
Let f(x) be the third derivative of -x**5/60 + x**4/24 + x**3/3 - 3*x**2. What is l in f(l) = 0?
-1, 2
Let c = 371 + -363. Determine y, given that 0*y + 4/3*y**2 - 14/3*y**5 - 2*y**3 - c*y**4 + 0 = 0.
-1, 0, 2/7
Let c(j) be the first derivative of -j**6/6 + 2*j**5/5 + j**4 - 2*j**3/3 - 3*j**2/2 - 8. Factor c(d).
-d*(d - 3)*(d - 1)*(d + 1)**2
Let o = 8 + -4. Suppose 2*b - 5*a = -2*b - 3, o*b - 3 = 3*a. Factor -5*r + 4*r**b + 4*r**5 - 3*r**5 - 3*r**5 + 3*r.
-2*r*(r - 1)**2*(r + 1)**2
Let c(z) be the first derivative of -2*z**6/21 - 8*z**5/35 + 8*z**3/21 + 2*z**2/7 + 7. Factor c(i).
-4*i*(i - 1)*(i + 1)**3/7
Let s be ((-1)/1)/((-3)/6). Suppose 2*m - 1 - s*m**2 + 0 + m**2 = 0. Calculate m.
1
Let z(m) be the second derivative of 2/3*m**3 + 0*m**2 - 2*m + 0 - 1/6*m**6 + 2/3*m**4 - 7/20*m**5. Suppose z(c) = 0. What is c?
-2, -2/5, 0, 1
Let z(a) = -a**2 - 5*a + 2. Let c(f) = f**2 - f + 1. Let i(l) = 4*c(l) + z(l). Factor i(k).
3*(k - 2)*(k - 1)
Suppose 7 + 2 = 3*r. Let p(u) be the third derivative of 0*u + 0 - 1/60*u**5 - 1/24*u**4 - 3*u**2 + 0*u**r. Factor p(l).
-l*(l + 1)
Factor 1/4*k**2 + 25/4 + 5/2*k.
(k + 5)**2/4
Let w be 17/7 + 18/(-42). Solve -3 + w*p**2 - 2*p + 2*p**3 + 1 + 0*p + 0 = 0 for p.
-1, 1
Let f(i) be the second derivative of i**5/5 + i**4/3 - 2*i**3/3 - 2*i**2 - 11*i. Factor f(u).
4*(u - 1)*(u + 1)**2
Let r(a) be the third derivative of -a**8/3360 - a**7/1680 + a**6/720 + a**5/240 + a**3/3 - 2*a**2. Let y(b) be the first derivative of r(b). Factor y(l).
-l*(l - 1)*(l + 1)**2/2
Factor 1/4 + 1/4*k**2 + 1/2*k.
(k + 1)**2/4
Let q(c) be the second derivative of c**5/20 + c**4/6 - 18*c. Suppose q(i) = 0. What is i?
-2, 0
Let a(f) be the first derivative of -f**4/12 + 2*f**3/9 - f**2/6 - 2. Solve a(t) = 0 for t.
0, 1
Let c = 64 - 45. Suppose -4*i = -2*i + 2*y - 12, y = 4*i - c. Solve 0*z + 2/7*z**4 - 2/7*z**i + 2/7*z**3 - 2/7*z**2 + 0 = 0 for z.
-1, 0, 1
Let z(m) be the third derivative of -m**9/5040 - m**8/2240 - m**4/6 - 4*m**2. Let i(v) be the second derivative of z(v). Factor i(w).
-3*w**3*(w + 1)
Let f(x) be the second derivative of 0*x**2 + x + 0 + 1/4*x**4 - 1/10*x**6 + 0*x**5 + 0*x**3. Suppose f(m) = 0. Calculate m.
-1, 0, 1
Let k(w) be the third derivative of -w**5/480 + w**4/64 - w**3/24 + 9*w**2. Factor k(m).
-(m - 2)*(m - 1)/8
Let t be 0 - (3 + 0 + 145/(-45)). Suppose 2/9 + 0*n - t*n**2 = 0. What is n?
-1, 1
Let i = -14 + 13. Let o be (i - 2)*2/(-12). Factor o*g**2 + 1/2*g**3 - 1/2*g - 1/2.
(g - 1)*(g + 1)**2/2
Suppose 2*q - 8 = -0. Factor -2*o**q - 6*o**3 + 16*o - 24*o**2 + 5*o**3 + 3*o**3 + 10*o**3.
-2*o*(o - 2)**3
Let h(a) be the third derivative of -a**7/42 + a**6/6 - a**5/6 - 5*a**4/6 + 5*a**3/2 + 38*a**2. Factor h(n).
-5*(n - 3)*(n - 1)**2*(n + 1)
Let p(z) be the first derivative of -z**5/3 - 5*z**4/6 - 5*z**3/9 - 6. Factor p(h).
