-1, 2
Let h(v) be the second derivative of 3/2*v**2 - 1/540*v**6 - 1/108*v**4 - 1/135*v**5 + 0 + 0*v**3 - v. Let q(s) be the first derivative of h(s). Factor q(x).
-2*x*(x + 1)**2/9
Let o(v) be the second derivative of 27*v**5/80 - 3*v**4/8 + v**3/6 - 7*v**2/2 - 2*v. Let p(u) be the first derivative of o(u). Factor p(l).
(9*l - 2)**2/4
Factor 0*t - 1/4*t**3 + 3/4*t**2 - 1.
-(t - 2)**2*(t + 1)/4
Solve -t**2 - 13*t**3 + 7*t**3 + 7*t**3 = 0.
0, 1
Let -3/8*d - 3/4*d**2 + 0 = 0. What is d?
-1/2, 0
Solve 3/5*j**3 + 0 - 18/5*j**2 + 3*j = 0.
0, 1, 5
Factor 8*z**2 - 15/4*z**3 - 19/4*z + 1/2.
-(z - 1)**2*(15*z - 2)/4
Let q be -2*(-5)/((-20)/(-6)). Factor -2*w**2 - 3*w - w**3 + 3*w**q - w.
2*w*(w - 2)*(w + 1)
Let q(l) be the second derivative of -l**7/84 - l**6/20 + l**5/40 + 7*l**4/24 - l**2 - 10*l. Determine w, given that q(w) = 0.
-2, -1, 1
Let j = -4/35 - -47/105. Factor 1/3*i**4 - 1/3*i + 0 - 1/3*i**2 + j*i**3.
i*(i - 1)*(i + 1)**2/3
Let r(s) = 4*s + 10. Let v be r(-4). Let u be (v/16)/(3/(-12)). Solve t**2 - 1 - u*t = 0 for t.
-1/2, 2
Suppose x + 27 - 2 = 5*c, -35 = -5*c + 3*x. Let m(j) be the second derivative of 1/27*j**3 + 1/9*j**2 - 1/90*j**5 + 3*j - 1/54*j**c + 0. Factor m(q).
-2*(q - 1)*(q + 1)**2/9
Let j(i) = i**3 + i + 1. Let u(f) = -6*f**2 + 3*f + 3. Let z(k) = 3*j(k) - u(k). Factor z(h).
3*h**2*(h + 2)
Let b(y) = y**2 + 4*y - 1. Let u be b(-5). Factor -3*a - a + 0*a - 2*a**2 + u + 6*a.
-2*(a - 2)*(a + 1)
Let i(f) be the first derivative of 2*f**6/21 + 6*f**5/35 - f**4/7 - 8*f**3/21 + 2*f/7 + 28. Let i(z) = 0. Calculate z.
-1, 1/2, 1
Let b = 48 + -142/3. Factor -8*a - b*a**3 + 16/3 + 4*a**2.
-2*(a - 2)**3/3
Suppose 171*t - 168*t = 12. Determine v, given that -3/7*v**t + 3/7*v**2 + 0*v**3 + 0*v + 0 = 0.
-1, 0, 1
Let u(d) be the first derivative of 2/9*d**3 - 2/3*d + 0*d**5 + 1/18*d**6 + 9 + 1/2*d**2 - 1/3*d**4. Solve u(k) = 0 for k.
-2, -1, 1
Let o(v) be the second derivative of v**4/6 + 5*v**3/9 - 2*v**2/3 - 15*v. Factor o(g).
2*(g + 2)*(3*g - 1)/3
Let o = -1637/20 + 333/4. Let i(w) be the second derivative of o*w**6 - 41/18*w**4 - 17/9*w**3 + 0 + 3*w - 1/10*w**5 - 2/3*w**2. What is x in i(x) = 0?
-1/3, -2/7, 1
Factor 798*j - 2*j**2 - 8*j**3 + 8 - 826*j + 30*j**2.
-4*(j - 2)*(j - 1)*(2*j - 1)
Let m(q) = q**2 + 11*q. Let p(c) = 2*c**2 + 16*c. Let s(l) = 7*m(l) - 5*p(l). Factor s(z).
-3*z*(z + 1)
Let c be (1 + 3)/(-24)*3/(-10). Let i(y) be the second derivative of 1/60*y**6 + 0*y**2 + 0*y**3 + y + 1/24*y**4 + c*y**5 + 0. Let i(z) = 0. What is z?
-1, 0
Let t(y) = y. Let k be t(1). Factor -2*d**2 - k + 1 + 0 - 3*d**3 - d**4.
-d**2*(d + 1)*(d + 2)
What is o in -1 - 14*o**2 + 15/2*o = 0?
1/4, 2/7
Let h = 94/5 - 257/15. Let m = 2 + 1. What is d in -2/3 + m*d**2 - 5/3*d**3 + h*d - 7/3*d**4 = 0?
