et g be (-6)/5*(-70)/21. Let z(n) be the third derivative of -2*n**2 + 0*n - 1/60*n**6 + 0 - 1/15*n**5 + 1/12*n**g + 2/3*n**3. Let z(d) = 0. What is d?
-2, -1, 1
Let k be 0/(2 - 3 - 1). Factor -1/2 + p**2 + k*p - 1/2*p**4 + 0*p**3.
-(p - 1)**2*(p + 1)**2/2
Let n(h) be the third derivative of h**9/13608 - h**7/1890 + h**5/540 + h**3/2 + 4*h**2. Let p(a) be the first derivative of n(a). Factor p(d).
2*d*(d - 1)**2*(d + 1)**2/9
Let x = 31 + -215/7. Let i(g) be the first derivative of 1 + x*g - 9/7*g**2 - 8/7*g**4 + 16/7*g**3. Determine n, given that i(n) = 0.
1/4, 1
Let y(t) = -t**4 - t**3 - t. Let u(v) = 2*v**4 + 7*v**3 - 2*v**2 - v + 3. Let r(i) = -u(i) - 3*y(i). Factor r(n).
(n - 3)*(n - 1)**2*(n + 1)
Factor 0*n - 2/9*n**3 + 0 + 4/9*n**4 + 0*n**2 - 2/9*n**5.
-2*n**3*(n - 1)**2/9
Let r(s) = s**3 - 4*s**2 - 7*s + 7. Let v be r(6). Factor -35*d + v*d - 3*d**2 + d**2.
-2*d*(d - 1)
Factor 0*w + 0 - 2/3*w**2.
-2*w**2/3
Let w(h) be the second derivative of -h**7/126 + h**6/90 + h**5/60 - h**4/36 - 2*h. Solve w(l) = 0.
-1, 0, 1
Let o(h) = -7*h**3 + 4*h**2 + 2*h. Let l(r) = 22*r**3 - 13*r**2 - 7*r. Let x = 3 - 17. Let s(n) = x*o(n) - 4*l(n). Factor s(c).
2*c**2*(5*c - 2)
Let i(h) be the first derivative of -2*h**6/21 - 4*h**5/7 - 9*h**4/7 - 4*h**3/3 - 4*h**2/7 - 20. Suppose i(p) = 0. What is p?
-2, -1, 0
Let 6*v + 22*v**4 - 22*v**3 + 0*v**3 - v**2 - 6*v**5 - 2*v + 3*v**2 = 0. Calculate v.
-1/3, 0, 1, 2
Let r(d) = -d**3 + d**2 + 8*d. Let k(l) = l. Let u(p) = 6*k(p) - r(p). Factor u(i).
i*(i - 2)*(i + 1)
Factor 2*v**2 - 3*v**4 + 3*v**2 - 5*v**3 + 13*v**5 - 8*v**5 - 2*v**4.
5*v**2*(v - 1)**2*(v + 1)
Let m(l) be the third derivative of -l**8/80640 + l**7/10080 + l**6/960 - 2*l**5/15 - 3*l**2. Let g(u) be the third derivative of m(u). Let g(c) = 0. What is c?
-1, 3
Solve 1/5*q**2 + 4/5*q + 4/5 = 0 for q.
-2
Let m(p) be the second derivative of 1/54*p**4 - 4/27*p**3 + 1/3*p**2 + 0 - 4*p. Factor m(o).
2*(o - 3)*(o - 1)/9
Suppose -3*i - 4*o = 2, -10 = -3*i + o + o. Solve 3*g**i - 4*g**2 - g - 2 - 2*g + 3*g**2 = 0.
-1/2, 2
Factor 14*i + 3*i**3 + 10*i + 15*i**2 + 12 + 0.
3*(i + 1)*(i + 2)**2
Let f = -3 - -9. Suppose o = -f*o. Factor 2/5*m**2 - 4/5*m + o.
2*m*(m - 2)/5
Let m(v) = 20*v**5 + 18*v**4 + 6*v**3 - 10*v**2 - 6. Let s(o) = o**5 - o**4 - o**2 - 1. Let j(y) = 2*m(y) - 12*s(y). Factor j(b).
4*b**2*(b + 1)**2*(7*b - 2)
Let t(k) be the second derivative of -k**6/120 - k**5/80 + k**4/16 + 5*k**3/24 + k**2/4 + 3*k. Let t(r) = 0. What is r?
-1, 2
Factor -15*v + 3*v**2 + 1887 - 1887.
3*v*(v - 5)
Let x be 4/(-12) + 64/3. Factor -x*f**2 - 39*f**4 + 3*f + 10*f**5 + 0*f + 45*f**3 + 2*f**5.
3*f*(f - 1)**3*(4*f - 1)
Suppose -4*o = -2*y - 2*y - 20, -5*y - 22 = -4*o. Let t be -2 + (1 - 0 - -1). Factor 2/7*i**o + t + 2/7*i**2 + 0*i.
