third derivative of -r**5/15 + r**4/5 - 2*r**3/15 - 12*r**2. Find h, given that d(h) = 0.
1/5, 1
Let o = 26 - 103/4. Let t be ((-4)/1)/(-21 + 20). Let 0 + 0*k + 1/4*k**t + o*k**2 - 1/2*k**3 = 0. What is k?
0, 1
Let o(q) be the second derivative of q**4/3 - 2*q**3 + 4*q**2 - 15*q. Determine l, given that o(l) = 0.
1, 2
Suppose -4*y + 16 = 3*g, 0 = -0*y - y + 4*g + 4. Factor 12*w**3 + w**4 - 6*w**2 - 16*w**y + 9*w**3.
-3*w**2*(w - 1)*(5*w - 2)
Factor 11*z**2 - 28*z + 13 + 39*z**3 - 41*z**3 + 3 + 3*z**2.
-2*(z - 4)*(z - 2)*(z - 1)
Suppose -2*o + 18 = o. Let t(i) be the first derivative of 1/3*i**3 - 1 + 1/6*i**o - 1/4*i**4 + 0*i - 1/5*i**5 + 0*i**2. Let t(f) = 0. Calculate f.
-1, 0, 1
Suppose x + 0 = 4. Suppose 4*s = -x*g + 28, 0 - 16 = -3*s - 2*g. Factor -n + n + n**2 - s*n**2.
-n**2
Suppose -5*w + 0*w = 5. Let o = w + 11. Let -19*l**3 - 8 + 46*l**3 + 18*l**3 - 27*l**5 - 20*l + o*l**2 = 0. Calculate l.
-2/3, 1
Suppose 0 = -w + 1 + 1. Factor -2*o**3 + 2 + 9*o**3 - 14*o**w - 5*o**2 + 2 + 8*o.
(o - 2)*(o - 1)*(7*o + 2)
Let h(m) be the first derivative of -m**7/210 + m**6/150 + m**5/50 - m + 3. Let j(n) be the first derivative of h(n). Factor j(x).
-x**3*(x - 2)*(x + 1)/5
Let q(f) = -f**2 + 4*f + 5. Let i be q(5). Let a(c) be the second derivative of i + 4/3*c**3 + 7/18*c**4 - c - 4/3*c**2. Suppose a(l) = 0. Calculate l.
-2, 2/7
Let k = 68/3 - 22. Let j(f) be the first derivative of 3 - k*f**3 + 28/5*f**5 + 0*f + 0*f**2 + 1/4*f**4. Factor j(o).
o**2*(4*o - 1)*(7*o + 2)
Determine c, given that 0 - 4/15*c**3 - 2/15*c - 2/5*c**2 = 0.
-1, -1/2, 0
Let w(m) be the third derivative of m**8/112 - 3*m**7/70 + m**6/20 - 16*m**2. Let w(a) = 0. Calculate a.
0, 1, 2
Suppose -5*k + 65 = -2*o, -2*o + o + 50 = 5*k. Suppose 3*t + k = 5*q, 3*q = -4*t + 7*q - 4. Suppose -2/9*y**t + 4/9*y**2 + 0 - 2/9*y = 0. Calculate y.
0, 1
Let y(f) be the second derivative of -f**5/4 - 5*f**4/3 - 25*f**3/6 - 5*f**2 + 5*f. Solve y(x) = 0.
-2, -1
Let o(t) be the first derivative of t**4/8 - 2*t**3/3 + t**2 - 1. Determine c, given that o(c) = 0.
0, 2
Suppose 4/7*w**2 - 2/7 + 0*w - 2/7*w**4 + 0*w**3 = 0. What is w?
-1, 1
Let s(v) = -2*v**2 + 4*v + 1. Let r(j) be the second derivative of -j**4/3 + 4*j**3/3 + j**2/2 - j. Let i(x) = 3*r(x) - 5*s(x). Find a, given that i(a) = 0.
1
Let p be -1 + 0 - (0 + -2). Suppose -4*j - p = -3*w, 0 = -2*j - 4*w + 16. Factor -g**2 - 10 + j - 8*g - g**2.
-2*(g + 2)**2
Let t(b) = -b**2 - 11*b - 28. Let a be t(-12). Let i be (-116)/a - (-3)/5. What is f in -1/2*f**5 + 1 - f**4 + f**3 + 4*f**2 + i*f = 0?
-1, 2
Let v = 2300 - 137993/60. Let h(r) be the second derivative of 0 - 1/5*r**2 + v*r**4 + 3*r - 1/6*r**3. Factor h(c).
(c - 1)*(7*c + 2)/5
Factor -1/2*r**2 + 1/2*r + 0.
-r*(r - 1)/2
Suppose -54 = -6*h - 42. Factor 0 + 2/9*s - 10/9*s**h.
