2
Let h(o) be the third derivative of 2*o**6/285 + o**5/95 + o**4/228 + 24*o**2. Factor h(y).
2*y*(2*y + 1)*(4*y + 1)/19
Let o be 90/315 - (52/(-14) + 0). Factor -4/9*h + 4/9*h**3 - 2/9*h**o + 2/9*h**2 + 0.
-2*h*(h - 2)*(h - 1)*(h + 1)/9
Let r be (10/(-105))/((-3)/9). Find k, given that 2/7*k - 2/7*k**3 + 0 + 2/7*k**2 - r*k**4 = 0.
-1, 0, 1
Let q(d) be the first derivative of -d**6/36 - 2*d**5/15 - d**4/4 - 2*d**3/9 - d**2/12 - 2. Factor q(w).
-w*(w + 1)**4/6
Let d(f) be the first derivative of 3*f**5/5 - 3*f**4 + 3*f**3 - 54. Solve d(r) = 0.
0, 1, 3
Let c(i) be the second derivative of -i**8/1680 + i**7/630 - i**4/6 + i. Let l(a) be the third derivative of c(a). Determine t so that l(t) = 0.
0, 1
Factor 0 + 1/4*h**2 + 0*h.
h**2/4
Suppose 2/7*v**4 - 4/7*v + 0*v**2 + 4/7*v**3 - 2/7 = 0. Calculate v.
-1, 1
Let r(u) be the first derivative of u**4/10 + 2*u**3/5 + 3*u**2/5 + 2*u/5 + 1. Factor r(m).
2*(m + 1)**3/5
Let p(i) be the second derivative of i**6/105 - i**4/21 + i**2/7 + 7*i. Factor p(a).
2*(a - 1)**2*(a + 1)**2/7
Let m = 4 - 2. Suppose w + 2*q + 2 = 5, -5*w = -m*q - 15. What is l in 2*l - 4*l**2 - l**3 - 1 + 3*l**w + 1 = 0?
0, 1
Let p = 39 - 34. Let m(c) be the third derivative of 1/30*c**p - c**2 + 0*c + 0 + 1/3*c**3 - 1/6*c**4. Factor m(z).
2*(z - 1)**2
Let g(x) = -4*x**3 - x**2 + 7*x. Suppose q - b + 7 + 2 = 0, 4*q + 81 = -5*b. Let i(u) = u**3 - 2*u. Let k(r) = q*i(r) - 4*g(r). Factor k(c).
2*c**2*(c + 2)
Suppose 0*w - w + 3 = 0. Factor 1/2*j**w + 0 - 1/2*j**2 + 0*j.
j**2*(j - 1)/2
Factor 46*i**3 + 80*i**4 + 5 + 5*i**2 + 30*i - 166*i**3 + 0.
5*(i - 1)**2*(4*i + 1)**2
Let -5/4*w**2 + 0 - 1/4*w**4 - 1/2*w - w**3 = 0. What is w?
-2, -1, 0
Let y = -5/31 + 46/93. Suppose 0 = -0*r - 4*r. Suppose y*s**2 + r + 1/3*s = 0. Calculate s.
-1, 0
Let d(v) be the third derivative of v**7/210 + 13*v**6/1800 + v**5/300 - v**3/3 - 2*v**2. Let t(r) be the first derivative of d(r). Solve t(f) = 0.
-2/5, -1/4, 0
Find j, given that 0 - 3/7*j**3 - 4/7*j - 8/7*j**2 = 0.
-2, -2/3, 0
Factor 0 + 3*g**2 - 3/2*g**3 - 3/2*g.
-3*g*(g - 1)**2/2
Suppose -1 + 4 = 3*r. Let g(j) = j**2 - j - 1. Let a(x) = -13*x**2 - 9*x + 9. Let d(i) = r*a(i) + 5*g(i). Factor d(c).
-2*(c + 2)*(4*c - 1)
Let j(w) be the first derivative of 0*w + 1/9*w**3 + 5 - 1/2*w**2. Suppose j(s) = 0. Calculate s.
0, 3
Let a(z) = 7*z**2 - z - 1. Let x be a(-1). Let u = x - 5. Find v such that 1/2*v + 1/2*v**5 + 3*v**3 + 0 - 2*v**u - 2*v**4 = 0.
0, 1
Let h(u) be the second derivative of u**8/3360 + u**7/1260 - u**6/360 - u**5/60 - u**4/4 - 3*u. Let a(c) be the third derivative of h(c). Factor a(m).
2*(m - 1)*(m + 1)**2
Let m(t) = -4*t**3 + 4*t**2 + t - 4. Let k(a) = -4*a**3 + 5*a**2 + a - 5. Let y(c) = -5*k(c) + 6*m(c). Let h be y(-1). Factor -h + 2*d + 3 + 2*d**2.
