**2*(o + 3)
Let k(d) be the second derivative of -2*d**6/5 + 8*d**5/5 + d**4 + 6*d. Determine c, given that k(c) = 0.
-1/3, 0, 3
Suppose -3*m + 2*q = 46, -4*m - 3*q = -2*m + 22. Let z be (-32)/m + 10/(-35). Determine o, given that 0*o**z + 1/3*o**5 - 2/3*o**3 + 0 + 1/3*o + 0*o**4 = 0.
-1, 0, 1
Let l(q) = -q**3 + 7*q**2 + 2*q - 10. Let w be l(7). Let a = 467/5 + -93. Let -2/5*h**3 + 0*h**2 + a*h - 1/5 + 1/5*h**w = 0. Calculate h.
-1, 1
Factor 0*n - 1/5*n**5 + 1/5*n**3 + 0 - 1/5*n**2 + 1/5*n**4.
-n**2*(n - 1)**2*(n + 1)/5
Let q = -994/5 - -200. Suppose 3/5*r**2 + 0 + q*r = 0. What is r?
-2, 0
Suppose -5*m = -0*g + 4*g - 118, 0 = -3*m + 3*g + 60. Suppose -4 = 2*s, 2 = 3*u - 3*s - m. Factor -2*n**4 + 2*n**2 - 2*n**3 + u*n**3 + 4*n**4.
2*n**2*(n + 1)**2
Let r(d) be the second derivative of 7*d**5/80 + d**4/24 - 4*d. Find a, given that r(a) = 0.
-2/7, 0
Let q(f) be the second derivative of 2*f**6/105 - f**5/5 + 6*f**4/7 - 40*f**3/21 + 16*f**2/7 - 6*f. Factor q(p).
4*(p - 2)**3*(p - 1)/7
Let m(u) be the third derivative of -u**6/120 + u**5/60 + 5*u**2. Factor m(r).
-r**2*(r - 1)
Suppose -5*b = 2*h - 32, -3*b - 2*h - 3*h + 23 = 0. Factor -b + 0*u**4 - 2*u**4 - 9*u**3 - 9*u + 4 - 14*u**2.
-(u + 1)**2*(u + 2)*(2*u + 1)
Let u(n) = -n**2 + 1. Let h(c) = -6*c**2 - 4*c + 7. Let v = -31 + 52. Let r(q) = v*u(q) - 3*h(q). Factor r(l).
-3*l*(l - 4)
Find j, given that 12*j**3 - 35*j + 2*j**4 + 2*j + 2*j**4 + 17*j = 0.
-2, 0, 1
Let g(h) be the second derivative of 0*h**2 + 0*h**4 + 0*h**3 + 2*h + 0 + 1/40*h**5. Let g(n) = 0. What is n?
0
Let b(o) be the third derivative of 4*o**7/945 + o**6/45 + o**5/30 + o**4/54 - 10*o**2. Factor b(c).
2*c*(c + 2)*(2*c + 1)**2/9
Let t(c) be the second derivative of -c**7/84 + c**6/30 + 3*c**5/40 - c**4/6 - c**3/3 + c + 24. Find s, given that t(s) = 0.
-1, 0, 2
Let m(p) be the second derivative of 5/6*p**4 + 0*p**2 - 9/5*p**5 + 4*p + 2/3*p**3 + 0. What is q in m(q) = 0?
-2/9, 0, 1/2
Factor -61*g**2 - 24*g - 64 + 57*g**2 - 8*g.
-4*(g + 4)**2
Let l = -20 + 35. Suppose -5 + l = 5*i. Factor -3 + 1 - 2*k**i - 4*k + 0*k**2.
-2*(k + 1)**2
What is z in 1/4*z + 1/2 - z**2 - 3/4*z**3 = 0?
-1, 2/3
Let v(j) be the first derivative of j**4/36 - j**3/27 - 2*j**2/9 + 4*j/9 - 43. Let v(s) = 0. What is s?
-2, 1, 2
Let a(f) be the first derivative of 0*f + 1/12*f**6 - 1/8*f**4 + 3 + 1/6*f**3 + 0*f**2 - 1/10*f**5. Suppose a(o) = 0. Calculate o.
-1, 0, 1
Suppose 2*w - 4*w = 0. Let h(y) be the third derivative of 0*y + w*y**3 + 1/60*y**5 + y**2 + 0 - 1/24*y**4. Factor h(v).
v*(v - 1)
Let f(o) = o**2 + 14*o - 18. Let u be f(-15). Let c be 5 + 9/(-3) - u. Factor -4/3*i**3 + 0*i**2 + 0*i**4 + 2/3*i + 0 + 2/3*i**c.
2*i*(i - 1)**2*(i + 1)**2/3
Factor 4*r + 16*r**2 + r**3 + 7*r**5 + 16*r**4 + 23*r**3 - 3*r**5.