-1, 2/7, 1
Suppose 2*w - v = 7, -5*w + 20 = -v - 4*v. Suppose -p + 0*d = -d + 1, -5*d + 21 = w*p. Factor -t + 2*t**2 + t + 4*t**3 + p*t**4.
2*t**2*(t + 1)**2
Let y(l) be the third derivative of -l**11/166320 + l**9/15120 - l**7/2520 - l**5/60 - 4*l**2. Let k(t) be the third derivative of y(t). Factor k(f).
-2*f*(f - 1)**2*(f + 1)**2
Let x(g) be the third derivative of 5*g**8/672 + g**7/6 + 13*g**6/8 + 9*g**5 + 495*g**4/16 + 135*g**3/2 - 19*g**2. Factor x(f).
5*(f + 2)*(f + 3)**4/2
Suppose 3*v = y + 18, -35 = -6*v + 2*v + 5*y. Suppose 0 = k + 2 - v. Let -k*m - 6*m**4 + 6*m**3 + 2*m + 3*m**5 - 2*m**4 = 0. Calculate m.
-1/3, 0, 1
Let y = -78 - -54. Let x be y/(-182) + 4/26. Factor 2/7*f**2 + 0 + x*f.
2*f*(f + 1)/7
Let t(d) be the third derivative of -d**7/945 + d**6/108 - 4*d**5/135 + d**4/27 + 8*d**2. Factor t(q).
-2*q*(q - 2)**2*(q - 1)/9
Let d(r) be the second derivative of r**4/6 - 4*r**3 + 36*r**2 + 9*r. Find x, given that d(x) = 0.
6
Let d(j) be the third derivative of -1/420*j**6 + 0*j + j**2 + 1/84*j**4 + 1/735*j**7 + 0*j**3 + 0 - 1/210*j**5. Find p, given that d(p) = 0.
-1, 0, 1
Let s(a) = -a**2 - a. Let i(l) = 24*l**2 + 33*l + 12. Let c(f) = i(f) - 3*s(f). Solve c(v) = 0.
-2/3
Let i(g) = -g**2 + 6*g - 5. Let t be i(3). Let a(k) = -k**2 + 12*k + 11. Let m(d) = d + 1. Let v(u) = t*a(u) - 44*m(u). Factor v(c).
-4*c*(c - 1)
Suppose 13 = 4*l - 3. Let h(n) be the first derivative of 0*n**3 + 0*n**2 - 1/2*n**l + 0*n + 4/5*n**5 - 1/3*n**6 - 1. Suppose h(a) = 0. What is a?
0, 1
Let t = 9 - 3. Let x(q) = -4*q**3 - q**2 - 6*q. Let f(k) = k + 3 - 3. Let w(u) = t*f(u) + x(u). Factor w(n).
-n**2*(4*n + 1)
Let x be (2/(-5))/(5/(-25)). Factor -1/2*b**x - 1/2*b + 0.
-b*(b + 1)/2
Let s = 35/4 + -167/20. Let i be 20/8*(-4)/(-25). Factor 0*l**4 + i*l**5 + s*l + 0 + 0*l**2 - 4/5*l**3.
2*l*(l - 1)**2*(l + 1)**2/5
Factor -3/4*x**3 - 3/2*x + 0 + 9/4*x**2.
-3*x*(x - 2)*(x - 1)/4
Factor -2*l**2 + 2*l**3 - l + 0*l**3 + 2*l**4 - 5*l + 4*l.
2*l*(l - 1)*(l + 1)**2
Suppose 4*k + k = 10. Let h be (-3 + 931/315)/(2/(-40)). Suppose -2/9*a**k + h*a - 8/9 = 0. Calculate a.
2
Factor 6/11*i + 2/11*i**3 + 0 - 8/11*i**2.
2*i*(i - 3)*(i - 1)/11
Factor 0 + 2/13*m**3 + 14/13*m**2 + 12/13*m.
2*m*(m + 1)*(m + 6)/13
Suppose -x - 8 + 10 = 0. Factor -8/5 + 6/5*q**x + 2/5*q**3 + 0*q.
2*(q - 1)*(q + 2)**2/5
Factor 0 - 8/3*v - 4/3*v**2.
-4*v*(v + 2)/3
Find g such that 8*g + 0 - 6 - 2 - 58*g**2 + 56*g**2 = 0.
2
Let b(j) be the first derivative of 1 + 1/10*j**5 + 0*j - 1/6*j**3 + 0*j**4 + 0*j**2. Solve b(s) = 0.
-1, 0, 1
Let f be 0/(4/(-4) - -5). Find y, given that 0*y**2 + f + 2/7*y**3 - 2/7*y = 0.
