5 - 9*q**4/7 - 72*q**3/7 + 3*q**2. What is l in d(l) = 0?
-6
Let i be 12/(-8)*10/(-3). Determine y so that 4*y**3 + i*y**2 - 13*y**2 + 4*y**2 = 0.
0, 1
Let d be 52/84 + 4/(-7). Let k(i) be the second derivative of 5/42*i**4 + 3*i + 0 + 1/35*i**6 + d*i**3 + 0*i**2 + 1/10*i**5. Factor k(v).
2*v*(v + 1)**2*(3*v + 1)/7
Let t(l) be the second derivative of -l**5/30 - 7*l**4/18 - 8*l**3/9 + 16*l**2/3 + 37*l. Factor t(u).
-2*(u - 1)*(u + 4)**2/3
Suppose 2*j - 14 = 3*g, 3*j - 20 = -j + 2*g. Let t(s) be the third derivative of 1/240*s**5 + 1/24*s**3 - 1/48*s**j + 0 + s**2 + 0*s. Let t(m) = 0. Calculate m.
1
Let c(u) be the first derivative of -3/4*u**4 - 2*u**3 - 3/2*u**2 - 5 + 0*u. Suppose c(r) = 0. What is r?
-1, 0
Let v be ((-4)/(-7))/((-12)/(-42)). Let i be v - -1*4/(-3). Factor -i*s**2 + 2/3 + 2/3*s**3 - 2/3*s.
2*(s - 1)**2*(s + 1)/3
Suppose -t + 4 = t. Let v = t + 1. Let 2*y**2 - 3*y + 4*y**3 - y**4 - 2*y**4 - 2*y**v + 1 + y**5 = 0. What is y?
-1, 1
Let g be 60/16 - (-3 + (-11)/(-4)). Let y(d) be the second derivative of 0 + 1/15*d**6 + 0*d**3 - 2*d + 1/18*d**g + 1/10*d**5 + 0*d**2 + 1/63*d**7. Factor y(l).
2*l**2*(l + 1)**3/3
Let s(x) be the third derivative of 0 + 1/120*x**5 + 0*x + 0*x**3 - 1/420*x**7 + 0*x**6 - 1/1344*x**8 + 1/96*x**4 + 2*x**2. Solve s(w) = 0 for w.
-1, 0, 1
Factor 256/7*t**2 + 0 + 2*t**4 - 64/7*t - 116/7*t**3.
2*t*(t - 4)**2*(7*t - 2)/7
Let p = -111 - -225/2. Suppose 0*z + 3/2*z**2 - p = 0. What is z?
-1, 1
Let y(b) = -198*b**2 + 45. Let g(v) = 9*v**2 - 2. Let u(d) = 45*g(d) + 2*y(d). Let t(q) = -8*q**2 + q + 1. Let h(f) = -3*t(f) - 2*u(f). Solve h(p) = 0 for p.
-1/2, 1
Let i(z) be the second derivative of z**10/6048 - z**9/2160 + z**8/3360 + z**4/4 + 4*z. Let c(f) be the third derivative of i(f). Factor c(r).
r**3*(r - 1)*(5*r - 2)
Suppose -5*c + 3 = -22. Let u(b) be the first derivative of -2 - 2/9*b + 0*b**3 + 1/9*b**4 - 2/9*b**2 + 2/45*b**c. Factor u(f).
2*(f - 1)*(f + 1)**3/9
Let m = 2 - 0. Let s be ((-40)/(-250))/(m/10). Factor s*b + 2/5*b**4 - 4/5*b**3 + 0*b**2 - 2/5.
2*(b - 1)**3*(b + 1)/5
Let z be 2 - (-2)/6*1*0. Let -1/4*n - 1/4*n**5 - 1/4*n**4 + 1/2*n**3 - 1/4 + 1/2*n**z = 0. What is n?
-1, 1
Factor 0 - 15/2*w + 3/2*w**2.
3*w*(w - 5)/2
Solve -7/9*i**4 - 4/3*i**3 + 2/9*i - 1/3*i**2 + 0 = 0 for i.
-1, 0, 2/7
Suppose 4*a = d + 18, d + 3*a - 9 = 8. Factor 4*r**3 - r**3 - r**3 + r**3 + r**4 + r + 3*r**d.
r*(r + 1)**3
Let c(m) = -m**3 + 5*m**2 + 4*m. Let d(s) = 6*s**3 - 26*s**2 - 21*s. Let o(z) = 11*c(z) + 2*d(z). Factor o(q).
q*(q + 1)*(q + 2)
Factor 4*w**2 + 0*w**2 + 6*w**2 - 8*w - 6*w**2.
4*w*(w - 2)
Let r(x) be the second derivative of -x**4/12 + x**3/18 + x**2/3 - 9*x. What is m in r(m) = 0?