2*i**2*(i + 1)/7
Let j(x) = -16*x**4 + 21*x**3 + 15*x**2 - 9*x - 9. Let c(o) = -3*o**4 + 4*o**3 + 3*o**2 - 2*o - 2. Let n(a) = -22*c(a) + 4*j(a). Suppose n(h) = 0. What is h?
-1, 2
Let y(v) be the second derivative of -v**7/168 + v**6/120 + 3*v**5/80 - 5*v**4/48 + v**3/12 + 4*v. Find b, given that y(b) = 0.
-2, 0, 1
Let b(u) = 2*u**3 - 12*u**2 + 4*u. Let z(h) = -4*h**3 + 23*h**2 - 9*h. Let q(m) = 7*b(m) + 4*z(m). Factor q(t).
-2*t*(t - 2)**2
Let r(m) = -4*m**5 + 5*m**4 - 11*m**3 - 7*m**2 + 7*m. Let u(k) = -6*k**5 + 8*k**4 - 16*k**3 - 10*k**2 + 10*k. Let g(p) = -7*r(p) + 5*u(p). Factor g(w).
-w*(w - 1)**3*(2*w + 1)
Suppose 3*t = 54 - 12. Suppose -2 = 4*r - t. Let 2/3*m**r + 1/3*m**2 + 0 - 1/3*m = 0. What is m?
-1, 0, 1/2
Let y(p) be the third derivative of -p**5/120 + p**4/16 + p**3/3 + 7*p**2. Suppose y(v) = 0. Calculate v.
-1, 4
Let f be -3*(12/(-18) + (-8)/(-15)). Suppose 0*t + f*t**2 + 0 + 2/5*t**3 = 0. Calculate t.
-1, 0
Let p be (-10)/6 - 40/(-6). Let b(y) be the second derivative of 4*y + 3/40*y**p + 0*y**2 + 0 - 1/8*y**4 - 1/60*y**6 + 1/12*y**3. Factor b(g).
-g*(g - 1)**3/2
Let g = 403/6 + -67. Let w(k) be the second derivative of k**2 - k - g*k**4 + 0*k**3 + 0. Solve w(c) = 0 for c.
-1, 1
Let b(z) = -6*z**3 + 2*z**2 - 2*z + 2. Let a(d) = -2*d**3 - 1 + 3*d**2 + 1 + 2 - 5*d**3 - 3*d. Let v(p) = 4*a(p) - 5*b(p). Solve v(r) = 0 for r.
-1, 1
Let j(w) be the third derivative of w**7/5040 - w**4/12 - 4*w**2. Let x(l) be the second derivative of j(l). Factor x(y).
y**2/2
Let g(s) be the third derivative of -s**7/560 - s**6/160 + 20*s**2. Factor g(a).
-3*a**3*(a + 2)/8
Let h(k) = 3. Let s(y) = 4. Let x(o) = 3*h(o) - 2*s(o). Suppose -3*w + 8 = -5*w. Let c(p) = -14*p**2 - 10*p. Let d(l) = w*x(l) - c(l). Factor d(q).
2*(q + 1)*(7*q - 2)
What is t in 3/7 + 75/7*t**2 + 30/7*t = 0?
-1/5
Let c be 16*(-1 - 2)/(-12). Suppose w = 3*w + c, 5*m + 5*w = 200. Solve -m*v**3 + 147/5*v**4 - 9/5*v**2 + 12/5 + 12*v = 0.
-2/7, 1
Suppose -18 = -2*k - y, -y = 4*k + 3*y - 36. Let x(j) = -3*j**2 + 3*j. Let t(w) = 7*w**2 - 7*w. Let z(v) = k*x(v) + 4*t(v). Factor z(p).
p*(p - 1)
Let r(w) = -3*w**5 - w**4 + 7*w**3 + w**2 - 4*w + 5. Let j(a) = a**5 - a**4 - a**3 + a**2 - 1. Let y(c) = 5*j(c) + r(c). Find h such that y(h) = 0.
-1, 0, 1, 2
Let r(u) = -u**2 + 4*u + 4. Let l(m) = m**2 - 5*m - 5. Let d(v) = 4*l(v) + 5*r(v). Suppose d(k) = 0. Calculate k.
0
Let i(b) = b**2 + 11*b + 10. Let z be i(-10). Let s(h) be the second derivative of z*h**3 + 0*h**2 + 0*h**4 + 0*h**5 - 1/20*h**6 + 0 + h. Solve s(d) = 0 for d.
0
Let a(b) be the first derivative of 3*b**4/20 + b**3/5 - 3*b**2/10 - 3*b/5 + 7. Factor a(i).
