Calculate z.
-2, 0
Let g(r) be the second derivative of -3/20*r**5 + 1/10*r**6 + 0*r**2 + 1/12*r**4 + 2*r + 0*r**3 + 0 - 1/42*r**7. Solve g(n) = 0.
0, 1
Let b = 11 + -8. Let j(h) = h**2 - 3*h - 5. Let l be j(5). Factor -t**2 - 3*t**2 - 16*t**4 + 24*t**4 - 4 + 8*t**b - 10*t + 2*t**l.
2*(t - 1)*(t + 1)**3*(t + 2)
Let s(k) = k**2. Let m(l) = -4*l**2. Let t be (2 - -3)/(3/15). Suppose -u + 2*c + 12 = 3*u, u = -5*c + t. Let y(a) = u*s(a) + m(a). Let y(q) = 0. Calculate q.
0
Let k(x) be the third derivative of x**5/4 - 3*x**4/4 - 4*x**3 - 9*x**2. Let d(p) = 7*p**2 - 9*p - 12. Let v(o) = -9*d(o) + 4*k(o). Factor v(j).
-3*(j - 4)*(j + 1)
Let k be (-22)/6 - (-32)/(3 + 5). Factor k*v**2 + 0 - 1/3*v**4 - 2/3*v**3 + 2/3*v.
-v*(v - 1)*(v + 1)*(v + 2)/3
Factor -75*n**5 + 245*n - 15*n**4 + 48*n**3 - 245*n - 12*n**2.
-3*n**2*(n + 1)*(5*n - 2)**2
Let w(l) be the second derivative of -l**10/45360 - l**9/11340 + l**7/1890 + l**6/1080 + l**4/3 + 2*l. Let f(c) be the third derivative of w(c). Factor f(d).
-2*d*(d - 1)*(d + 1)**3/3
Let x be 9/(-27) - (-10)/3. Factor -2*h**2 + 2 - 26*h**x - 2 + 25*h**3.
-h**2*(h + 2)
Let s(k) = k**2 - 8*k - 9. Let l be s(9). Suppose -3*p + 2*j = -8, l = 2*p + 2*j - j - 3. Factor -a**4 - a**5 + a**3 - a**p - 6*a**2 + 8*a**2.
-a**2*(a - 1)*(a + 1)**2
Factor 0 - 16/5*o + 4/5*o**2.
4*o*(o - 4)/5
Let i(y) be the first derivative of y**5/15 + y**4/6 - y**3/3 - 2*y**2/3 + 4*y/3 - 8. Factor i(p).
(p - 1)**2*(p + 2)**2/3
Let h(b) be the third derivative of 0*b + 0*b**3 - 7*b**2 + 0*b**5 + 1/56*b**4 + 0 - 1/280*b**6. What is r in h(r) = 0?
-1, 0, 1
Let a(w) be the first derivative of w**2 - 3 + 0*w**5 + 1/3*w**6 - w**4 + 0*w + 0*w**3. Factor a(i).
2*i*(i - 1)**2*(i + 1)**2
Determine x, given that 5*x**2 + 100*x + 24 + 6*x**2 + 89*x**2 = 0.
-3/5, -2/5
Factor 217*b**3 - 109*b**3 - 105*b**3 + 6*b**2.
3*b**2*(b + 2)
Find v such that -6 - 11*v - v**2 + 38*v - 22*v = 0.
2, 3
Let f(x) be the third derivative of 0 + 1/90*x**5 + 0*x**3 + 1/945*x**7 - 1/180*x**6 + 0*x + 2*x**2 - 1/108*x**4. Suppose f(u) = 0. What is u?
0, 1
Let f(u) be the first derivative of u**4/6 + 2*u**3/3 + u**2 + 2*u/3 - 4. Find p, given that f(p) = 0.
-1
Let k be 6 + 29/10*-2. Find p, given that 0 - 2/5*p - 1/5*p**2 + k*p**4 + 2/5*p**3 = 0.
-2, -1, 0, 1
Let u be 0/(0 - 3) + 0. Let x(t) be the third derivative of 1/36*t**4 - 1/18*t**3 + u + 0*t - 1/180*t**5 - 2*t**2. Suppose x(w) = 0. Calculate w.
1
Let u(s) be the first derivative of 5 + 4/25*s**5 - 1/10*s**2 + 0*s + 4/15*s**3 - 1/30*s**6 - 3/10*s**4. Factor u(p).
-p*(p - 1)**4/5
Let f(q) be the second derivative of -5*q**4/12 - 25*q**3/6 - 15*q**2 - 13*q. Determine y, given that f(y) = 0.
-3, -2
Let c(y) = -11*y**5 - 9*y**4 + 26*y**3 + 80*y**2 - 6*y - 80. Let b(a) = -a**5 + a**4 + a**3 - a. Let t(j) = 6*b(j) - c(j). Factor t(p).
