b**4 + 1/6*b**3 + 1/20*b**5. Suppose t(k) = 0. What is k?
-2, -1, 0
Suppose 2*m - 5*d + 16 = -10*d, 4*d + 14 = -m. Suppose 1 = x - 2. Factor 13*r**x - 12*r**3 + m*r - 2*r.
r**3
Let n(h) = h**3 + 13*h + 2. Let y(s) = -s**3 - 25*s - 5. Let m be -3 - (-7 - 0/1). Let l(w) = m*y(w) + 7*n(w). Let l(i) = 0. What is i?
-1, 2
Let a(d) be the third derivative of -2*d**6/15 + d**5/5 - d**4/8 + d**3/24 + 3*d**2. Factor a(x).
-(4*x - 1)**3/4
Let p(t) be the first derivative of -3/5*t**5 + 1/2*t**6 - 3/2*t**4 - 3*t + 3/2*t**2 - 3 + 2*t**3. Factor p(x).
3*(x - 1)**3*(x + 1)**2
Let l(s) be the second derivative of 8*s**7/105 + 2*s**6/15 - 3*s**5/25 - s**4/3 - 2*s**3/15 + 10*s. Suppose l(w) = 0. What is w?
-1, -1/4, 0, 1
Let o(l) be the second derivative of -3/10*l**5 + 0 + 2*l - 2/7*l**7 + 7/10*l**6 + 0*l**2 + 0*l**3 - 1/4*l**4. Factor o(k).
-3*k**2*(k - 1)**2*(4*k + 1)
Let k(o) be the second derivative of 1/3*o**3 + 1/30*o**6 + 0*o**2 - 1/10*o**5 + 0 + 8*o - 1/12*o**4. Find b such that k(b) = 0.
-1, 0, 1, 2
Factor -3*t**4 + 3*t**3 + 297*t - 297*t.
-3*t**3*(t - 1)
Let h be 3/(-4) + 1/12*33. Let t(s) be the second derivative of 1/84*s**7 + 0*s**5 - 1/30*s**6 + 2*s - 1/12*s**3 + 0*s**h + 0 + 1/12*s**4. Factor t(p).
p*(p - 1)**3*(p + 1)/2
Let n be (-20)/42*(-4)/20. Let h(f) be the first derivative of -2/7*f + 1/7*f**2 + n*f**3 - 2 - 1/14*f**4. Solve h(o) = 0 for o.
-1, 1
Let a(l) be the second derivative of l**9/3024 - l**8/840 + l**6/180 - l**5/120 - l**3/2 + l. Let y(j) be the second derivative of a(j). Solve y(f) = 0.
-1, 0, 1
Let s be ((-2)/(-5))/(72/3510). Solve 3/2*k + 33/2*k**4 + 15*k**5 + 3 - s*k**2 - 33/2*k**3 = 0.
-1, -1/2, 2/5, 1
Let f**4 + 1/2 - 3/2*f**2 + f**3 - 3/4*f**5 - 1/4*f = 0. What is f?
-1, -2/3, 1
Let i = -77 - -77. Let z(r) be the first derivative of 1 - 2/9*r**3 + 1/3*r**2 + i*r. Factor z(d).
-2*d*(d - 1)/3
Suppose -4*q = -2*n - 16, q + 2*n = -0*q + 4. Factor -2 - q*t + 2 + 0 - 3 - t**2.
-(t + 1)*(t + 3)
Let q(s) be the third derivative of s**8/1344 + s**7/840 - s**6/160 - s**5/48 - s**4/48 + 22*s**2. Suppose q(j) = 0. What is j?
-1, 0, 2
Let u(a) be the first derivative of -3*a**4/2 + 9*a**3 - 11. Factor u(t).
-3*t**2*(2*t - 9)
Suppose -2*w + 2*q = 0, 0*w = 4*w - 2*q. Determine z so that 0 + w*z - 3/4*z**2 = 0.
0
Let b = 150 + -741/5. Let j = b - 17/15. Determine x, given that j*x**2 + 2/3*x - 4/3 = 0.
-2, 1
Let v(u) be the first derivative of u**3/21 + u**2/7 - 2. Factor v(p).
p*(p + 2)/7
Factor 23*l + 0 - 22*l - 4*l**2 + 0*l**3 + 4 - l**3.
-(l - 1)*(l + 1)*(l + 4)
Let s(g) be the second derivative of -g**5/140 - g**4/42 + g**3/42 + g**2/7 - 11*g. Factor s(f).
-(f - 1)*(f + 1)*(f + 2)/7
Let i be 4/(-14) - 224/(-441). Let m = i - -23/18. Factor 1/2*g - 1/2*g**4 + m*g**3 - 3/2*g**2 + 0.
-g*(g - 1)**3/2
Let h(q) be the third derivative of 1/108*q**4 + 0*q + 4*q**2 + 0 - 1/540*q**6 + 1/27*q**3 - 1/270*q**5. Suppose h(d) = 0. What is d?