2*d*(d + 1)
Let g(m) = -3 + 2*m**2 + 9*m - 5*m - m**3 + 0*m**3. Let y be g(3). Find t, given that -2/9*t + 0*t**2 + y + 2/9*t**3 = 0.
-1, 0, 1
Let f(y) be the first derivative of y**4/12 - 2*y**3/9 + y**2/6 + 6. Solve f(p) = 0 for p.
0, 1
Let l(d) be the third derivative of 0 + 1/270*d**6 + 0*d**3 - d**2 - 1/945*d**7 - 1/270*d**5 + 0*d**4 + 0*d. Factor l(k).
-2*k**2*(k - 1)**2/9
Let s(i) be the third derivative of i**5/30 + i**4/6 + i**2. Determine p, given that s(p) = 0.
-2, 0
Let a be (-1 - 1)/((70/15)/(-7)). Factor 7/2*i**a + 0*i - 4*i**4 + 0 - i**2 + 3/2*i**5.
i**2*(i - 1)**2*(3*i - 2)/2
Let l(n) be the second derivative of -n**5/100 + n**4/20 + n**3/30 - 3*n**2/10 - 3*n + 6. Solve l(x) = 0 for x.
-1, 1, 3
Let m be -1 - 12/9*-1. Let f = 61/3 - 20. Determine w so that -f - 2/3*w - m*w**2 = 0.
-1
Let a(p) = p - 2. Let n be a(1). Let z be n - 2 - (-3 + 0). Factor 2/5*d**3 + 1/5*d**4 + z + 1/5*d**2 + 0*d.
d**2*(d + 1)**2/5
Factor -3/4*k**5 + 9/4*k**4 - 3/2*k**2 - 3/4 - 3/2*k**3 + 9/4*k.
-3*(k - 1)**4*(k + 1)/4
Factor 0*x**3 + 2/15*x**4 + 0*x + 0*x**2 + 0.
2*x**4/15
Suppose 3 = g - 0. Let y be ((-24)/18)/((-2)/g). Let y*a**3 + 2*a**2 - 5*a**3 - 15*a + 6 + 11*a**2 - a**2 = 0. Calculate a.
1, 2
Let j be (24/16)/((-1)/(-2)). Let r(u) be the second derivative of 2/15*u**j + 1/5*u**2 + 0 - 1/10*u**4 + 2*u. Factor r(x).
-2*(x - 1)*(3*x + 1)/5
Let q(h) = -3*h**4 - 24*h**3 + 33*h + 3. Let j(m) = m**4 + 6*m**3 - 8*m - 1. Let s(a) = -9*j(a) - 2*q(a). Factor s(o).
-3*(o - 1)*(o + 1)**3
Let b = 63 - 61. Find s such that -8/5*s - 8/5 + 118/5*s**b + 168/5*s**3 = 0.
-2/3, -2/7, 1/4
Let q be 41 + -1 + 1 + -4. Solve 0*j - 1 - 2*j - q*j**2 + 40*j**2 = 0.
-1/3, 1
Suppose 5*c - 5*v - 20 = 0, -4*v = -5*v - 4. Let d(r) be the second derivative of r + c*r**3 - 1/16*r**4 + 0 + 0*r**2. Factor d(i).
-3*i**2/4
Suppose -5*r = -11 + 1. Let p(k) be the first derivative of 0*k + k**r + 0*k**3 - 1/2*k**4 + 2. Factor p(q).
-2*q*(q - 1)*(q + 1)
Suppose 0*a - 4/7*a**2 + 2/7 + 0*a**3 + 2/7*a**4 = 0. What is a?
-1, 1
Factor 0 - 15/8*y**3 - 3*y**2 + 3/2*y.
-3*y*(y + 2)*(5*y - 2)/8
Let 4/9*g + 2/9*g**3 + 0 + 2/3*g**2 = 0. Calculate g.
-2, -1, 0
Factor -3/2*d**2 + 3/2*d**4 + 0*d**3 + 3/4*d + 0 - 3/4*d**5.
-3*d*(d - 1)**3*(d + 1)/4
Let a(b) = -b**4 + b**3 + b**3 - 2*b**4 + 6*b**2 + 6*b + b**4. Let j(s) = 2*s**4 - 3*s**3 - 7*s**2 - 7*s. Let h(w) = -5*a(w) - 4*j(w). Solve h(r) = 0 for r.
-1, 0, 1
Let m(w) be the second derivative of -3*w**6/20 + 21*w**5/40 - 3*w**4/8 - 3*w**3/4 + 3*w**2/2 + 30*w. Factor m(j).
-3*(j - 1)**3*(3*j + 2)/2
Let d(s) be the first derivative of -s**6/33 + 3*s**4/22 + 4*s**3/33 + 9. Factor d(v).
-2*v**2*(v - 2)*(v + 1)**2/11
Let x(p) = -3*p**3 + 7*p**2 + 4*p - 8. Let i(f) = -5*f**3 + 13*f**2 + 7*f - 15. Let a(t) = 4*i(t) - 7*x(t). Factor a(v).