5*(p - 2)*(p - 1)*(p + 2)**3
Let l(b) = 4*b - 1. Let y be l(1). Let z = -11 - -7. Let v(t) = 6*t**3 + 2*t**2 + 2*t. Let d(k) = 7*k**3 + k**2 + 2*k. Let o(s) = y*d(s) + z*v(s). Factor o(u).
-u*(u + 1)*(3*u + 2)
What is s in 20/3*s - 2*s**2 + 16/3 = 0?
-2/3, 4
Let b = 32 + -215/7. Determine q so that -6/7*q + 1/7*q**2 + b = 0.
3
Suppose -q + 3*a = 0, 0 = -5*q + 3*q - 2*a + 8. Suppose -q*x = -7 + 1. Let 2/3*o - 1/3 - 1/3*o**x = 0. Calculate o.
1
Let d be -1 + ((-8)/(4 + -6) - 0). What is p in 9/2*p + 1/2 + 9/2*p**5 + 15*p**2 + 33/2*p**4 + 23*p**d = 0?
-1, -1/3
Let m(t) be the third derivative of -1/70*t**7 + 1/4*t**4 + 0 + 0*t - 1/20*t**6 + t**2 + 1/2*t**3 + 0*t**5. Determine k so that m(k) = 0.
-1, 1
Let y(g) = -6*g**3 - 16*g**2 - 22*g - 20. Let v(l) = 2*l**3 + 5*l**2 + 7*l + 7. Let o(u) = -8*v(u) - 3*y(u). Solve o(c) = 0.
-2, -1
Suppose -2*u + 12 - 2 = 0. What is p in 3*p**2 + 3*p - 3*p**3 + u*p**3 - 5*p**3 + 25*p**4 - 28*p**4 = 0?
-1, 0, 1
Let g be (-2 + 0 + 0 + 1)*0. Let d(z) be the third derivative of 0 + 0*z + 1/12*z**4 + 0*z**3 - 1/60*z**6 + z**2 + g*z**5. Find r such that d(r) = 0.
-1, 0, 1
Suppose 2*y + 76 = 3*u, 2*y + 3*u + 18 + 46 = 0. Let m = y + 247/7. Determine s so that -6/7*s**2 + 8/7*s**4 - m + 8/7*s - 8/7*s**3 = 0.
-1, 1/2, 1
Let n be 50/15 - 4/(-6). Suppose 0 = -2*s + n. Factor y**3 - 12 + 3*y**4 - 2*y**s + 12.
y**2*(y + 1)*(3*y - 2)
Let j(a) = -6*a**2 - 6*a + 2. Let o(r) = -r**2 + r + 1. Let k(v) = -j(v) + 2*o(v). Determine f so that k(f) = 0.
-2, 0
Let s(p) be the third derivative of -p**8/1680 - p**7/525 + p**6/200 + p**5/75 - p**4/30 - 4*p**2. Determine r so that s(r) = 0.
-2, 0, 1
Let g(d) be the third derivative of d**7/1050 + d**6/600 - d**5/100 - d**4/24 - d**3/15 + 4*d**2. Determine x, given that g(x) = 0.
-1, 2
Let q(h) be the first derivative of -h**8/504 + h**6/90 - h**4/36 - 3*h**2/2 - 3. Let u(l) be the second derivative of q(l). Factor u(w).
-2*w*(w - 1)**2*(w + 1)**2/3
Let q(r) be the first derivative of 0*r**2 - 1/12*r**3 + r + 4 + 1/8*r**4 + 1/60*r**6 - 3/40*r**5. Let f(n) be the first derivative of q(n). Factor f(m).
m*(m - 1)**3/2
Let i(l) = 5*l**2 - 9*l + 4. Let t(m) = 14*m**2 - 26*m + 11. Let f(c) = 17*i(c) - 6*t(c). Suppose f(r) = 0. What is r?
-2, -1
Let q(l) = 3*l**3 - 2*l**2 - 2*l + 3. Let h be q(2). Suppose n - 5*n + 12 = -x, -5*n = -h. Factor 0*m**2 - 2/5*m + x + 2/5*m**3.
2*m*(m - 1)*(m + 1)/5
Let w(f) be the first derivative of 2 + 0*f**4 + 0*f + 0*f**3 + 0*f**2 - 6/5*f**5 - 3/2*f**6. Suppose w(d) = 0. What is d?
-2/3, 0
Let q(g) be the second derivative of g**4/60 - g**3/30 + 3*g. Let q(v) = 0. What is v?
0, 1
Let x be (-10)/50 + (-2366)/(-30). Let p = x - 78. Factor -4/3*k - p*k**2 - 2/3.
-2*(k + 1)**2/3
Suppose -2 = 4*g - 10, 5*i + g = 32. Let l(m) be the third derivative of 0*m + 0*m**3 + 0*m**4 + 1/360*m**i - m**2 + 0 + 1/180*m**5. Factor l(h).
h**2*(h + 1)/3
Let c(p) be the first derivative of -2*p**6/3 - 12. Let c(x) = 0. What is x?
0
Let b(y) be the first derivative of 2*y**4 + 2*y**3/3 - 4*y**2 - 2*y + 9. Determine p so that b(p) =