-1, 0, 1
Let g(x) = x**2 + 3. Suppose 0*o + 5*n = 2*o - 15, 5*o = -n - 3. Let r be g(o). Factor f**2 - f - 3*f**2 + r*f**2.
f*(f - 1)
Let r = -9 - -11. Suppose o + 4*t = 20, -2*o - t = r - 14. Factor 40/7*y + 2*y**3 + 36/7*y**2 + 2/7*y**o + 16/7.
2*(y + 1)*(y + 2)**3/7
Let i be (3 - 7)/2 - -22. Let f = i + -15. Factor -2/5*x**f + 2*x**2 + 6/5*x**3 + 0 + 4/5*x - 2/5*x**4.
-2*x*(x - 2)*(x + 1)**3/5
Let y(c) be the first derivative of 3*c**5/20 - 3*c**4/16 + 4. Suppose y(s) = 0. Calculate s.
0, 1
Let w be (-3)/(26/8 + -4). Let k(p) be the second derivative of -1/15*p**6 - p - 1/21*p**7 + 4*p**2 + 1/6*p**w - 8/3*p**3 + 1/2*p**5 + 0. Factor k(r).
-2*(r - 1)**3*(r + 2)**2
Let v(t) be the third derivative of -t**6/30 - 2*t**5/15 + t**4/6 + 4*t**3/3 + 6*t**2. Factor v(g).
-4*(g - 1)*(g + 1)*(g + 2)
Factor 2*l**3 + 42*l**2 + 2*l**3 - 50*l**2.
4*l**2*(l - 2)
Let t(g) be the third derivative of g**5/15 + 8*g**2. Factor t(x).
4*x**2
Let g(p) = -5*p**3 - 2*p**2 + 1. Let i be g(1). Let y be 3/(-1)*4/i. Find m, given that 0 + 1/3*m**y + 1/3*m = 0.
-1, 0
Suppose 8 = 4*n - a, -a = 2*a. Factor 4*r**2 + 0*r**2 + r - 3*r**n.
r*(r + 1)
Suppose 2*k - 10 = -3*l, 6*k = 2*k - 4. Factor -3*p**3 + 3*p**l + 3*p**5 - 2*p**3 - 3*p**2 + 2*p**3.
3*p**2*(p - 1)*(p + 1)**2
Let k(s) = -9*s**2 + 3*s. Let z(f) = 28*f**2 - 8*f. Let p(h) = -16*k(h) - 5*z(h). Factor p(l).
4*l*(l - 2)
Let g(b) be the second derivative of 2/3*b**3 + 0*b**2 - 1/5*b**5 + 0 + 1/15*b**6 - 1/6*b**4 - 3*b. Factor g(n).
2*n*(n - 2)*(n - 1)*(n + 1)
Let i be (9/3)/((-15)/(-100)). Let b be (-11 - -9)*(-2)/i. Factor 0 + 1/5*g**3 + 0*g + 2/5*g**2 - b*g**4.
-g**2*(g - 2)*(g + 1)/5
Let f(z) be the second derivative of z**5/20 + 7*z**4/4 + 49*z**3/2 + 343*z**2/2 - 2*z. Find l such that f(l) = 0.
-7
Suppose 0*u**2 + 0*u + 18/7*u**4 + 0 - 4/7*u**3 - 2*u**5 = 0. What is u?
0, 2/7, 1
Factor -1/4*s**4 + 0 + 1/4*s**2 + 0*s**3 + 0*s.
-s**2*(s - 1)*(s + 1)/4
Let x(f) be the third derivative of f**8/560 - 17*f**7/1050 + 37*f**6/600 - 13*f**5/100 + f**4/6 - 2*f**3/15 - 12*f**2. Factor x(j).
(j - 2)*(j - 1)**3*(3*j - 2)/5
Let b(f) be the second derivative of f**4/36 - f**3/9 + f**2/6 + 23*f. Factor b(l).
(l - 1)**2/3
Let o be (-21 - -1)/(-4) - 2. Factor 2/7*r**o + 4/7 + 8/7*r**2 + 10/7*r.
2*(r + 1)**2*(r + 2)/7
Let g(v) be the first derivative of 3*v**3 + 11*v**2/2 + 2*v - 22. Determine i, given that g(i) = 0.
-1, -2/9
Let a(t) be the first derivative of -t**5/5 + 3*t**4/4 + t**2 + 2. Let m(b) = 2*b**4 - 4*b**3 - 3*b. Let k(v) = -3*a(v) - 2*m(v). Factor k(p).
-p**3*(p + 1)
Suppose -31*h - 24 = -39*h. Find u, given that 0*u - 2/11*u**h + 0 + 0*u**2 + 4/11*u**4 - 2/11*u**5 = 0.
0, 1
Suppose -1/4*n**2 + 3 - 11/4*n = 0. What is n?
-12, 1
Let u(y) be the second derivative of 0 + 0*y**2 - 7*y + 0*y**3 + 2/45*y**6 - 1/5*y**5 + 2/9*y**4. Find j such that u(j) = 0.
0, 1, 2
Let j(x) be the secon