2, 0, 2/5
Let t(w) be the first derivative of -w**8/168 - w**7/105 + 2*w**2 + 5. Let d(r) be the second derivative of t(r). Find i, given that d(i) = 0.
-1, 0
Let w be (-4 - 0) + 7/((-28)/(-36)). Let 1/5*o**3 - 6/5*o**2 + 1/5*o + 16/5*o**w + 24/5*o**4 + 0 = 0. What is o?
-1, 0, 1/4
Let x(h) be the second derivative of h**7/147 - h**6/35 + h**5/70 + h**4/14 - 2*h**3/21 + 3*h. Let x(b) = 0. What is b?
-1, 0, 1, 2
Let z = 18 + -14. Suppose 0 + z = 2*l. Factor 1/4*t**l + 1/4*t - 1/2.
(t - 1)*(t + 2)/4
Let n = 14/13 + -73/104. Let s(k) be the first derivative of -1/12*k**3 - 1/2*k - 2 - n*k**2. Let s(h) = 0. Calculate h.
-2, -1
Let b(k) = k**2 + k - 10. Let a be b(-4). What is w in -2*w**3 - 2/3*w**a - 2/3 + 2*w + 4/3*w**4 = 0?
-1, 1/2, 1
Let k(w) = -15*w**3 - 30*w**2 - 25*w. Let t(g) = g**2 - g - 1. Let z(d) = -k(d) + 10*t(d). Factor z(n).
5*(n + 1)*(n + 2)*(3*n - 1)
Let y(s) be the second derivative of -s**5/5 + s**4/3 + 8*s. Find r, given that y(r) = 0.
0, 1
Let 0*b**3 + 1/3 + 0*b - 2/3*b**2 + 1/3*b**4 = 0. Calculate b.
-1, 1
Suppose 0 = -5*k + 2*k + 6. Let q be 18/(-4)*64/(-48). Let -2*g**3 + g**4 + g**2 - 6*g**2 + q*g**k = 0. Calculate g.
0, 1
Let u = 638 + -636. Factor 1/5*k**u + 0*k - 1/5.
(k - 1)*(k + 1)/5
Factor -12*m + 15*m**2 - m**5 + 16*m**3 - 3*m**5 - 23*m**2 + 8.
-4*(m - 1)**3*(m + 1)*(m + 2)
Let z = -1 - -14. Suppose -5*o + 2*i = -50, 3*o - 2*i - 21 = z. Solve -14*p**2 - 2*p - 2*p + o*p + 10*p**3 = 0 for p.
0, 2/5, 1
Let y(g) be the third derivative of -g**5/150 - g**4/15 + 2*g**2 - 15. Factor y(b).
-2*b*(b + 4)/5
Let m(v) = -v**3 + v**2 - v - 1. Let s(b) = 4*b**3 - 6*b**2 + 5*b + 5. Let l(z) = 5*m(z) + s(z). Factor l(d).
-d**2*(d + 1)
Let v = -62 - -127/2. Factor -4*a**4 + 0*a - a**2 + 0 - 7/2*a**3 - v*a**5.
-a**2*(a + 1)**2*(3*a + 2)/2
Let v(d) be the first derivative of -36*d**5/5 - 16*d**4 - 20*d**3/3 + 4*d**2 - 11. Factor v(r).
-4*r*(r + 1)**2*(9*r - 2)
Suppose -19*o = -73 - 3. Factor -2/3*n**2 + 0 - 1/3*n + 1/3*n**5 + 2/3*n**o + 0*n**3.
n*(n - 1)*(n + 1)**3/3
Suppose 5 - 14 = -3*r. Suppose r = 3*s - 2*s. Let 0 - 1/3*c**2 - 2/3*c**s - 1/3*c**4 + 0*c = 0. What is c?
-1, 0
Let l(i) be the second derivative of i**5/60 + i**4/12 + i**3/9 + 6*i. Suppose l(o) = 0. Calculate o.
-2, -1, 0
Let j(x) be the first derivative of -15*x**4/16 + 3*x**3/4 + 9*x**2/2 + 3*x - 10. Factor j(n).
-3*(n - 2)*(n + 1)*(5*n + 2)/4
Let j be (12/(-2 + 5))/2. Let d = 2 - -1. Suppose j*n - n**2 + 2*n**2 + 0*n**2 + d*n**2 = 0. Calculate n.
-1/2, 0
Suppose 0 = 11*c - 0*c. Factor 1/4*t**2 + c*t - 1/4.
(t - 1)*(t + 1)/4
Let m(q) be the first derivative of q**7/3780 - q**5/540 - q**3 + 2. Let t(x) be the third derivative of m(x). Suppose t(n) = 0. What is n?
-1, 0, 1
Let v(t) be the third derivative of 0*t**3 + 0*t**4 - 1/300*t**6 + 0*t - 2*t**2 + 0 + 0*t**5 + 1/525*t**7. Factor v(u).