-1, 1
Let w(j) = -11*j**2 - 11*j + 10. Let b(g) = -45*g**2 - 45*g + 40. Let q(a) = 6*b(a) - 25*w(a). Suppose q(c) = 0. Calculate c.
-2, 1
Let z(a) = a**3 + 3*a**2 - 6*a - 18. Let p be z(-3). Determine h, given that 1/7*h**2 - 1/7*h**4 + p*h + 0 + 0*h**3 = 0.
-1, 0, 1
Let r(t) = -t**3 - 6*t**2 + 6*t + 5. Let y be r(-7). Factor -6*l**2 + 3*l**2 + y*l**3 + 6*l**2.
3*l**2*(4*l + 1)
Let o = 49/6 - 23/3. Suppose 0 + 3/2*z**4 + o*z - 3/2*z**2 - 1/2*z**3 = 0. Calculate z.
-1, 0, 1/3, 1
Let m(z) be the third derivative of z**5/60 + z**4/12 + z**3/6 + 10*z**2. Find r, given that m(r) = 0.
-1
Let f(m) be the first derivative of -m**4/16 - 5*m**3/12 - 29. Determine x, given that f(x) = 0.
-5, 0
Let a(q) = -q**2 + 5*q. Let w be a(5). Suppose w = -2*i - c - 5, -2*i + 0*i + c = -5. Determine o so that -o**4 + i + 1/2*o**5 + o**2 - 1/2*o + 0*o**3 = 0.
-1, 0, 1
Let s(b) = -b**2 + 8*b - 6. Let k be s(5). Let y be (-2)/(-9) - (-25)/k. What is c in 4*c**5 + c**4 - c**2 - 3*c**y - c**5 + 0*c**2 = 0?
-1, -1/3, 0, 1
Let i(t) be the first derivative of t**5/55 - t**4/44 + 13. Suppose i(y) = 0. Calculate y.
0, 1
Let q = 1 - -2. Let s be (1/q)/((-2)/(-6)). Factor -3*d**2 - 6*d - s + 1 + 6*d**2.
3*d*(d - 2)
Suppose -1/6*p**2 - 1/6*p + 0 + 1/6*p**3 + 1/6*p**4 = 0. What is p?
-1, 0, 1
Factor -3*h**2 - 658 + 3*h + 661 - 3*h.
-3*(h - 1)*(h + 1)
Suppose -6*s + 3 - 15*s**2 + 9*s**3 - 1 - 2 = 0. Calculate s.
-1/3, 0, 2
Suppose 6/7*a**4 + 4/7*a**5 + 0 + 0*a**2 + 2/7*a**3 + 0*a = 0. Calculate a.
-1, -1/2, 0
Let j(r) = 2*r**2. Let m be j(-1). Factor 8 + h**2 - 6*h**2 + 4*h + h**m.
-4*(h - 2)*(h + 1)
Let m be (-4)/(-14)*(-53)/(-6). Let n = m + -13/7. Suppose 0*g**4 - 8/9*g**3 + 4/9*g**2 - 4/9 + 2/9*g**5 + n*g = 0. What is g?
-2, -1, 1
Suppose 2*l = 3*z + 16 - 15, -12 = -4*z. Factor -5/4*u + 1/4 + 5/2*u**2 - 1/4*u**l + 5/4*u**4 - 5/2*u**3.
-(u - 1)**5/4
Let h(v) = 2*v**5 - 4*v**4 - 3*v + 3. Let z(d) = d**5 - d**4 - d + 1. Let u(s) = -h(s) + 3*z(s). Factor u(q).
q**4*(q + 1)
Let d = -7 + 31. Suppose 0 = 2*b - 4*b + 64. Solve -23*g**2 + 77*g**4 + 49*g**5 - b*g - d*g**3 + 7*g**3 - 50*g**2 - 4 = 0.
-1, -2/7, 1
Factor 1/4*n - 1/4*n**3 - 1/4*n**4 + 1/4*n**2 + 0.
-n*(n - 1)*(n + 1)**2/4
Let y(n) be the third derivative of -n**7/630 + n**6/180 - n**4/36 + n**3/18 - 4*n**2. What is g in y(g) = 0?
-1, 1
Let h = -6 + 11. Suppose 2*l = -1 + h. Factor 9*j**4 - j**2 - 2*j + 4*j**2 + 3*j**5 + l*j + 9*j**3.
3*j**2*(j + 1)**3
Let o be (-2)/(-3) - 0/(-1). Let r(l) be the first derivative of 1/6*l**4 - 2/3*l - o*l**3 + 2 + l**2. Factor r(i).
