
Let l(x) be the first derivative of -x**5/10 + 5*x**4/8 - 3*x**3/2 + 7*x**2/4 - x - 1. Determine h, given that l(h) = 0.
1, 2
Factor 1/5*u**4 + 6/5*u**3 - 6/5*u - 1 + 4/5*u**2.
(u - 1)*(u + 1)**2*(u + 5)/5
Let h = 2/67 - -124/335. Suppose 0*z + h - 2/5*z**2 = 0. Calculate z.
-1, 1
Let i(s) = -s**3 + 2*s**2 + 3*s. Let g be i(-2). Let n be 0 + -2 + 28/g. What is o in -6/5*o**2 + 14/5*o - n - 16/5*o**3 + 8/5*o**4 = 0?
-1, 1/2, 2
Let h(f) = -2*f**2 - 6*f. Let v(j) = j**2 - j. Let p(b) = h(b) + 6*v(b). Determine n, given that p(n) = 0.
0, 3
Suppose -5*q + q + 4 = -2*n, -2*n + 2*q = 4. Let c(y) = 14*y**2 - 8*y - 4. Let t(i) = 0*i - 5*i + 4*i. Let o(u) = n*t(u) - c(u). Factor o(x).
-2*(x - 1)*(7*x + 2)
Let f(b) be the third derivative of 0*b**3 + 0*b + 0 - 1/525*b**7 - 1/300*b**6 + 0*b**4 - 9*b**2 + 1/840*b**8 + 1/150*b**5. Find o, given that f(o) = 0.
-1, 0, 1
Let k be (1 - (-30)/(-54))*2. Factor -4/3*u**2 - 8/9*u - 2/9 - k*u**3 - 2/9*u**4.
-2*(u + 1)**4/9
What is f in -3/7 - 3/7*f**5 - 6/7*f**3 + 9/7*f**4 + 9/7*f - 6/7*f**2 = 0?
-1, 1
Let i(z) be the first derivative of z**8/6720 + z**7/1120 + z**6/720 + z**3/3 + 3. Let y(d) be the third derivative of i(d). Solve y(g) = 0 for g.
-2, -1, 0
Let f(g) be the first derivative of g**3/2 + 3*g**2/2 - 34. Factor f(h).
3*h*(h + 2)/2
Let p(h) be the first derivative of 2*h**3/3 - 6*h**2 + 18*h - 2. Factor p(f).
2*(f - 3)**2
Let h(w) be the second derivative of w**4/8 + 5*w**3/4 + 9*w**2/2 - 53*w + 2. Determine g so that h(g) = 0.
-3, -2
Let c(g) = -6*g**2 - 4. Let l(z) = 7*z**2 + 5. Let f(t) = 6*c(t) + 5*l(t). Let f(n) = 0. What is n?
-1, 1
Let i be (-16)/(1 - 0/2). Let p be (i/(-12))/((-4)/(-6)). Factor 4*u - u**3 - 1 + 5*u**p - 3*u - 4*u**2.
-(u - 1)**2*(u + 1)
Let a(j) be the second derivative of -j**5/20 + 7*j**4/12 + 2*j**3/3 + 5*j**2/2 - 3*j. Let x(d) = d**2 + d + 1. Let n(m) = 3*a(m) - 15*x(m). Factor n(h).
-3*h*(h - 1)**2
Let k(q) be the first derivative of -49*q**4/8 + 7*q**3/2 + 6*q**2 + 2*q - 4. Factor k(b).
-(b - 1)*(7*b + 2)**2/2
Let a = 20/69 + 1/23. Factor a*s**2 + 0 + 1/3*s.
s*(s + 1)/3
Let v(y) be the second derivative of y**6/195 + 2*y**5/65 - y**4/39 - 4*y**3/13 + 9*y**2/13 + 12*y. Factor v(g).
2*(g - 1)**2*(g + 3)**2/13
Let x(m) = -2*m**4 + m**3 + m**2. Let c(t) = 5*t**4 - 6*t**3 - 3*t**2 + 4*t. Let g(b) = -2*c(b) - 4*x(b). Suppose g(o) = 0. What is o?
-1, 0, 1, 4
Let z = 121 - 241/2. Find t such that -z*t - 2*t**2 + 0 = 0.
-1/4, 0
Let k(g) be the first derivative of -4/5*g**5 + 3*g**4 - 4/3*g**3 - 6*g**2 + 7 + 8*g. Suppose k(u) = 0. Calculate u.
-1, 1, 2
Let u(i) be the second derivative of -10*i**6/3 + 6*i**5 + 11*i**4/3 - 8*i**3 - 8*i**2 + 5*i. Suppose u(v) = 0. Calculate v.
-2/5, 1
Factor 0*q - 4/21*q**2 - 2/21*q**3 + 2/21*q**4 + 0.