-2*s*(5*s - 1)/9
What is v in 1/5*v**3 - 3/5*v**2 + 0 + 2/5*v = 0?
0, 1, 2
Let a be -3*(-12)/(-54)*-60. Factor 98/3*r**3 - 84*r**2 + a*r - 16/3.
2*(r - 2)*(7*r - 2)**2/3
Let w(r) = 3*r**2 - 3*r + 4. Let z(t) = -4*t**2 + 4*t - 4. Let k(f) = -6*w(f) - 5*z(f). Factor k(g).
2*(g - 2)*(g + 1)
Let m = 2228/5 - 442. Determine u so that 0 + 0*u + 6/5*u**4 + m*u**5 + 2/5*u**2 - 2*u**3 = 0.
-1, 0, 1/3
Solve -10*i**2 - 5*i**4 - 78*i - 15*i**3 + 78*i = 0 for i.
-2, -1, 0
Suppose -3*o - 12*o = -45. Let 6/7*p**2 + 4/7*p + 0 + 2/7*p**o = 0. Calculate p.
-2, -1, 0
Let r(h) = h**3 - h**2 + h. Let k(q) = -11*q**3 + 61*q**2 - 6*q. Let t(i) = k(i) + 6*r(i). Let t(u) = 0. What is u?
0, 11
Let y(r) = -3*r**2 + 2*r + 5. Let d(o) = -80*o**2 + 55*o + 135. Let u(h) = -2*d(h) + 55*y(h). Determine p so that u(p) = 0.
-1, 1
Let l(d) be the third derivative of -10*d**5/3 + 5*d**4/3 - d**3/3 + 7*d**2. Factor l(k).
-2*(10*k - 1)**2
Factor 4 + 1/3*d**2 + 8/3*d.
(d + 2)*(d + 6)/3
Suppose -5*w - 2*v = -v, 0 = 5*w + 2*v. Let l(d) be the third derivative of -1/96*d**4 + w*d + 0*d**3 + 2*d**2 - 1/240*d**5 + 0. Factor l(o).
-o*(o + 1)/4
Let k(g) be the first derivative of 3*g**4/16 + 15*g**3/4 + 225*g**2/8 + 375*g/4 + 35. Determine j so that k(j) = 0.
-5
Let l(d) be the third derivative of d**5/75 + d**4/4 - 8*d**3/15 - 7*d**2. Factor l(v).
2*(v + 8)*(2*v - 1)/5
Let i(d) be the first derivative of d**3/12 - d**2/4 - 2*d - 32. Suppose i(y) = 0. Calculate y.
-2, 4
Let w(z) = -22*z + 2. Let y be w(-3). Determine p so that -64*p - 2 - y*p**2 + 4 - 18 - 20*p**3 = 0.
-2, -1, -2/5
Determine p so that -2*p**4 - 2/5*p**5 - 18/5*p**3 - 14/5*p**2 + 0 - 4/5*p = 0.
-2, -1, 0
Suppose -18 = -12*w + 18. Solve 0 + 4/7*t**4 + 0*t**2 - 2/7*t**5 - 2/7*t**w + 0*t = 0.
0, 1
Let j(k) = k**3 - 8*k**2 - 10*k + 9. Let g be j(9). Suppose 12 = 4*m - g. Solve 6*h**2 + m*h**2 - 7*h**2 = 0 for h.
0
Let o(u) = u**2 + 6*u + 6. Let c be o(-4). Let i = 6 + c. Factor 2/9*h**2 - 2/9*h**3 + 2/9*h - 2/9*h**i + 0.
-2*h*(h - 1)*(h + 1)**2/9
Let l(g) be the second derivative of -g**5/130 - g**4/26 - g**3/13 - g**2/13 - 6*g. Let l(y) = 0. What is y?
-1
Let g(o) be the second derivative of o**9/1512 - o**8/840 - o**7/420 + o**6/180 - o**3/3 + 2*o. Let l(s) be the second derivative of g(s). Solve l(c) = 0 for c.
-1, 0, 1
Let s be 8/36 - (-52)/9. Let u(v) be the first derivative of 18*v + 2*v - s*v**2 - 8*v + v**3 + 1. Factor u(g).
3*(g - 2)**2
Let l(s) be the second derivative of -1/90*s**5 - 2/27*s**3 - 1/18*s**4 + 0*s**2 - s + 0. Solve l(p) = 0.
-2, -1, 0
Let v be 6*(-2 + (-15)/(-6)). What is f in f**2 - 4*f**2 - 4*f - 2*f**2 + v*f**2 = 0?
-2, 0
Suppose 7 = c + 4. Let v(b) be the third derivative of 0 - 1/48*b**5 + 1/160*b**6 + 0*b + c*b**2 + 1/48*b**4 + 0*b**3. Let v(f) = 0. Calculate f.