-2/3, 1
Suppose 3*w = -15, -4*w - 15 = -m + 2*m. Factor 6*v + 16*v**2 - m*v - 2*v**3 - 17*v**2 + v**3 + v**4.
v*(v - 1)**2*(v + 1)
Let l(n) = n + 10. Let a be l(-7). Let j be -2 + ((-15)/(-2))/a. Factor v**3 - 3/2*v - j - v**2 + 1/2*v**5 + 3/2*v**4.
(v - 1)*(v + 1)**4/2
Let f(q) be the second derivative of 1/80*q**5 + 0 + 1/48*q**4 - 1/24*q**3 + 0*q**2 + 4*q - 1/120*q**6. Factor f(z).
-z*(z - 1)**2*(z + 1)/4
Let z(j) be the first derivative of -j**5/40 + j**4/4 - j**3 + 2*j**2 - 10*j + 5. Let u(o) be the first derivative of z(o). Find p, given that u(p) = 0.
2
Let t be (8/(-50))/(8/(-40)). Factor 2/5 - t*k + 2/5*k**2.
2*(k - 1)**2/5
Let q(m) be the second derivative of m**5/10 + 2*m**4/3 + m**3 + 3*m**2 + 3*m. Let l(c) = c**2 + c + 1. Let z(x) = 6*l(x) - q(x). Solve z(s) = 0.
-1, 0
Suppose 3*w = d - 6 + 3, 5*d - 15 = w. Let u(g) be the first derivative of -1/2*g**2 + w*g**3 + 7/16*g**4 + 4 + 0*g + 3/20*g**5. Factor u(i).
i*(i + 1)*(i + 2)*(3*i - 2)/4
Factor 15*n**3 - 24 - 16*n**2 - 25*n - 11*n**3 + 0*n**3 - 19*n.
4*(n - 6)*(n + 1)**2
Let g = 2711695/118 + -22980. Let t = g + 2/59. Solve -3/2*m**4 + t*m**2 + 0 + 0*m - m**3 = 0 for m.
-1, 0, 1/3
Let t be -4*5/(-70)*1. Let q = -1186/7 - -170. Suppose q*z**3 - 2/7*z**4 - 2/7 + 4/7*z**2 - t*z - 2/7*z**5 = 0. What is z?
-1, 1
Suppose 5*l + 0*h + 3*h - 4 = 0, 4 = -3*l - 5*h. Let f(i) be the first derivative of 8/3*i**3 + 3 - i**4 - 6/5*i**5 + l*i**2 - 2*i. Find z such that f(z) = 0.
-1, 1/3, 1
Find c, given that -3/2 + 3/4*c - 3/4*c**3 - 3/4*c**4 + 9/4*c**2 = 0.
-2, -1, 1
Let x(a) be the first derivative of 1/6*a**4 - 2 + 0*a + 0*a**3 - 1/3*a**2. Factor x(y).
2*y*(y - 1)*(y + 1)/3
Let c(g) be the third derivative of -g**6/360 - g**5/90 + 7*g**4/72 - 2*g**3/9 + 25*g**2. Determine h, given that c(h) = 0.
-4, 1
Suppose -3*r = -u + 15, 5*u - r - 4 = 1. Suppose -4*k - k = u. Factor 1/3*f**3 + k + 0*f + 2/3*f**2.
f**2*(f + 2)/3
Let p = 56 - 56. Let a(o) be the second derivative of p - 2*o + 0*o**3 + 0*o**6 - 1/21*o**7 + 0*o**2 + 3/10*o**5 - 1/3*o**4. Let a(x) = 0. What is x?
-2, 0, 1
Let p(d) be the second derivative of 0*d**3 - 2/21*d**4 - 4/35*d**5 + 0 - 1/21*d**6 + 0*d**2 - 1/147*d**7 - d. Factor p(g).
-2*g**2*(g + 1)*(g + 2)**2/7
Suppose 30 = 4*n - 6. Let w = n - 6. Factor w*r**4 - 4*r**4 - 2*r**3 + 3*r**4 + 2*r - 2*r**2.
2*r*(r - 1)**2*(r + 1)
Let w(y) = y**2 + 3*y + 2. Let t be w(-3). Let z(g) be the third derivative of -1/18*g**4 - g**t - 1/90*g**5 + 0*g + 0 + 0*g**3. Factor z(m).
-2*m*(m + 2)/3
Let i(r) be the second derivative of r**6/30 + 3*r**5/10 + r**4/12 - 4*r**3 + 8*r**2 + 7*r. Suppose i(f) = 0. Calculate f.
-4, 1
Let h = 43 + -39. Determine p so that 2/5*p**h + 2/5*p**2 + 4/5*p**3 + 0*p + 0 = 0.
-1, 0
Let r(g) = -g**2 + 3*g. Let b(z) = -2*z. Let h(l) = -5*b(l) - 2*r(l). Determine y, given that h(y) = 0.
