6 + 2*d**3/21 + 5*d - 1. Let m(h) be the first derivative of k(h). Factor m(p).
2*p*(p + 1)*(5*p + 2)/7
Let f be (10 + 2)*(-1)/(-3). Let 3*k**2 + 6*k**4 + f*k**4 - 9*k**4 + 3*k**2 - 4*k**3 - 4*k + 1 = 0. What is k?
1
Let g(x) be the first derivative of x**6/120 - x**5/24 + x**4/12 - x**3/12 + 4*x**2 - 2. Let v(i) be the second derivative of g(i). Factor v(j).
(j - 1)**2*(2*j - 1)/2
Suppose 3*y - 26 = -17. Determine u, given that -y*u**2 - 4 + 6*u + 1/2*u**3 = 0.
2
Let y be ((-3)/36)/((-2)/6). Let o = 0 + y. What is x in -x**3 - x - 3/2*x**2 - 1/4 - o*x**4 = 0?
-1
Let v(i) = -i**2 + 5*i - 1. Let a be v(4). Let d(w) = w**2 - 7*w + 4. Let m be d(7). Determine z, given that -z**m - z**3 + 5*z**a + 3*z**4 - 2*z**3 = 0.
-1, 0
Let t be 3/(-1) - 5*-1. Suppose -k - 4 = -t*k. Find v such that 5 - 3 - v - v**2 + 2*v**2 - k = 0.
-1, 2
Let u(r) be the first derivative of -r**5/210 + r**3/21 - 3*r**2 + 2. Let t(l) be the second derivative of u(l). Factor t(x).
-2*(x - 1)*(x + 1)/7
Let a(k) be the third derivative of k**8/80640 + k**7/5040 + k**6/960 + k**5/30 + k**2. Let s(c) be the third derivative of a(c). Factor s(l).
(l + 1)*(l + 3)/4
Suppose 0 = -3*k - 3*k + 24. Factor -2/3*a**3 + 0 - 2/3*a**k - 2/9*a**2 + 0*a - 2/9*a**5.
-2*a**2*(a + 1)**3/9
Suppose 0 = k - 6 + 3, 0 = -2*p + 5*k - 9. Determine u so that 5/2*u**2 - u - 1/2*u**p - u**4 + 0 = 0.
-2, 0, 1/2, 1
Let y(j) be the first derivative of 4*j**3/21 + 2*j**2/7 + 6. Factor y(f).
4*f*(f + 1)/7
Let c(l) be the first derivative of l**3/9 + l**2/3 - l + 2. What is a in c(a) = 0?
-3, 1
Let a be (2/(-4))/(1/116). Let i = -400/7 - a. Solve 2/7*n**4 - 2/7*n**2 + 4/7*n + i*n**5 - 10/7*n**3 + 0 = 0 for n.
-1, 0, 2/3, 1
Let s(t) be the second derivative of 7*t**4/36 + 23*t**3/18 + t**2 + 17*t. Factor s(n).
(n + 3)*(7*n + 2)/3
Let m(u) be the second derivative of u**8/336 + u**7/105 - u**6/120 - u**5/30 - u**2 + 2*u. Let f(r) be the first derivative of m(r). Factor f(q).
q**2*(q - 1)*(q + 1)*(q + 2)
Let p be 4 + 6 + 282/(-30). Find t, given that 0 - p*t**2 - 6/5*t = 0.
-2, 0
Let s(w) = w**2 + 6*w - 5. Let k be s(-7). Let m = 1969/1393 + 3/199. Find p, given that -2/7 + m*p - 8/7*p**k = 0.
1/4, 1
Factor 2/17*t**2 + 2/17 + 4/17*t.
2*(t + 1)**2/17
Let j(w) = -17*w**2 + 3*w + 67. Let d(n) = -8*n**2 + 2*n + 33. Let o(g) = -7*d(g) + 3*j(g). Factor o(r).
5*(r - 3)*(r + 2)
Let o be 7 + (0 - (-1 - -4)). Factor -2*c**3 + 0*c + o*c**2 + 4*c**3 + 0*c.
2*c**2*(c + 2)
Let z(g) be the third derivative of -g**9/7560 + g**8/1680 - g**7/1260 + g**4/12 + 6*g**2. Let t(k) be the second derivative of z(k). Find m such that t(m) = 0.
0, 1
Let o = -104 + 417/4. Let m(b) be the third derivative of 0*b**5 + o*b**4 + 2*b**2 - 1/60*b**6 + 0*b + 2/3*b**3 + 0. Factor m(u).
-2*(u - 2)*(u + 1)**2
Suppose 3/2*x**3 + 0 + 0*x**4 - 1/2*x**5 - x**2 + 0*x = 0. Calculate x.