3*(i - 1)*(i + 1)**2/5
Let d(m) = -2*m**3 - 8*m**2 + 4*m + 10. Let n(x) = -x**3 - 8*x**2 + 4*x + 11. Let r(t) = -3*d(t) + 2*n(t). Let r(h) = 0. Calculate h.
-2, -1, 1
Let w(m) be the third derivative of 0 + 0*m**3 - m**2 - 1/112*m**8 - 2/35*m**7 + 0*m - 3/20*m**6 - 1/5*m**5 - 1/8*m**4. Factor w(g).
-3*g*(g + 1)**4
Suppose o = 6*o - 10. Let r = 4 - o. Solve 4*i**r - 10*i**2 + 16*i**4 - 3*i**3 - 7*i**4 = 0 for i.
-2/3, 0, 1
Let c = 6 - 4. Factor -3*s**4 + 12*s + 9*s**3 + 5*s**3 + 4*s**c - 22*s**2 - 3 - 2*s**3.
-3*(s - 1)**4
Let t = 12/55 + -161/990. Let z(u) be the first derivative of 2/9*u**3 + 2 + 4/9*u - 2/45*u**5 - 5/9*u**2 + t*u**4. Determine k so that z(k) = 0.
-2, 1
Let u(k) be the third derivative of -1/30*k**6 + 0 + 1/15*k**7 + 1/3*k**3 + 0*k + 1/42*k**8 - 4/15*k**5 - 9*k**2 - 1/6*k**4. What is h in u(h) = 0?
-1, 1/4, 1
Let n(x) be the third derivative of x**6/660 + x**5/165 - 2*x**4/33 - 39*x**2. Find u such that n(u) = 0.
-4, 0, 2
Let j(y) = -19*y + 2. Let m be j(-1). Let k(w) = -8*w**5 + 2*w**4 - 2*w**2 + 8*w. Let r(v) = v**5 - v. Let n(p) = m*r(p) + 3*k(p). Factor n(x).
-3*x*(x - 1)**3*(x + 1)
Let c = 10 - 7. Determine t so that 3*t**2 + 6*t**2 - 2*t**c + 4*t**3 - 5*t**2 + 2*t = 0.
-1, 0
Let w = -123 - -619/5. Factor 0 - 2*i**3 + w*i - 6/5*i**2.
-2*i*(i + 1)*(5*i - 2)/5
Let k(a) be the third derivative of -a**5/60 + a**2. Let k(f) = 0. Calculate f.
0
Let j be 36/20 - 3/(-15). Determine t so that -16*t - 4*t + 6 + 3 - 5 + 25*t**j = 0.
2/5
Suppose -z = m + 2*m - 3, -3*z + 9 = m. Let j be 21/12*(-10)/(-35). Suppose 1/2*g - j*g**z - g**2 + 1 = 0. What is g?
-2, -1, 1
Suppose -3*m = -0*m + 15, -l + 4*m + 22 = 0. Factor -4*o**2 - 2*o**l + 3*o**3 + 2*o + o.
3*o*(o - 1)**2
Let d(k) be the second derivative of -k**8/3360 + k**7/140 - 3*k**6/40 + 9*k**5/20 + 5*k**4/12 - 2*k. Let g(v) be the third derivative of d(v). Factor g(i).
-2*(i - 3)**3
Let o(k) be the second derivative of k**6/15 + k**5/10 - k**4/6 - k**3/3 - 3*k. Factor o(s).
2*s*(s - 1)*(s + 1)**2
Suppose -2 = 5*l - 12. Determine o so that 32/9*o**3 - 10/9*o**l - 2*o**4 + 0 - 4/9*o = 0.
-2/9, 0, 1
Suppose 14/3*i**5 + 8/3*i**2 + 18*i**3 + 52/3*i**4 + 0 - 8/3*i = 0. What is i?
-2, -1, 0, 2/7
Let k = -3/55 + 5/11. Suppose 15*q - 51 - 9 = 0. Find b, given that 2/5*b**5 - k*b**q + 0*b**3 + 0*b**2 + 0 + 0*b = 0.
0, 1
Let v(x) = -5*x**2 - 3*x - 2. Let g(q) = -q**2 - q - 1. Let r(y) = 4*g(y) - v(y). Factor r(n).
(n - 2)*(n + 1)
Suppose 0 = 3*r + 3*q - 4*q - 5, 2*r + 5*q = -25. Let v(x) be the third derivative of -1/80*x**5 - 1/48*x**4 + r*x - 3*x**2 + 0 + 0*x**3. Factor v(i).
-i*(3*i + 2)/4
Let q(c) be the third derivative of -c**5/270 - c**4/108 + 8*c**2. Determine f, given that q(f) = 0.
-1, 0
Let r = 22 - 24. Let u be (-6)/r + 2/(-5). Let 6*f**2 + 3/5*f**5 + 32/5*f**3 + 2/5 + 16/5*f**4 + u*f = 0. What is f?
-2, -1,