(v - 1)*(v + 2)**2
Let u(g) be the third derivative of 1/12*g**5 + 1/12*g**4 - 5*g**2 + 0*g**3 + 0*g + 0. Let u(t) = 0. What is t?
-2/5, 0
Let a(v) be the third derivative of 0*v**3 - 1/20*v**5 + 0 + 1/8*v**4 + 0*v - 5*v**2. Factor a(y).
-3*y*(y - 1)
Let 0*j**5 + 2*j**2 - 3*j - j**5 - 1089*j**3 + 1093*j**3 - 2*j**4 = 0. Calculate j.
-3, -1, 0, 1
Let d = 212 + -423/2. Factor -d*y**2 + 0 - 1/2*y.
-y*(y + 1)/2
Suppose -12 = 251*t - 254*t. Determine n so that 0*n + 1/4*n**t + 0*n**3 + 0 - 1/4*n**2 = 0.
-1, 0, 1
Factor 38 + 20*r**3 + 0*r**2 - 10*r**2 - 16*r**4 + 7 + 21*r**4 - 60*r.
5*(r - 1)**2*(r + 3)**2
Let r be 2/26*(-299)/(-46). Factor -1/4*h**5 + 1/4*h + 0 + 1/2*h**2 - r*h**4 + 0*h**3.
-h*(h - 1)*(h + 1)**3/4
Let d(i) be the third derivative of i**7/35 - i**6/15 - 7*i**5/30 + i**4/3 + 4*i**3/3 - 12*i**2. What is h in d(h) = 0?
-1, -2/3, 1, 2
Let m(f) be the first derivative of -f**5/5 + f**4/2 + 1. Let m(z) = 0. Calculate z.
0, 2
Suppose 2276*t**2 - 26 + 54*t + 0 + 2*t**3 - 2306*t**2 = 0. What is t?
1, 13
Let t be 3/(-1) + (1 - -6). Let u**3 + 5*u**3 + 0*u**t + 4*u**2 - 4*u**3 - 2*u**4 = 0. What is u?
-1, 0, 2
Let s(x) be the third derivative of x**7/420 + x**6/60 + x**5/20 + x**4/12 + x**3/12 - 4*x**2. Find q such that s(q) = 0.
-1
Let j = 1 - -2. Let i = j + 0. Suppose -4*a**i + 2 + 5*a**3 + 4*a - 9*a - a**4 + 3*a**2 = 0. Calculate a.
-2, 1
Let m(s) = -6*s + 2*s**2 + 0*s + 2 + 2*s. Let c(a) = a**2 - 2*a + 1. Let o(w) = -5*c(w) + 2*m(w). Solve o(j) = 0.
1
Let l(k) = -3*k**3 - 16*k**2 - 19*k - 2. Let d(v) = -3*v**3 - 17*v**2 - 20*v - 1. Let q(w) = 4*d(w) - 5*l(w). Factor q(x).
3*(x + 1)**2*(x + 2)
Let n be 2*-1 - (-6)/2. Let o be 100/26 + 12/78. Find r, given that -r**3 - 1 + n + r**2 - r**o - 2*r**5 + 3*r**5 = 0.
-1, 0, 1
Let l(z) be the first derivative of 1/30*z**5 - 1/3*z + 1/18*z**3 + 1/8*z**4 - 1 - 1/4*z**2. Let l(t) = 0. What is t?
-2, -1, 1
Let r(n) be the first derivative of -n**4/4 - n**3/2 + n**2/2 - 48. Suppose r(y) = 0. Calculate y.
-2, 0, 1/2
Suppose -21 = -4*g - 5. Let s be 22/8 - (-1)/g. Solve -2*k - k**4 - 3 + 1 + 3 + 2*k**s = 0.
-1, 1
Let u = -2 - -6. Let n(l) = -2*l**4 - 7*l**2 - 9*l. Let j(x) = -x**4 - 3*x**2 - 4*x. Let z(s) = u*n(s) - 9*j(s). Factor z(v).
v**2*(v - 1)*(v + 1)
Let k(n) be the second derivative of -n**6/120 + n**5/20 + 9*n**2/2 - 8*n. Let r(z) be the first derivative of k(z). Factor r(c).
-c**2*(c - 3)
Let s = 21722/77 - 2074/7. Let x = 710/33 + s. Factor x*f**2 + 34/3*f**4 - 4/3*f - 14*f**3 - 10/3*f**5 + 0.
-2*f*(f - 1)**3*(5*f - 2)/3
Let z(k) be the first derivative of -2*k**3/33 - 13*k**2/11 - 24*k/11 - 1. Factor z(g).
-2*(g + 1)*(g + 12)/11
Let i = -442 - -1328/3. Factor i*u**2 +