t b(a) = -a**3 - 5*a**2 - 4*a. Let w be b(-4). Suppose -13*l = -4*l - 18. Let 1/2*h**3 + w*h**l - 1/4*h**4 - 1/2*h + 1/4 = 0. What is h?
-1, 1
Let v(x) = -4*x**3 - 4*x**2. Suppose 4*b = -0*b + 4*n + 44, 19 = 3*b + 4*n. Let d(y) = -17*y**3 - 17*y**2. Let q(c) = b*v(c) - 2*d(c). Factor q(j).
-2*j**2*(j + 1)
Let r(t) be the first derivative of 3/10*t**2 + 0*t + 1 - 1/5*t**3 + 3/25*t**5 - 3/20*t**4. Solve r(h) = 0 for h.
-1, 0, 1
Let b = 9 - 5. Let t = 0 + b. Factor -4*k**2 + k**2 - 2*k**4 - t*k**3 + k**2.
-2*k**2*(k + 1)**2
Suppose -9 = 4*b - 21. Let d = -1 + b. Let -2*r**3 + 2*r + 9*r**3 - 10*r**d + r**3 = 0. What is r?
0, 1/4, 1
Let u = -4 - -6. Suppose 2*w**5 + w**5 + 4*w**4 + w**4 + 0*w**3 + u*w**3 = 0. Calculate w.
-1, -2/3, 0
Let g(z) be the third derivative of 0*z**5 + 0*z**4 + 0*z - 1/180*z**6 - z**2 + 0 + 0*z**3. What is y in g(y) = 0?
0
Let w(m) be the first derivative of m**5 + m**4/2 - 5*m**3/3 - m**2 - 19. Factor w(t).
t*(t - 1)*(t + 1)*(5*t + 2)
Let h = 8422/7 + -1202. Find b such that -2/7*b + 8/7*b**4 - 2/7*b**5 + 0 - 12/7*b**3 + h*b**2 = 0.
0, 1
Let o(j) be the third derivative of j**5/60 - j**4/12 + 3*j**2. Let w be o(3). Suppose -3*g + g - g**3 - 4*g**w - 7*g**2 = 0. Calculate g.
-1, -2/5, 0
Let p(l) be the third derivative of l**6/420 - l**5/105 - l**4/21 + 8*l**3/21 + 30*l**2. Factor p(h).
2*(h - 2)**2*(h + 2)/7
Suppose -4 = 10*z - 4. Determine r, given that -1/4*r**2 - 1/4*r**3 + 0*r + z = 0.
-1, 0
Let a = -121/60 - -13/5. Let b = a + -1/12. Factor -y - 1/2 - b*y**2.
-(y + 1)**2/2
Suppose 17 = 2*j + 9. Factor -2*u**4 + 4*u**3 - 4*u**5 - 3*u**4 + 2*u**4 + 4*u**2 - u**j.
-4*u**2*(u - 1)*(u + 1)**2
Let x = 53 - 105/2. Factor -x*p**2 - 2*p - 2.
-(p + 2)**2/2
Let s(c) = c + 7. Let u be s(-3). Factor 21*g**2 - 3 + 15*g**2 + 24*g + u*g**3 + 7 + 12*g**3.
4*(g + 1)**2*(4*g + 1)
Let t = -4 - -6. Determine l so that -l**4 - 3*l + 3*l + 4*l**4 + t*l**3 = 0.
-2/3, 0
Let d = 9 - 9. Let i(o) be the second derivative of 2/5*o**6 + 1/6*o**7 + 0*o**2 - 1/6*o**4 + o + 0*o**3 + d + 3/20*o**5. Factor i(z).
z**2*(z + 1)**2*(7*z - 2)
Let t(y) be the first derivative of -1/14*y**2 + 0*y + 5 - 1/21*y**3. Determine a, given that t(a) = 0.
-1, 0
Let w(p) = 4*p**3 - 5*p**2 + 4*p + 25. Let y(c) = -c**3 + 2*c**2 - c - 8. Let b(u) = 2*w(u) + 7*y(u). Let b(k) = 0. What is k?
-3, -2, 1
Suppose 4 = a + 2. Factor 0 - 3*g**5 - 2*g**3 + 6*g**4 + 8*g**3 - 6 - 24*g**a + 21*g.
-3*(g - 1)**4*(g + 2)
Let k = -20 + 40. Let o = 29 - k. Find j, given that -5*j - 4*j**4 + 11*j**3 + 1 + 5*j - o*j**2 + j = 0.
-1/4, 1
Let n = 0 + 4. Suppose n*o + o = 10. Factor -1/3*g - 1/3*g**3 - 2/3*g**o + 0.
-g*(g + 1)**2/3
Let g be -14*(-2)/(3 + -1). Let x = -10 + g. Factor 4*b - b - x*b - b**2.