4*r*(r + 1)**4
Suppose c - 11 = -4*c + i, 1 = -5*c + 4*i. Let o(d) be the third derivative of -2/21*d**c + 0*d + 3*d**2 + 0*d**5 + 0 - 1/420*d**6 + 1/28*d**4. Factor o(p).
-2*(p - 1)**2*(p + 2)/7
Let y be ((-27)/(-12) + -2)*(-216)/(-63). Factor 2/7*w**5 - y*w**3 - 2/7*w**4 - 4/7*w + 0 + 10/7*w**2.
2*w*(w - 1)**3*(w + 2)/7
Let y(u) = -2*u**2 + 9*u. Let n(j) = -26 + 26 + 8*j - 2*j**2. Let g(r) = -7*n(r) + 6*y(r). Let g(c) = 0. What is c?
0, 1
Let x(j) = -j**2 - j. Let p(g) = 8*g**2 + 18*g - 8. Let l(r) = p(r) + 10*x(r). Determine o so that l(o) = 0.
2
Let c be (0 - 4 - -2)*60/(-24). Factor 1/2*d**2 + 5/4*d**c + 9/4*d**3 + 0*d + 0 + 3*d**4.
d**2*(d + 1)**2*(5*d + 2)/4
Let r(y) = -y**2 + 3*y + 13. Let h be r(5). Factor 0 - 1/2*j**2 - 1/2*j**4 + 0*j - j**h.
-j**2*(j + 1)**2/2
Let s be (0 + 10/6)*(-80)/(-150). Suppose s*r + 8/9 + 2/9*r**2 = 0. Calculate r.
-2
Let u be (-44)/88 - (-5)/2*2. Factor -1/2*r**2 - 3*r - u.
-(r + 3)**2/2
Let j(s) = 6*s**5 + 7*s**4 + s**3 - 5*s**2 + 5. Let v(o) = 9*o**5 + 11*o**4 + 2*o**3 - 7*o**2 + 7. Let g(a) = -7*j(a) + 5*v(a). Let g(n) = 0. Calculate n.
-1, 0
Let y be 12/(-9)*12/(-8). Factor 2/5 - 2/5*z**y - 2/5*z + 2/5*z**3.
2*(z - 1)**2*(z + 1)/5
Let u = -395 - -1189/3. Solve -2/3*q**5 - 8/3*q**2 + u*q**4 + 4/3 - 2/3*q + 4/3*q**3 = 0 for q.
-1, 1, 2
Let a = -5 - 5. Let v = a + 12. Factor 0 + 2/9*m**v - 2/9*m.
2*m*(m - 1)/9
Let u(x) be the second derivative of -x**3 + 2*x + 2*x**2 + 0 + 1/10*x**5 + 0*x**4. Factor u(m).
2*(m - 1)**2*(m + 2)
Factor 0 + 3/4*n**4 + 0*n + 0*n**2 + 3/4*n**3.
3*n**3*(n + 1)/4
Let s = -122 + 122. Factor -9/4*o**2 + 3/4*o + s.
-3*o*(3*o - 1)/4
Let z be -1*2 - (-35)/7. Suppose h - 20 = -z*h. Find f such that -2/7*f - 16/7*f**4 + 20/7*f**2 - 4/7 - 8/7*f**3 + 10/7*f**h = 0.
-1, -2/5, 1
Let c(t) be the second derivative of -1/147*t**7 + t + 0 - 2/105*t**6 + 1/21*t**4 + 0*t**2 + 0*t**5 + 1/21*t**3. Find b, given that c(b) = 0.
-1, 0, 1
Suppose -u + 6 = 2*u. Factor 8*q + 0*q**5 + q**5 - 7*q - 4*q**4 - 3*q**3 - 4*q**u + 9*q**3.
q*(q - 1)**4
Let w = 24 - 21. Let h(v) be the third derivative of 0 + 0*v - 1/20*v**6 - 1/252*v**8 + 2*v**2 - 1/45*v**7 + 0*v**w - 1/36*v**4 - 1/18*v**5. Factor h(j).
-2*j*(j + 1)**3*(2*j + 1)/3
Let b(m) be the second derivative of m**6/120 - m**5/20 + m**4/12 - 5*m**2/2 - m. Let q(s) be the first derivative of b(s). Suppose q(u) = 0. What is u?
0, 1, 2
Solve 32*k**4 + 2*k**5 - 28*k**4 - 4*k**3 - 3*k**5 = 0 for k.
0, 2
Let t(o) be the first derivative of -o**7/2520 + o**6/120 - 3*o**5/40 + 3*o**4/8 + 2*o**3/3 - 3. Let b(f) be the third derivative of t(f). Factor b(k).
-(k - 3)**3/3
Let k be ((-30)/(-9) - 5)/((-25)/45). Factor -2/13 + 6/13*s + 2/13*s**k - 6/13*s**2.
2*(s - 1)**3/13
Suppose 14*h - 31*h = -14*h. Solve -1/2*d**4 + 0*d + 1/4*d**5 + 0 + h*d**2 + 1/4*d**3 = 0.