-5*h**2*(h + 1)**2/3
Let m(b) be the second derivative of -1/30*b**5 + 1/9*b**3 - 1/18*b**4 + 0 + 1/3*b**2 + b. Factor m(w).
-2*(w - 1)*(w + 1)**2/3
Let a(v) = 46*v**3 + v**2 - 80*v - 1. Let z(y) = -15*y**3 + 27*y. Let h(f) = 6*a(f) + 17*z(f). Factor h(u).
3*(u - 1)*(u + 1)*(7*u + 2)
Suppose 5*g + 40 = 2*f, -g = -3*f + 2 + 6. Let l(v) = -v**2 - 8*v + 2. Let u be l(g). Factor -w**u - 1/3*w**3 - w - 1/3.
-(w + 1)**3/3
Let x = 3 - 7. Let w = x - -7. Factor 1/2*t**w + 0 + 0*t + 1/2*t**2.
t**2*(t + 1)/2
Let l(m) be the third derivative of -5*m**8/168 - 94*m**7/105 - 2389*m**6/300 - 282*m**5/25 - 27*m**4/5 - 21*m**2. Solve l(z) = 0.
-9, -2/5, 0
Suppose 26*z = 27*z. Let 1/3*o**5 - 5/3*o**4 + z + 0*o - o**2 + 7/3*o**3 = 0. What is o?
0, 1, 3
Suppose -2/3*w**3 - 2/9*w + 2/3*w**2 + 0 + 2/9*w**4 = 0. What is w?
0, 1
Let d be ((-4)/6)/(2/(-9)). Let f be 1/((-18)/(-4))*d. Factor 0 - f*a**4 + 0*a - 2/3*a**3 + 0*a**2.
-2*a**3*(a + 1)/3
Let f(d) = -9*d**2 - 3*d + 6. Let q(u) = 10*u**2 + 3*u - 6. Let s(a) = -7*f(a) - 6*q(a). Factor s(z).
3*(z - 1)*(z + 2)
Let r be 2*4/(-28) + (-6)/(-21). Let r*m**2 + 0*m + 0*m**3 - 1/3*m**4 + 0 = 0. Calculate m.
0
Let v(n) = 0*n + 3 + 2*n + 5*n + 6*n**2 - 3*n. Let m(r) = -5*r**2 - 3*r - 2. Let d(a) = -a - 1. Let y be d(-5). Let k(i) = y*v(i) + 5*m(i). Factor k(w).
-(w - 2)*(w + 1)
Suppose 0 = 5*d - 10*d + 15. Factor -2*p**2 + 0*p**2 - 8*p - 8 + 3*p**2 - d*p**2.
-2*(p + 2)**2
Let k(b) be the third derivative of 2*b**7/105 + 8*b**6/5 + 288*b**5/5 + 1152*b**4 + 13824*b**3 + 3*b**2. Factor k(f).
4*(f + 12)**4
Let j(w) be the first derivative of 0*w + 1/5*w**3 - 3/25*w**5 - 6 - 3/20*w**4 + 0*w**2 + 1/10*w**6. Suppose j(n) = 0. Calculate n.
-1, 0, 1
Suppose -6*x + 11*x**2 + 4 + 3*x**3 + 15*x + 3*x = 0. Calculate x.
-2, -1, -2/3
Suppose -i - i = -8, -4*i + 24 = -2*o. Let z = o - -9. Factor -h**5 + 2*h**z - 2*h**4 + 0*h**5 + h**3.
h**3*(h - 1)**2
Let v(r) be the third derivative of -2/9*r**3 + 1/90*r**5 + 0*r + 6*r**2 + 0 - 1/36*r**4. Factor v(f).
2*(f - 2)*(f + 1)/3
Let o = -3469/5 - -695. What is j in 26/5*j**2 - 2*j**3 - 22/5*j + o = 0?
3/5, 1
Let h = 6 + -18. Let a be (9/h)/((-5)/4). Factor -a*w**2 + 0 - 1/5*w.
-w*(3*w + 1)/5
Let f(r) be the second derivative of r**4/12 + r**3/6 - r**2 - 4*r. What is y in f(y) = 0?
-2, 1
Let i(b) = -b**2 + b - 2. Let h(t) = -6*t**2 + 5*t - 10. Let c be 0/((3 - 0)/3). Let y = c - -2. Let a(z) = y*h(z) - 11*i(z). Factor a(k).
-(k - 1)*(k + 2)
Let o(j) be the third derivative of -1/36*j**4 + 0 + 0*j - 2/9*j**3 - j**2 + 1/90*j**5. Solve o(y) = 0 for y.
-1, 2
Factor 0*g**3 + 0 + 0*g**2 + 0*g - 2/7*g**4.