-b*(b + 1)
Let q(u) be the second derivative of 25*u**9/12096 - 3*u**8/448 + u**7/140 - u**6/360 - u**3/6 - 3*u. Let f(w) be the second derivative of q(w). Factor f(a).
a**2*(a - 1)*(5*a - 2)**2/4
Let c(u) = -u**2 - 6*u + 3. Let p(k) = -7*k**2 + 1. Let n be p(1). Let q be c(n). Solve 0*d + 0 + 2/3*d**q + 0*d**2 = 0.
0
Let m(d) be the third derivative of d**8/840 - d**6/180 - 5*d**3/3 - 2*d**2. Let f(o) be the first derivative of m(o). Suppose f(v) = 0. What is v?
-1, 0, 1
Let z be 6/6 - (-2 - 0). Let y be (-10)/60 - (-1)/z. Let 1/6*s**3 - 1/6*s**2 + y - 1/6*s = 0. Calculate s.
-1, 1
Suppose 22 = s - 5*m, 0*s - 5*m = -3*s + 26. Find u such that 0*u**2 - 3 + 15*u + 35 + u + 2*u**s = 0.
-4
Factor 10 - 9*m**2 + 59*m + 5*m**3 - 6*m + 29*m**2 - 28*m.
5*(m + 1)**2*(m + 2)
Let p be 2*((-2)/14)/(-1). Let i = -38/7 - -6. Suppose -i*z - p*z**2 - 2/7 = 0. What is z?
-1
Let j(w) be the first derivative of -2*w**3/15 + w**2/5 + 4*w/5 + 13. Suppose j(a) = 0. Calculate a.
-1, 2
Factor 1/3*x - 1/3*x**3 - 1/3*x**4 - 2/3 + x**2.
-(x - 1)**2*(x + 1)*(x + 2)/3
Let r = -109 - -111. What is m in 2/3*m + 2/3*m**5 - 8/3*m**r + 4/3*m**4 + 4/3 - 4/3*m**3 = 0?
-2, -1, 1
Suppose 40*d + 8*d - 3*d**4 - 49*d**2 - d**4 - 3*d**2 + 24*d**3 - 16 = 0. What is d?
1, 2
Let a(z) = 3*z**3 - 7*z**2 + 9*z. Let m(j) be the first derivative of 5*j**4/2 - 22*j**3/3 + 14*j**2 - 2. Let i(h) = 16*a(h) - 5*m(h). Factor i(o).
-2*o*(o - 1)*(o + 2)
Suppose -4/3*x**2 + 2/9*x**4 - 2/3 - 16/9*x + 0*x**3 = 0. Calculate x.
-1, 3
Let w(a) = 11*a**3 - 15*a**2 + 9*a - 1. Let h be (-2)/(3/3) + -2. Let j(f) = 5*f**3 - 7*f**2 + 4*f. Let z(d) = h*w(d) + 9*j(d). Factor z(g).
(g - 2)**2*(g + 1)
Let f(o) be the third derivative of -3*o**2 + 11/120*o**6 - 3/70*o**7 + 0*o**4 + 0 + 0*o - 1/30*o**5 + 0*o**3. Factor f(y).
-y**2*(y - 1)*(9*y - 2)
Let y be 11/((-231)/(-6)) + 20/77. Find l, given that 0 - 4/11*l - 2/11*l**4 + 0*l**3 + y*l**2 = 0.
-2, 0, 1
Find p, given that -77*p**2 - 2*p**3 + 6*p**3 + 73*p**2 = 0.
0, 1
Let t(r) be the second derivative of -r**4/21 + 2*r**3/21 + r - 10. Suppose t(z) = 0. Calculate z.
0, 1
Let j(b) be the third derivative of -b**6/60 - b**5/10 + 4*b**3/3 - 29*b**2. Factor j(n).
-2*(n - 1)*(n + 2)**2
What is c in 1/3*c**5 + 1/3*c**2 + 4/3 + 7/3*c**3 - 8/3*c - 5/3*c**4 = 0?
-1, 1, 2
Let z(d) be the first derivative of d**9/5292 + d**8/1960 - d**6/1260 + d**3 - 4. Let m(o) be the third derivative of z(o). Let m(x) = 0. Calculate x.
-1, 0, 1/2
Factor 2/9*w**2 + 2/9*w**3 + 0*w + 0.
2*w**2*(w + 1)/9
Let c = -15 - -20. Determine x, given that 4*x + 2*x**4 + 2*x**c + 2*x - 2*x - 2*x**2 - 6*x**3 = 0.
-2, -1, 0, 1
Let d(h) = 5*h**3 - 3*h + 4. Let a be 2 - (2 - 3)*2. Let i(l) = -6*l**3 + 2*l - 4. Let p(y) = a*d(y) + 3*i(y). Factor p(g).