-2, 0, 1
Let c(r) be the third derivative of 0 + 0*r**3 - 5*r**2 - 1/165*r**5 + 0*r**4 + 0*r + 1/660*r**6. Factor c(y).
2*y**2*(y - 2)/11
Let n(f) = -f**3 - 8*f**2 - 8*f - 3. Let x be n(-7). Solve 0 + 0*b - b**x + 1/3*b**5 + 0*b**2 + 2/3*b**3 = 0.
0, 1, 2
Suppose -3*d + 14 = -n + d, -n + 2*d - 6 = 0. Let q = 3 + -1. Let -2*a**4 - a**5 + a - 3 + 3 + 2*a**q + 0*a**n = 0. What is a?
-1, 0, 1
Let m be (18/2 - -1)*3/6. Let t(l) be the third derivative of 0*l**3 - 2*l**2 + 0*l**m + 0 - 1/168*l**8 + 0*l + 1/30*l**6 + 0*l**7 - 1/12*l**4. Solve t(f) = 0.
-1, 0, 1
Let s = -5 + 5. Factor s*k**2 + 2*k**2 + k - 2 - k**2.
(k - 1)*(k + 2)
Let z(t) = -t**3 + t**2 - 1. Let d(k) = 5*k**3 + k**2 + 2*k + 3. Let r = 6 + -7. Let c(v) = r*d(v) - 3*z(v). Factor c(w).
-2*w*(w + 1)**2
Let m(i) be the second derivative of -i**2 - 1/3*i**3 + 1/10*i**5 + 1/6*i**4 + 0 - i. Suppose m(h) = 0. Calculate h.
-1, 1
What is p in 5/3*p + 1/3*p**2 + 4/3 = 0?
-4, -1
Let w(b) be the third derivative of b**8/2016 + b**7/420 - b**6/144 - b**5/120 + b**4/36 + 27*b**2. Let w(y) = 0. Calculate y.
-4, -1, 0, 1
Factor 0*r - 3*r**3 + 0 + 9/8*r**2 - 9/8*r**4.
-3*r**2*(r + 3)*(3*r - 1)/8
Let q(o) be the second derivative of -1/18*o**4 - o - 1/18*o**3 + 0 - 1/126*o**7 + 1/90*o**6 + 1/6*o**2 + 1/30*o**5. Determine h, given that q(h) = 0.
-1, 1
Let t = -39 + 42. Let l(j) be the second derivative of 1/21*j**7 - 2/3*j**2 + 1/3*j**4 - 4/45*j**6 + 0 + 1/9*j**t - 2/15*j**5 - j. Solve l(m) = 0 for m.
-1, -2/3, 1
Factor -115*g + 60*g + 56*g - g**2.
-g*(g - 1)
Suppose -6*x - 4 + 16 = 0. Let c = x - 3/2. Factor -c + 3/2*q - q**2.
-(q - 1)*(2*q - 1)/2
Let y(g) be the second derivative of -g**7/3780 - g**6/540 + g**4/27 - g**3/2 + 3*g. Let u(z) be the second derivative of y(z). Suppose u(o) = 0. Calculate o.
-2, 1
Let p be (((-1)/(-4))/(-1))/(6/(-8)). Determine l so that 1/3*l**5 - 2/3*l**3 + 1/3 - 2/3*l**2 + 1/3*l**4 + p*l = 0.
-1, 1
Let b be 0/4 + (-4)/(-22). Let w(g) be the second derivative of 0 + 3*g + 1/33*g**3 - b*g**2 + 1/66*g**4. Factor w(j).
2*(j - 1)*(j + 2)/11
Let v(g) be the first derivative of g**4/12 + 2*g**3/3 + 3*g**2/2 + 4*g/3 - 25. Factor v(a).
(a + 1)**2*(a + 4)/3
Let o = 0 + 3. Suppose 0 = -2*t + 5*c - 16 - 0, 0 = 4*t + 5*c - 28. Factor f - f**2 - 2*f**2 - f**4 - t*f - 3*f**o.
-f*(f + 1)**3
Suppose -u + 41 = 9. Factor 23*j**4 - 6 + 4*j**4 + 24*j**2 - 10 - 72*j**3 + u*j.
(j - 2)*(3*j - 2)**2*(3*j + 2)
Let i(f) = -16*f + 162. Let a be i(10). Factor 1/2*n**a + 1/2*n**3 + 0 + 0*n.
n**2*(n + 1)/2
Suppose 0 = 2*g + 4*g - 12. Suppose -1/2*t - 1/4 - 1/4*t**g = 0. What is t?
-1
Let s(g) = g**3 - 2*g**2 - g + 2. Suppose -2*y + 10 - 6 = 0. Let i(d) = d**2 + 2*d**2 - 1 + d**y - 3*d**2. Let u(p) = -2*i(p) - s(p). Factor u(c).