0, 1
Factor 68 - 57*b**2 - 8*b - 15*b**3 - 59 - 25*b.
-3*(b + 1)*(b + 3)*(5*b - 1)
Suppose 0 = -3*k + 2*f + 14, 22 = k - 0*k - 5*f. Let u(i) = -i - 2. Let c be u(-5). Factor 2/5*h**5 + 0*h**k + 2/5*h**c - 4/5*h**4 + 0*h + 0.
2*h**3*(h - 1)**2/5
Factor -15*t**2 + 5*t**2 - 4*t**3 + 6*t**2.
-4*t**2*(t + 1)
Let z = 179/2 + -89. Suppose 0 + w + z*w**2 = 0. Calculate w.
-2, 0
Let n(d) be the third derivative of -1/36*d**4 + 1/60*d**5 + 0 - 1/270*d**6 + 0*d - 1/3*d**3 - d**2. Let m(z) be the first derivative of n(z). Factor m(p).
-2*(p - 1)*(2*p - 1)/3
Let y(i) be the third derivative of -i**7/525 + i**6/300 + i**5/50 - i**4/12 + 2*i**3/15 - 2*i**2. Determine s, given that y(s) = 0.
-2, 1
Let z(g) be the third derivative of -g**6/480 - g**5/240 - 8*g**2. Let z(c) = 0. What is c?
-1, 0
Suppose -2*w - 108 = -4*w. Let -w*y**4 - 36*y**3 - 15*y + 54*y**5 + 2 + 32*y**2 + 20*y**2 - 3*y = 0. Calculate y.
-1, 1/3, 1
Factor 7*x**3 - 5*x**3 - 7*x - 4 + 2*x**2 + 2*x**2 + 5*x.
2*(x - 1)*(x + 1)*(x + 2)
Let g = -17/8 + 21/8. Let f = -484 - -484. Solve g + 1/2*m**4 + f*m**3 + 0*m - m**2 = 0.
-1, 1
Suppose 0 = 3*k - 3*i, -6*i - 3 = -3*k - 4*i. Solve 2/9*v**4 + 2/9*v**k - 2/9*v**2 - 2/9*v + 0 = 0.
-1, 0, 1
Let f(u) be the second derivative of u**7/420 + u**6/42 + 3*u**5/35 + 2*u**4/21 + u**3/3 - 4*u. Let h(m) be the second derivative of f(m). Factor h(x).
2*(x + 2)**2*(7*x + 2)/7
Let u = 0 + -4. Let v(p) = -2*p**3 + 7*p - 5. Let m(t) = 3*t**3 + 0 + 5 - 6*t - t**3 - 1. Let o(r) = u*v(r) - 5*m(r). Suppose o(n) = 0. Calculate n.
-1, 0, 1
Let d(z) be the second derivative of -3*z**5/20 + 7*z**4/16 + z**3/4 + 4*z. Determine t, given that d(t) = 0.
-1/4, 0, 2
Let r be (1 + -2)/(12 - 13). Solve r + 1/2*v**2 + 3/2*v = 0 for v.
-2, -1
Let z(n) = 7*n**4 - 6*n**3 + 3*n**2 - 11*n. Let o(f) = 3*f**4 - 3*f**3 + f**2 - 5*f. Let y(x) = 9*o(x) - 4*z(x). Factor y(t).
-t*(t + 1)**3
Let q(r) be the third derivative of 1/330*r**5 + 0*r**3 + 0*r**4 - 2*r**2 + 0*r**6 + 0 + 0*r - 1/1155*r**7. Factor q(b).
-2*b**2*(b - 1)*(b + 1)/11
Let p(t) = 3*t**4 - 21*t**3 + 47*t**2 - 47*t + 18. Let j(s) = -3*s**4 + 21*s**3 - 48*s**2 + 48*s - 18. Let q(f) = -4*j(f) - 3*p(f). Solve q(g) = 0.
1, 2, 3
Let t be 45/18 + 1 + -1. Factor -5/2*q**3 - 1/4*q**5 - t*q**2 - 1/4 - 5/4*q - 5/4*q**4.
-(q + 1)**5/4
Let t(x) = 3*x - 3. Let b(h) = -7*h + 7. Let s(w) = 2*b(w) + 5*t(w). Let m be s(5). Factor -4*p**2 + 2*p**2 - m*p + 2*p.
-2*p*(p + 1)
Let l(s) = -s**2 - 3*s - 4. Let y(w) = -2*w**2 - 6*w - 9. Suppose -4*f + 3*v + 1 = 0, f + 5*v = v + 24. Let g(r) = f*y(r) - 9*l(r). Solve g(m) = 0.
-3, 0
Suppose -11*d + 15*d - 16 = 0. Let l(q) be the first derivative of -1/2*q**3 - 1/20*q**5 + 1/4*q