-2, 0
Let g be -3*(-1)/1 + -1. Let q(a) be the third derivative of 1/120*a**6 - 1/24*a**4 - 1/20*a**5 + 0*a + 1/70*a**7 + 0*a**3 + 0 - g*a**2. Solve q(u) = 0 for u.
-1, -1/3, 0, 1
Let o(d) be the second derivative of -d**7/105 + d**5/25 - d**3/15 - 3*d. Let o(s) = 0. Calculate s.
-1, 0, 1
Let o(v) = 4*v**2 - v. Let l be o(-1). Let y be ((-2)/(-4))/((-1)/(-4)). Suppose -2*u**3 + 7*u**y - u + 2*u + u**l - 7*u**2 = 0. Calculate u.
-1, 0, 1
Let u(x) be the third derivative of -x**10/50400 - x**9/20160 + x**5/20 - 2*x**2. Let d(g) be the third derivative of u(g). Factor d(i).
-3*i**3*(i + 1)
Let d(j) be the third derivative of j**6/40 + j**5/20 + 5*j**2. Determine t so that d(t) = 0.
-1, 0
Suppose -3*g - 2*r + 11 = 5, -5*r - 31 = -4*g. Let t be (-3)/g - (-40)/32. What is b in 1/4*b - 1/4*b**2 + t = 0?
-1, 2
Let j(v) = -2*v**3 + 25*v**2 - 51*v + 12. Let p be j(10). Factor k + 2/3 + 1/3*k**p.
(k + 1)*(k + 2)/3
Let p(g) be the second derivative of -g**4/42 + 2*g**3/21 - g**2/7 + 5*g. Factor p(m).
-2*(m - 1)**2/7
Let u(w) = w**2 + w. Suppose 0 = 3*y - 0*y - 9. Let d(n) = -n**2 + n + n**3 - n**2 + 4 + 0*n**y + 0. Let o(p) = -d(p) + u(p). Determine b so that o(b) = 0.
-1, 2
Factor 16/3*b - 25/3*b**3 + 4/3 + 5/3*b**2.
-(b - 1)*(5*b + 2)**2/3
Suppose 0 = 2*i + 3*m + 9, -i = 2*m + 7 - 1. Factor -2/5*v**3 + i*v**2 - 4/5 + 6/5*v.
-2*(v - 1)**2*(v + 2)/5
Let k(j) be the third derivative of 0 + 0*j + 0*j**3 + 0*j**4 - 1/525*j**7 + 1/150*j**5 + 9*j**2 + 0*j**6. Let k(h) = 0. What is h?
-1, 0, 1
Suppose 3*m - 4 = -19. Let v(q) = q**3 + 3*q**2 + 2*q - 5. Let z(u) = -1. Let d(p) = m*z(p) + v(p). Factor d(c).
c*(c + 1)*(c + 2)
Let k(m) be the second derivative of 1/6*m**3 + 0 - 1/48*m**4 - 3/8*m**2 + m. Factor k(h).
-(h - 3)*(h - 1)/4
Let p = -38 + 42. Determine k so that 2/3*k**5 - 2*k**p + 0 + 2/3*k**3 + 2*k**2 - 4/3*k = 0.
-1, 0, 1, 2
Suppose -475*j**4 + 474*j**4 + 3*j**3 + j**2 - 4*j + 0*j**3 + j**3 = 0. Calculate j.
-1, 0, 1, 4
Factor 0 + j**3 - j - 71*j**2 + 2 + 69*j**2 + 0*j**3.
(j - 2)*(j - 1)*(j + 1)
Let r(b) = -b**3 + b**2 - b - 1. Let f(z) = 21*z**3 - 33*z**2 + 39*z + 9. Let a(i) = -f(i) - 18*r(i). Factor a(h).
-3*(h - 3)*(h - 1)**2
Suppose s + 2*s - 12 = 3*v, -3*v + 18 = 3*s. Suppose 3*m - 10 = -5*b, -m - 1 - s = -3*b. Factor -t + 4*t**b + t - 1 + 3*t.
(t + 1)*(4*t - 1)
Let r(n) be the second derivative of n**4/6 - 2*n**3/3 - 3*n**2 + 4*n. Find w such that r(w) = 0.
-1, 3
Let m(n) be the third derivative of n**8/336 + n**7/35 + n**6/15 - 4*n**5/15 - 2*n**4 - 16*n**3/3 - 13*n**2. Factor m(u).
(u - 2)*(u + 2)**4
Suppose 28*a - 23*a - 15 = 0. Suppose 0 + 1/5*u + 0*u**2 - 1/5*u**a = 0. What is u?
-1, 0, 1
Let t be (-1)/5 - (-16)/30. Solve 0*p - 1/3 + t*p**2 = 0 for p.
-1, 1
Suppose -2*