-c*(c - 1)*(c + 1)
Let w(r) be the first derivative of 3/10*r**3 - 7/60*r**4 + 2 - r - 1/5*r**2. Let y(m) be the first derivative of w(m). Solve y(h) = 0 for h.
2/7, 1
Let o(s) be the first derivative of -2*s**3/3 - 8*s**2 - 32*s - 10. Find b, given that o(b) = 0.
-4
Suppose -2*i**2 + 7*i**2 + 4*i**2 - 2*i**2 - 2*i - 3*i**3 = 0. What is i?
0, 1/3, 2
Let a be 893/(-2100) + (-3)/(-7). Let t(q) be the third derivative of 0 + 0*q - 1/60*q**4 + 2*q**2 + 1/75*q**5 - a*q**6 + 0*q**3. Factor t(w).
-2*w*(w - 1)**2/5
Let p(c) be the second derivative of 2/15*c**3 + 0*c**2 - 1/6*c**4 + 2*c + 0. Find h, given that p(h) = 0.
0, 2/5
Let a(w) be the second derivative of -3*w**5/50 + w**4/15 + w**3/5 - 2*w**2/5 + 12*w. Let a(z) = 0. Calculate z.
-1, 2/3, 1
Let h(d) be the second derivative of d**7/84 + d**6/90 - 3*d**5/40 + d**3/9 - 9*d. Solve h(g) = 0 for g.
-2, -2/3, 0, 1
Factor 0*m + 0*m + m**2 + 2*m.
m*(m + 2)
Factor -128/7 - 2/7*p**2 - 32/7*p.
-2*(p + 8)**2/7
Let h(r) be the second derivative of -r**6/150 + 3*r**5/100 - r**4/30 + 6*r. Factor h(z).
-z**2*(z - 2)*(z - 1)/5
Suppose -u + 4*x = -2*u + 4, 4*u + 4 = 4*x. Suppose u*t + 2*t - 50 = 0. Factor 39*j + 6*j**2 - t*j + 4 + 4*j**2.
2*(j + 1)*(5*j + 2)
Let t(u) be the second derivative of -3/2*u**2 + 0 - 1/10*u**6 - 3/2*u**4 + 3/5*u**5 + 6*u + 2*u**3. Factor t(m).
-3*(m - 1)**4
Let f be (6/(-3) + (-21)/(-9))*1. Let r(m) be the first derivative of -m - f*m**3 - 2 - m**2. Determine t, given that r(t) = 0.
-1
Suppose 4*s + 12 = -0*l - 3*l, 0 = -4*l + 5*s + 15. Suppose l*u = 2*u. Let 2/7*o**2 + 2/7*o + u = 0. Calculate o.
-1, 0
Let k(p) = -5*p**5 + 4*p**3 + 3*p**2 + p. Let o(w) = 4*w**5 - 4*w**3 - 2*w**2. Let z(l) = -2*k(l) - 3*o(l). Let z(n) = 0. Calculate n.
-1, 0, 1
Let b(g) be the first derivative of -3 - 1/20*g**5 - 1/12*g**3 + 0*g**2 + 1/8*g**4 + 0*g. Determine d, given that b(d) = 0.
0, 1
Solve -2*k + 10*k**2 - 35 - 31 + 2*k**3 + 56 = 0.
-5, -1, 1
Let d = -9 + 13. Suppose 28 = 4*t + 4*p, 0 = -d*t - 5*p - 0 + 33. Factor g**2 + g + g**2 - g**t.
g*(g + 1)
Let s(o) be the second derivative of -5*o + 0*o**2 + 1/30*o**4 + 0 + 2/15*o**3. Factor s(m).
2*m*(m + 2)/5
Let j be 136/(-14) - 2/7. Let s = j + 14. Solve 1/3*v + v**3 + 1/3*v**s + v**2 + 0 = 0.
-1, 0
Suppose 0 = 5*f - 51 + 11. Suppose f = 2*u - 0. What is n in 4*n + 1 - u*n - n**2 = 0?
-1, 1
Let y(w) = -w**2 - 5*w + 8. Let q be y(-6). Let j be 4 - (8/2 - q). Factor -1 + 3 + 4*h**3 - j*h - 4*h**2 - 4*h**5 + 2*h**5 + 2*h**4.
-2*(h - 1)**3*(h + 1)**2
Let v(n) = -4*n**4 + 4*n**3 - 4*n**2. Suppose 0 = -5*f + 8 + 7. Let j(m) = m**5 + 3*m**4 - 3*m**3 + 5*m**2. Let r(d) = f*v(d) + 2*j(d). Factor r(g).
2*g**2*(g - 1)**3
Let j(r