0, 2/3, 1
Suppose -7*v + 3*v = -g + 26, -3*g = 5*v + 7. Suppose -g*b + 5*b + 2 = 0. Factor 2/5 + 4/5*w + 2/5*w**b.
2*(w + 1)**2/5
Factor -4*o**3 + 8*o**2 + 5*o**2 - 24*o + 13*o**2 - 6*o**2.
-4*o*(o - 3)*(o - 2)
Factor 4*g**3 + 8/3*g - 19/3*g**2 - 1/3.
(g - 1)*(3*g - 1)*(4*g - 1)/3
Let g(x) = -x - 5. Let b be g(-5). Let n = 2 + b. Factor 2*y**5 - 4*y**n - 2*y**4 + 4*y**4 + 2*y**4 - 2*y**3.
2*y**2*(y - 1)*(y + 1)*(y + 2)
Let r(o) be the third derivative of o**7/105 + o**6/30 + o**5/30 + 11*o**2. Factor r(t).
2*t**2*(t + 1)**2
Let o(p) be the second derivative of -p**8/3360 - p**7/1260 + p**4/3 - 3*p. Let j(r) be the third derivative of o(r). Factor j(i).
-2*i**2*(i + 1)
Let c(k) be the third derivative of k**8/112 + k**7/70 - k**6/20 - k**5/10 + k**4/8 + k**3/2 - 46*k**2. Let c(j) = 0. Calculate j.
-1, 1
Let m(q) = -q**2 - 8*q - 4. Let b be m(-7). Suppose 5*i - b*i = 4. Factor -6/7*s**i - 4/7*s + 2/7.
-2*(s + 1)*(3*s - 1)/7
Factor -4*w**3 + 0*w**3 + 11*w**2 + 2*w**4 - 4*w**3 - 3*w**2.
2*w**2*(w - 2)**2
Let a(n) = -14*n**5 + 5*n**4 + 3*n**3 + 8*n**2. Let o(x) = -5*x**5 + 2*x**4 + x**3 + 3*x**2. Let q(m) = 3*a(m) - 8*o(m). Factor q(c).
-c**3*(c + 1)*(2*c - 1)
Let s(j) = j + 9. Let l be s(9). Suppose 5*h = -2*v + l, -v + 10 = 3*h + v. Factor 0*m**h - m**3 + 0 + 1/2*m**5 + 0*m**2 + 1/2*m.
m*(m - 1)**2*(m + 1)**2/2
Let p(k) be the second derivative of -k**8/6720 + k**7/1260 - k**6/720 + k**4/4 - 2*k. Let q(v) be the third derivative of p(v). Factor q(s).
-s*(s - 1)**2
Let u(j) be the second derivative of 7*j**4/6 + 17*j**3 + 14*j**2 + 42*j. Factor u(s).
2*(s + 7)*(7*s + 2)
Let n = 127/3 + -42. What is y in n*y**2 + 1/3*y - 2/3 = 0?
-2, 1
Let j(w) be the third derivative of -w**6/360 - w**5/120 + w**3/6 + 3*w**2. Let n(x) be the first derivative of j(x). Factor n(p).
-p*(p + 1)
Determine n, given that -115*n**4 + 20 + n - 35*n**5 + 95*n**2 - 65*n**3 - 5*n + 104*n = 0.
-2, -1, -2/7, 1
Let c(t) be the first derivative of 1 - 1/2*t**4 + 2/3*t**3 + 2*t**2 + 0*t. Factor c(k).
-2*k*(k - 2)*(k + 1)
Let d(y) be the first derivative of -y**3/3 + y + 12. Let d(u) = 0. Calculate u.
-1, 1
Let n(q) = -3*q - 7. Let j be n(-3). Suppose j*k - k - 5*m + 15 = 0, -4*k - 3*m + 9 = 0. Factor 4*x**3 - 8/3*x**2 + k - 8/3*x**4 + 2/3*x**5 + 2/3*x.
2*x*(x - 1)**4/3
Determine n, given that 6/17*n**3 - 8/17*n + 0 + 2/17*n**5 + 8/17*n**2 - 8/17*n**4 = 0.
-1, 0, 1, 2
Let i = 14/51 - -542/255. Solve -i*o + 12/5*o**2 - 3/5*o**3 + 0 = 0.
0, 2
Let u(w) be the first derivative of w**4/16 + w**3/6 - w**2/2 - 2*w + 34. Suppose u(r) = 0. What is r?
-2, 2
Let m(t) = -t + 3. Let i be m(3). Let f(y) be the second derivative of 0*y**2 - 1/50*y**5 - 3*y + 0*y**4 + 