2*u**3*(u - 1)/5
Let b = -12 + 16. Let j(s) be the first derivative of 0*s**3 + 1 + 0*s**2 + 0*s**b + 2/35*s**5 + 0*s. Factor j(w).
2*w**4/7
Let t be (10/(-35))/(20/(-14)). Factor 2/5*z**2 + 0*z**3 - t - 1/5*z**4 + 0*z.
-(z - 1)**2*(z + 1)**2/5
Let y be (-6)/4 + 88/16. Let -6/5*h**3 - 2*h**2 - 2/5*h + 8/5*h**5 + 2*h**y + 0 = 0. Calculate h.
-1, -1/4, 0, 1
Let s(y) = -20*y**2 - 24*y + 16. Let u(j) = -4*j**2 - 5*j + 3. Let h(m) = -m**2 - 8*m - 7. Let x be h(-9). Let w(f) = x*u(f) + 3*s(f). Solve w(n) = 0.
-2, 0
Let r(i) be the third derivative of i**6/60 + i**5/40 - 2*i**3/3 + 4*i**2. Let k(h) be the first derivative of r(h). Factor k(a).
3*a*(2*a + 1)
Let o(j) be the second derivative of -j**5/20 + j**4/4 - j**3/2 + j**2/2 + 23*j + 2. Factor o(n).
-(n - 1)**3
Let b(t) = -t**3 + 8*t**2 - 8*t + 9. Let w be b(7). Factor -4 - 2 - 3*f**w - 6*f + 1 + 2.
-3*(f + 1)**2
Suppose -183*x = -184*x + 2. Factor -3/4 + 3/4*t**x + 3/4*t**3 - 3/4*t.
3*(t - 1)*(t + 1)**2/4
Suppose 97*o = 105*o. Factor 0*g + 2/13*g**3 + o*g**2 + 2/13*g**5 - 4/13*g**4 + 0.
2*g**3*(g - 1)**2/13
Let c(r) = -11*r**2 - 25*r + 6. Let o(h) = -100*h**2 - 225*h + 55. Let i(z) = 55*c(z) - 6*o(z). Suppose i(u) = 0. What is u?
-5, 0
Suppose -12 + 3*w**2 + 0*w + 3*w + 6 = 0. What is w?
-2, 1
Let b(j) be the second derivative of j**7/63 + j**6/15 + j**5/15 + 34*j. Determine i so that b(i) = 0.
-2, -1, 0
Let w(g) = -36*g**2 - 6*g + 27. Let p(d) = 5*d**2 + d - 4. Let l(m) = 15*p(m) + 2*w(m). Factor l(s).
3*(s - 1)*(s + 2)
Let t(m) = -m**3 + m**2 + m - 9. Let p be t(0). Let d = -5 - p. Factor o**5 + d*o**4 + 0*o - 4*o**2 + o**5 - 2*o.
2*o*(o - 1)*(o + 1)**3
Let i be -1 - 3 - 22/(-5). Let k(f) be the first derivative of 2/15*f**3 - i*f - 2 + 0*f**2. Solve k(w) = 0 for w.
-1, 1
Let t be (-9)/3 - (-13 + 4). Suppose -2*f - 4*k + 6 = 0, -5*f + t = 3*k - 9. Factor -10/7*j + 8/7*j**2 - 2/7*j**f + 4/7.
-2*(j - 2)*(j - 1)**2/7
Let t(w) be the first derivative of -w**4/16 + 2*w**3/3 - 21*w**2/8 + 9*w/2 + 12. Factor t(k).
-(k - 3)**2*(k - 2)/4
Let s be 2/(-15) + (42/(-45))/(-7). Factor 4/7*m - 2/7*m**2 + s.
-2*m*(m - 2)/7
Let u(t) be the first derivative of -1/24*t**6 + 1/16*t**4 - 1/20*t**5 + 0*t + 1/12*t**3 + 0*t**2 + 1. Solve u(m) = 0 for m.
-1, 0, 1
Determine g so that 9/2 + 25/2*g**2 - 15*g = 0.
3/5
Factor -4622*b**2 + 2*b**4 + 0*b**4 + 4616*b**2 + 4*b.
2*b*(b - 1)**2*(b + 2)
Let c = 2/1743 + 110/581. Let v(d) be the first derivative of -1 + 0*d**4 - 2/7*d + 0*d**2 + c*d**3 - 2/35*d**5. Factor v(w).
-2*(w - 1)**2*(w + 1)**2/7
Let d(f) be the second derivative of -2/9*f**4 - 2/3*f**2 + 1/30*f**5 - 3*f + 0 + 5/9*f**3. Suppose d(k) = 0. Calculate k.