2*(g - 1)**2*(g + 2)
Factor 50 + 12*h + 5*h + 3*h + 2*h**2.
2*(h + 5)**2
Suppose 0 = -3*a - 11 + 2. Let l = a - -6. Find r, given that -r - 1 - l*r**2 + 5*r**2 + 0*r = 0.
-1/2, 1
Determine d so that 14/3*d**2 + 0*d - 2*d**4 - 2/3*d**3 - 8/3 + 2/3*d**5 = 0.
-1, 1, 2
Let j be (-4)/(-18) - (-4)/(-18). Find i such that 0*i - 2 + j*i + 0*i + 2*i**2 = 0.
-1, 1
Determine s so that 564*s + 0 + 3185*s**3 + 937*s**2 - 164*s + 1128*s**2 + 20 = 0.
-2/7, -1/13
Let k(j) be the first derivative of j**4/4 + j**3/3 - 5*j**2/2 + 3*j + 43. Let k(q) = 0. Calculate q.
-3, 1
Find g, given that 122/7*g**3 - 50/7*g**5 + 16/7 + 44/7*g**2 - 60/7*g**4 - 72/7*g = 0.
-2, -1, 2/5, 1
Let c(h) be the second derivative of h**6/480 - h**4/96 + 2*h**2 + h. Let x(o) be the first derivative of c(o). Suppose x(f) = 0. What is f?
-1, 0, 1
Let j(v) be the second derivative of -1/12*v**4 - 1/2*v**2 - 1/3*v**3 + 0 + 3*v. Factor j(k).
-(k + 1)**2
Find w, given that 7/11*w**3 + 4/11 + 20/11*w + 23/11*w**2 = 0.
-2, -1, -2/7
Let u(c) = c**5 - c**2 + c. Let x = 5 + -4. Let y(v) = v**4 + 2*v**3 - 3*v**2 + 1. Let z(j) = x*y(j) - u(j). Let z(d) = 0. Calculate d.
-1, 1
Let j(d) be the third derivative of d**8/84 + 2*d**7/35 + d**6/15 - 2*d**5/15 - d**4/2 - 2*d**3/3 - 22*d**2. Determine h, given that j(h) = 0.
-1, 1
Suppose -8*p + 10*p - 4 = 0. Let k = p - 1. Factor 3/2*m + k + 1/2*m**2.
(m + 1)*(m + 2)/2
Suppose 2*l = -2*l - 20, -5*a + 40 = -l. Suppose 4*q + 8 = 0, 3*i + 2*q = q + a. Let -y - 4*y**3 + 0*y + i*y**3 + 2*y**2 = 0. What is y?
0, 1
Let o be (-5)/(-2)*(36/20 + -1). Find w such that -10/3*w**o - 2/3*w - 4/3*w**3 + 4/3 = 0.
-2, -1, 1/2
Let f(w) be the third derivative of w**5/90 + 4*w**4/9 + 12*w**2. Let f(n) = 0. Calculate n.
-16, 0
Let h(l) be the third derivative of -l**8/2016 + l**7/315 - l**6/144 + l**5/180 + 8*l**2. Factor h(s).
-s**2*(s - 2)*(s - 1)**2/6
Let g(v) be the third derivative of v**6/90 - v**4/18 - 9*v**2. Factor g(k).
4*k*(k - 1)*(k + 1)/3
Let b(f) be the first derivative of -2 + 7/2*f**2 - 5/3*f**3 - 2*f. Factor b(t).
-(t - 1)*(5*t - 2)
Let o(x) = -x**2 + x + 1. Let a(k) = 7*k**2 - k - 4. Let n be 16/(-6)*(-6)/4. Let d(r) = n*o(r) + a(r). Determine q so that d(q) = 0.
-1, 0
Find u, given that -8*u**2 + 13 + 4 - u - 4*u**3 - 9 + 5*u = 0.
-2, -1, 1
Factor -4/9*o - 2/9 - 2/9*o**2.
-2*(o + 1)**2/9
Let n(l) be the second derivative of l**6/25 + l**5/50 - l**4/18 + l**3/45 + 7*l. Solve n(p) = 0.
-1, 0, 1/3
Let r be (-8)/(-32)*4 + 1. Solve 0 + 1/5*m**r - 3/5*m = 0 for m.
0, 3
Let k be (-6)/10*10/(-14). Factor 3/7*n**2 + k*n + 0.
3*n*(n + 1)/7
Suppose s - 1 = 0, 2*q - 4*s - 2 = -q. Let f(y) be the third derivative of 0*y - 1/18*y**3 + 0*y**4 + 1/180*y**5 + 0 + y**q. Let f(p) = 0. What is p?
-1, 1
Let i(m) be the first derivative of -2 - 1/