-2*g**4/7
Let b(n) be the first derivative of n**4/12 - n**3/6 + n**2/12 + 8. Factor b(o).
o*(o - 1)*(2*o - 1)/6
Let 2/3*c**3 - 2/3*c + 4/3 - 4/3*c**2 = 0. Calculate c.
-1, 1, 2
Factor x**2 - x**4 + x**5 + 6*x**5 + 2*x - 5*x**3 - 4*x**5.
x*(x - 1)**2*(x + 1)*(3*x + 2)
Let z(g) be the second derivative of 0*g**3 - 1/10*g**5 + 0*g**4 + 0 + 1/15*g**6 + 0*g**2 - 3*g. Factor z(b).
2*b**3*(b - 1)
Let j(k) be the third derivative of 0*k + 1/40*k**5 + 0 + 2*k**2 - 1/4*k**4 + k**3. Factor j(m).
3*(m - 2)**2/2
Let n be 6 + 3/6*-8. Let w(q) be the first derivative of -2 + 1/3*q + 1/9*q**3 - 1/3*q**n. Factor w(s).
(s - 1)**2/3
Suppose 3*s + 10 = 25. Let c = s + -13/3. Factor -4*i**3 + 8/3*i**4 - 2/3*i**5 + 0 + 8/3*i**2 - c*i.
-2*i*(i - 1)**4/3
Let c(y) be the second derivative of -y**5/20 - 5*y**4/12 - y**3/6 - y**2 - y. Let a be c(-5). Determine n so that 8*n**a - 3*n**3 + 2*n + 7*n**2 + 0*n = 0.
-1, -2/5, 0
Let o = 2 + 0. Let a be (2/(-6))/(o/(-18)). Let 1 - 49*f**4 - 4*f - 1 - 32*f**2 - 77*f**a = 0. Calculate f.
-1, -2/7, 0
Let y = -11 - -17. Factor -z + y + z**2 - 6.
z*(z - 1)
Suppose 12*k = 7*k + 10. Let -9*z + 2*z**5 - 4*z**3 + 11*z + 2 - k = 0. What is z?
-1, 0, 1
Let u(k) be the third derivative of 0*k**3 + 1/40*k**6 + 0*k + 3*k**2 + 0*k**4 + 0 + 1/20*k**5. Solve u(f) = 0 for f.
-1, 0
Suppose -1 = -2*s + s. Let w = 1 - s. Factor 0*z + w - 1/3*z**2.
-z**2/3
Suppose 2/3 + 1/6*o**2 - 2/3*o = 0. Calculate o.
2
Let h(j) be the second derivative of j**8/20160 - j**7/2520 + j**6/1080 + j**4/4 + 2*j. Let i(s) be the third derivative of h(s). Factor i(f).
f*(f - 2)*(f - 1)/3
Let -2/9*z**2 + 2/9*z**4 + 2/9*z**3 + 0 - 2/9*z = 0. Calculate z.
-1, 0, 1
Let k = -3 + 7. Determine i, given that 9*i**4 + 4*i**2 + 16*i**3 + i**4 - k*i - 2*i**2 = 0.
-1, 0, 2/5
Let b(k) = -3 - 10*k**2 - 11*k**4 - 5*k + 6*k + 2*k**3 + 5*k + k**5 - 3. Let u(p) = p**4 + p**3 + p**2 - p + 1. Let d(i) = b(i) + 6*u(i). Factor d(v).
v**2*(v - 2)**2*(v - 1)
Let b(l) be the second derivative of 1/15*l**6 + 1/3*l**4 + 0*l**2 + 4*l + 0 + 3/10*l**5 + 0*l**3. Let b(q) = 0. What is q?
-2, -1, 0
Find x, given that -3*x - 9/2*x**2 + 3/2*x**4 + 0 + 0*x**3 = 0.
-1, 0, 2
What is o in -21/2*o - 9/2*o**4 + 21/2*o**3 + 3/2*o**2 + 3 = 0?
-1, 1/3, 1, 2
Let n = -7 + 12. Suppose 0 = z - n*k - 13, -z - 4*k + 5*k = -5. Suppose 0 + z*h**2 + 3/4*h = 0. What is h?
-1/4, 0
Let x(p) be the third derivative of -p**3 - 1/6*p**4 + 0 - 4*p**2 - 1/90*p**5 + 0*p. Factor x(z).
-2*(z + 3)**2/3
Let x(t) be the third derivative of 0 - 1/630*t**7 + 1/90*t**5 + 0*t**6 + 0*t**4 + 0*t - 1/18*t**3 + 3*t**2. What is b in x(b) = 0?
-1, 1
Let n be (-26)/(-208) + 1/(-12). Let z(x) be the third derivative of 0*x**3 - 1/30*x**5 + 0 + 1/120*x**6 - 4*x**2 + 0*x + n*x**4. Solve z(l) = 0.
0, 1
Suppose 5*r - 3*r + 3*j = 7, -5*j - 3 = -4*r. Find k, g