2*q**2*(q - 2)*(q + 1)/21
Suppose 94 = 4*g - 338. Let w be (-2)/6*g/(-8). Let -1/2 - w*n**2 + 2*n**3 + 3*n = 0. Calculate n.
1/4, 1
Let j = 536/217 - -74/31. Let d = j - 292/63. Factor 0 + d*s**4 + 4/9*s**3 + 0*s + 0*s**2.
2*s**3*(s + 2)/9
Let x(n) be the third derivative of n**5/12 - 10*n**4/3 - 85*n**3/6 + 60*n**2. Find j, given that x(j) = 0.
-1, 17
Let y(x) be the third derivative of 0 + 1/180*x**6 + 1/9*x**3 + 2*x**2 + 1/30*x**5 + 0*x + 1/12*x**4. Suppose y(k) = 0. What is k?
-1
Let s = -32 + 36. Let n(t) be the first derivative of 0*t + 2/5*t**5 - t**2 - 1 - 2/3*t**3 + 1/2*t**s. Let n(r) = 0. Calculate r.
-1, 0, 1
Let r(k) be the third derivative of -1/12*k**5 + 0 + 1/12*k**4 - 1/210*k**7 + 0*k**3 + 0*k + k**2 + 1/30*k**6. Factor r(o).
-o*(o - 2)*(o - 1)**2
Let w(v) be the third derivative of 0*v - 5/96*v**4 + 0 - 2*v**2 - 1/480*v**6 - 1/12*v**3 - 1/60*v**5. Solve w(b) = 0.
-2, -1
Factor 0 - 3/2*n - 3/2*n**2 + 3/2*n**3 + 3/2*n**4.
3*n*(n - 1)*(n + 1)**2/2
Let x(t) be the third derivative of -t**10/100800 + t**8/13440 - t**5/60 + t**2. Let w(h) be the third derivative of x(h). Factor w(l).
-3*l**2*(l - 1)*(l + 1)/2
Let c(m) be the first derivative of m**3/3 + 2*m - 3. Let g be c(0). What is a in 2*a**2 - 5*a**2 + a**5 - a + g*a**4 + 3*a**2 - 2*a**2 = 0?
-1, 0, 1
Let t(a) be the third derivative of a**8/2856 - a**7/595 + 4*a**2. Determine n, given that t(n) = 0.
0, 3
Let a(h) be the second derivative of 115/21*h**4 + 8/7*h**2 - 241/70*h**5 + 0 + 104/105*h**6 + 7*h - 76/21*h**3 - 16/147*h**7. Factor a(z).
-2*(z - 2)**3*(4*z - 1)**2/7
Let o(n) be the second derivative of -2/3*n**3 - 7/6*n**4 + 0 - 1/2*n**5 + 0*n**2 + 4*n. Find x such that o(x) = 0.
-1, -2/5, 0
Let n = 0 - -9. Factor 0 + 4*t - n + 15 - 2*t**2.
-2*(t - 3)*(t + 1)
Suppose -40 = -3*z + z. Let p be 5/z + 22/8. Factor -2*k**5 - 4*k**p + 5*k**5 + 2*k**3 - k**5.
2*k**3*(k - 1)*(k + 1)
Let h be ((-10)/35)/((-6)/(-56)*-2). Let p be -1*((-8)/(-3))/(-4). Let h*d**4 + 2/3*d - p*d**5 - 4/3*d**2 + 0 + 0*d**3 = 0. What is d?
-1, 0, 1
Let h be (16/(-20))/(4/(-10)). Let s be (-12)/20 - (-26)/10. What is d in 2*d**2 + 5*d**2 - h*d**2 + 3*d - 2*d**s = 0?
-1, 0
Let t = 933/7 - 133. Let k = 40 - 278/7. Factor k*y**2 + 2/7*y - t - 2/7*y**3.
-2*(y - 1)**2*(y + 1)/7
Let g(d) = -15*d**4 - 45*d**3 - 36*d**2 + 45*d + 9. Let r(i) = 3*i**4 + 9*i**3 + 7*i**2 - 9*i - 2. Let o(c) = 4*g(c) + 21*r(c). Factor o(p).
3*(p - 1)*(p + 1)**2*(p + 2)
Factor -11*j - 7*j + 10*j - 8 - 2*j**2.
-2*(j + 2)**2
Let q(u) = 5*u**5 + 12*u**4 - 33*u**3 + 31*u**2 - u. Let g(k) = 3*k**5 + 6*k**4 - 17*k**3 + 16*k**2. Let l(b) = -7*g(b) + 4*q(b). Factor l(a).
-a*(a - 2)**2*(a - 1)**2
Let r(x) be the third derivative of x**8/168 + 2*x**7/35 + 2*x**6/15 - x**5/5 - 3*x**4/4 - 9*x**2. Factor r(a).