2*(i - 1)**3/3
Let c = -15 - -19. Factor 9*b**5 - 14*b**5 - 2*b**c + 6*b**5 - 3*b**3 + 4*b**3.
b**3*(b - 1)**2
Let r(c) = c**2 + 7*c - 8. Let d be 9/(-1) - (-1 - 0). Let x be r(d). Suppose 0*o**4 + 0*o**2 - 1/5*o - 1/5*o**5 + x + 2/5*o**3 = 0. What is o?
-1, 0, 1
Let m(d) = -3 + 0 - d**2 - 5*d**4 - d + 4*d. Let f(g) = 131*g - 2*g**2 - 5*g**4 - 127*g - 4 - g**4. Let c(q) = -3*f(q) + 4*m(q). Let c(o) = 0. Calculate o.
-1, 0, 1
Let z be 86/10 + 40/(-8). Factor 54/5*f - 54/5 - z*f**2 + 2/5*f**3.
2*(f - 3)**3/5
Let m(y) = -y**2 - y - 1. Let z be 0 + 0 + (-20)/2. Let c(g) = 3 - 3 - 2 - 4*g + 0 - 4*g**2. Let u(k) = z*m(k) + 3*c(k). Factor u(o).
-2*(o - 1)*(o + 2)
Let v be 6/6*2/(8/12). Find w such that -13/4*w**2 + 3/2*w**3 + v*w - 1 - 1/4*w**4 = 0.
1, 2
Let b(w) be the third derivative of w**7/210 - w**6/15 + 7*w**5/60 + 8*w**2. Factor b(i).
i**2*(i - 7)*(i - 1)
Suppose 0 = -4*f + 3*v - 4, -f + 3*v = -4*f + 18. Suppose -i + 1 + 4 = 0. Factor i*h**2 - 2 - 5*h + h**3 - 9*h**f + 10*h.
(h - 2)*(h - 1)**2
Let b be (-6)/(-1) - (-21)/(-4). What is q in 3 - b*q**2 + 0*q = 0?
-2, 2
Let r(x) = 10*x**2 - 2*x - 12. Let d(y) = -y**2 + 1. Let u(z) = 12*d(z) + r(z). Factor u(a).
-2*a*(a + 1)
Let m(q) be the first derivative of -q**4/4 - 25*q**3/12 - 3*q**2/4 + 19. Solve m(a) = 0.
-6, -1/4, 0
Let u(z) be the first derivative of z**5 - 5*z**4/4 - 10*z**3/3 - 12. Solve u(j) = 0.
-1, 0, 2
Let w(r) be the third derivative of 0*r - 1/24*r**4 + 0 - 2*r**2 + 0*r**3 - 1/30*r**5 - 1/120*r**6. Factor w(u).
-u*(u + 1)**2
Let -f**2 + 0 - 1/2*f**3 - 1/2*f = 0. What is f?
-1, 0
Let n(c) = -5*c**5 - 4*c**4 - 3*c**3 + c**2 + 2*c - 3. Let r(k) = -6*k**5 - 4*k**4 - 4*k**3 + 2*k - 4. Let d(v) = -4*n(v) + 3*r(v). Find a, given that d(a) = 0.
-1, 0, 1
Let c(o) be the first derivative of 0*o + 0*o**2 + 15/4*o**4 + 8 + 12/5*o**5 + 1/2*o**6 + 2*o**3. Let c(n) = 0. Calculate n.
-2, -1, 0
Let t = -3 - -4. Let p = 3 - t. Solve -4/3*l**3 + p*l**4 - 4/3*l**2 - 2/3 + 2*l - 2/3*l**5 = 0 for l.
-1, 1
Let d(q) = -5*q**3 - 6*q**2 + 2*q. Let l(x) = -11*x**3 - 12*x**2 + 5*x. Let k(i) = -5*d(i) + 2*l(i). Factor k(b).
3*b**2*(b + 2)
What is d in 1/6*d**2 - 2/3 - 1/2*d = 0?
-1, 4
Let l(f) be the third derivative of f**8/84 + 2*f**7/105 - f**6/15 - 2*f**5/15 + f**4/6 + 2*f**3/3 + 3*f**2. Solve l(t) = 0 for t.
-1, 1
Let l(h) be the first derivative of h**5/210 + h**4/84 - 3*h**2/2 - 2. Let t(n) be the second derivative of l(n). Solve t(q) = 0.
-1, 0
Let p(s) be the second derivative of 0 - 2*s - 1/33*s**3 + 0*s**2 - 1/110*s**5 - 1/33*s**4. Suppose p(z) = 0. What is z?
-1, 0
Let n = 40 - 40. Suppose 0 = -n*k - 6*k. Factor 1/2*f + 3/2*f**2 + k.
f*(3*f + 1)/2
Factor -3/4*q**5 + 0*q + 3/2*q**3 + 0*q**2 + 0 - 3/4*q**4.
-3*q**3*(q - 1)*(q + 2)/4
Let o(c) = -11*c**3 + 11*c**2 + c - 6. Let g(q