1, 2
Suppose -5*d - 2*u + 2 = 0, -d + 0*d - 2 = u. Let -d - 3*y**2 + 5*y**2 - y + 4*y = 0. Calculate y.
-2, 1/2
Let u be (-176)/64*6/(-33). Solve 1/2*v - 1/2*v**3 + u - 1/2*v**2 = 0.
-1, 1
Let p be 0 - (9/6)/(189/(-28)). Factor -p*s**2 - 8/9 + 8/9*s.
-2*(s - 2)**2/9
Let k(d) be the first derivative of -d**3/21 - 4*d**2/7 - 16*d/7 - 10. Determine q so that k(q) = 0.
-4
Let s(u) = u**2 + 7*u + 5. Let j be s(-6). Let y be ((-1)/(2 - j))/(-1). Let 2/3*g**2 - 2/3 - 1/3*g + y*g**3 = 0. Calculate g.
-2, -1, 1
Let b(q) be the first derivative of -7*q**2 - 4*q - 4/3*q**3 - 2 + 3/2*q**4. Factor b(p).
2*(p - 2)*(p + 1)*(3*p + 1)
Let m(w) = 5*w**5 - 5*w**4 + 12*w**3 + 4*w + 4. Let f(g) = -4*g**5 + 5*g**4 - 11*g**3 + g**2 - 3*g - 3. Let s(h) = -4*f(h) - 3*m(h). Factor s(j).
j**2*(j - 2)**2*(j - 1)
Let u(v) be the first derivative of -5/3*v**3 - 1/4*v**2 + 2 + v. Determine s, given that u(s) = 0.
-1/2, 2/5
Let i be 25/(-4)*(-26)/195. Let t(u) be the first derivative of -1/3*u**3 - 2 + i*u**2 + 2/3*u. Determine k, given that t(k) = 0.
-1/3, 2
Suppose 45*y - 4 = 46*y + 2*f, 3*y - 21 = 5*f. Factor 2/3 - 2/3*l**y + 2/3*l**3 - 2/3*l.
2*(l - 1)**2*(l + 1)/3
Let u be (-2)/(-8) + 11/4. Suppose u*z + z = 12. Solve 6*l**2 - 6*l**2 - l**2 + 2*l**z - l**4 + 0*l**2 = 0 for l.
0, 1
Suppose 18 = -2*b + 22. Solve -2/5*m + 2/5*m**b + 0 = 0 for m.
0, 1
Let m(b) be the second derivative of -b**7/2 - b**6/2 + 27*b**5/20 + 5*b**4/4 - b**3 + 8*b. What is z in m(z) = 0?
-1, 0, 2/7, 1
Let l(b) = -b**5 - 3*b**4 + 7*b**3 + 3*b**2 - 3. Let g(q) = -4*q**5 - 16*q**4 + 36*q**3 + 16*q**2 - 16. Let o(j) = -3*g(j) + 16*l(j). Factor o(k).
-4*k**3*(k - 1)*(k + 1)
Suppose -5 = -5*s - 5*h, 9*s + 4*h = 4*s + 8. Factor 2*r**4 - r**3 + 3*r**3 - r**3 - r**s.
r**3*(r + 1)
Let l be 5/(150/365) - (-1)/(-6). Factor -45/4*o + 3/2 + l*o**3 + 18*o**2.
3*(o + 2)*(4*o - 1)**2/4
Let u(r) be the third derivative of r**8/168 - r**6/15 - r**5/15 + r**4/4 + 2*r**3/3 + r**2. Find z, given that u(z) = 0.
-1, 1, 2
Factor -4 + 16*s - 20*s - 3*s**2 + 2*s**2.
-(s + 2)**2
Find o such that -34*o - 55*o**2 + 65*o**3 + 30 + 9*o + 3*o**4 - 18*o**4 = 0.
-2/3, 1, 3
Let d(g) = 10*g**2 - 167*g - 7. Let w(i) = -5*i**2 + 84*i + 4. Let a(x) = -4*d(x) - 7*w(x). Factor a(c).
-5*c*(c - 16)
Let k be 1/(-1 + (-40)/(-38)). Let z be k/6 + 1/(-2). Find w such that 16*w + 50/3*w**3 + z + 30*w**2 = 0.
-1, -2/5
Let p(z) be the first derivative of z**3/6 + z**2/4 + 8. Factor p(b).
b*(b + 1)/2
Let j(p) be the first derivative of p + 1/6*p**3 + 1/20*p**5 + 0*p**2 - 1/6*p**4 - 1. Let t(x) be the first derivative of j(x). Solve t(l) = 0 for l.
0, 1
Find i, given that 2/9*i**3 - 2/9*i**4 + 0*i - 2/9*i**5 + 0 + 2/9*i**2 = 0.
-1, 0, 1
Let r(u) = -u**3 - 7*u**2 - 8*u - 3. Let m be r(-6). Suppose -m = 