2*a*(a - 1)*(a + 1)*(a + 3)**2
Suppose -5*v**4 + 81*v**2 + 50*v**3 - 35 + 45*v**2 + 110*v - 246*v**2 = 0. Calculate v.
1, 7
Let h(f) = -f**2 - f + 1. Let g(x) = 12*x**2 + 18*x - 2. Let t(y) = -y**3 + 7*y**2 + y - 8. Let o be t(7). Let q(i) = o*g(i) - 10*h(i). Factor q(k).
-2*(k + 2)**2
Solve -16*z**4 - 14*z + 0 - 16*z**5 - 14*z + 4 + 8*z**2 + 4 + 44*z**3 = 0.
-2, -1, 1/2, 1
Let h(s) be the second derivative of -s**6/70 - s**5/140 + 2*s**4/21 - 2*s**3/21 + s. Factor h(l).
-l*(l - 1)*(l + 2)*(3*l - 2)/7
Let h(c) be the first derivative of 0*c**2 + 0*c**4 - c + 2/3*c**3 + 5 - 1/5*c**5. Factor h(a).
-(a - 1)**2*(a + 1)**2
Let b(c) = 15*c**4 + 9 + 3*c**2 + c**2 - c**2 + 0*c**2. Let m(x) = 7*x**4 + x**2 + 4. Let v(i) = 4*b(i) - 9*m(i). Find w such that v(w) = 0.
-1, 0, 1
Let k = -2 - -2. Let c be 1*(15/(-21) + 1). What is x in -c*x**2 + k - 2/7*x = 0?
-1, 0
Let s = 11/105 - 2/35. Let o(l) be the first derivative of -3 + 0*l**4 - 1/7*l**2 - 4/21*l**3 + 4/35*l**5 + s*l**6 + 0*l. Factor o(y).
2*y*(y - 1)*(y + 1)**3/7
Determine p, given that 0*p + 7*p**4 - 4*p**5 + 10*p**2 - 23*p**3 + 7*p**4 + 5*p**3 - 2*p = 0.
0, 1/2, 1
Let x(z) = z**3 - 9*z**2 + 13*z + 7. Let s be x(7). Factor -2/7*l**2 + s*l + 2/7.
-2*(l - 1)*(l + 1)/7
Suppose 27 = 5*r - 3*d, -4*r - 5*d = -13 + 21. Determine j, given that 3*j**r + 1/2*j**4 + 6*j + 2 + 13/2*j**2 = 0.
-2, -1
Let g(f) be the third derivative of f**8/336 - f**7/105 - f**6/60 + 2*f**5/15 - 7*f**4/24 + f**3/3 + 22*f**2. Suppose g(p) = 0. Calculate p.
-2, 1
Suppose -5 = c + 2*y, 4*c - 6*y + y = 32. Let k = 57/212 - 1/53. Let -1/4*i**c + k*i + 0*i**2 + 0 = 0. What is i?
-1, 0, 1
Let n(s) be the second derivative of -1/6*s**4 + 3*s - 2/3*s**3 - s**2 + 0. Factor n(w).
-2*(w + 1)**2
Let h(d) be the third derivative of 13*d**6/80 + 11*d**5/40 - d**4/8 - 2*d**2. Factor h(b).
3*b*(b + 1)*(13*b - 2)/2
Let f(y) be the second derivative of -y**5/45 - y**4/9 - 2*y**3/9 - 2*y**2/9 - 8*y + 1. Find r, given that f(r) = 0.
-1
Let p(k) = -k**2 - 1. Let y(f) = -7*f**2 - 10*f - 7. Let i(d) = -2*p(d) + y(d). Let i(u) = 0. What is u?
-1
Find a such that 1/4*a + 0 + 0*a**2 - 1/4*a**3 = 0.
-1, 0, 1
Let i(v) be the third derivative of -1/1176*v**8 + 0*v - 1/420*v**6 - 2/735*v**7 + 0 + 0*v**5 + 0*v**3 + 0*v**4 + 3*v**2. Determine b so that i(b) = 0.
-1, 0
Suppose -1/5*y + 0 + 1/5*y**2 = 0. What is y?
0, 1
Let u(w) = 4*w**3 + 3*w - 1. Let b be -2*(2 - (-9)/(-6)). Let o(s) = -s**2 + 29*s**3 + 3*s**2 - 30*s**3 - 3*s**2. Let j(h) = b*u(h) - 3*o(h). Factor j(y).
-(y - 1)**3
Let q be 3/24 - 6/(-16). Let b(n) be the first derivative of 0*n**3 - 1/5*n**5 + 0*n - 3 - q*n**4 + 0*n**2. Factor b(v).
-v**3*(v + 2)
Find u such that -7 - 10*u + 5*u**3 + 4*u**4 - 16*u**