et u(n) be the second derivative of -1/4*n**2 - 2*n - 1/20*n**5 + 1/24*n**3 - 1/30*n**6 + m*n**4 + 1/56*n**7 + 0. Factor u(g).
(g - 1)**3*(g + 1)*(3*g + 2)/4
Let t(k) be the first derivative of -1 + 0*k**2 + 1/5*k - 1/15*k**3. Factor t(a).
-(a - 1)*(a + 1)/5
Let s(w) = w**3 + 4*w**2 + 2*w - 2. Let o be s(-2). Factor 0*j - 1/5*j**o + 1/5.
-(j - 1)*(j + 1)/5
Let r(c) be the first derivative of 0*c - 1/8*c**4 - 1/3*c**3 + 0*c**2 + 4. Factor r(m).
-m**2*(m + 2)/2
Let k = -129328 - -903857/7. Let p = 207 + k. Suppose p*j**2 - 4/7*j - 2*j**5 + 0 + 18/7*j**3 - 10/7*j**4 = 0. Calculate j.
-1, 0, 2/7, 1
Let g(i) be the first derivative of -1/17*i**4 + 0*i**3 - 8 + 0*i**2 + 0*i + 2/85*i**5. Determine x, given that g(x) = 0.
0, 2
Let f(a) = 6*a + 86. Let z be f(-14). Let h(i) be the first derivative of -3 - 1/20*i**5 - 1/4*i + 1/6*i**3 + 0*i**z + 0*i**4. Find x such that h(x) = 0.
-1, 1
Let s(r) = r**5 - r**4 + r**3 - r**2 - r. Let v(t) = -9*t**5 + 2*t**4 - 4*t**3 + 10*t**2 + 7*t. Let b(c) = -6*s(c) - v(c). Factor b(f).
f*(f - 1)*(f + 1)**2*(3*f + 1)
Let d(a) = 2*a**2 + 2*a - 1. Let y be d(1). Suppose 3*x - 35 = -5*c - 6, y*x = 4*c - 7. Let -2*p**3 - 1 + p**4 + 0*p**4 + 0*p**x + 2*p = 0. What is p?
-1, 1
Let w(r) be the third derivative of -r**6/180 + r**5/30 - r**3/2 + 4*r**2. Let q(t) be the first derivative of w(t). Factor q(f).
-2*f*(f - 2)
Factor 2/3*o + 0 + 1/6*o**3 + 2/3*o**2.
o*(o + 2)**2/6
Let h(c) be the first derivative of 10/3*c**3 - 3 + 0*c - 3/2*c**4 - 2/5*c**5 + 1/3*c**6 - 2*c**2. Determine a, given that h(a) = 0.
-2, 0, 1
Determine o so that 0*o + 15*o - 3*o + 12*o**2 + 3*o**3 = 0.
-2, 0
Let b(y) be the third derivative of -y**7/420 - y**6/240 + 15*y**2. Factor b(r).
-r**3*(r + 1)/2
Let a = 23 - 16. Find i, given that -i**3 - a*i**5 + 5*i**5 + 3*i**5 = 0.
-1, 0, 1
Let o be -2 - (0 - (2 + 11)). Suppose -g + 5*k - o = 6, 2*g = -3*k + 18. Factor -2*i**g + i**2 - i**3 + 4*i**3.
i**2*(i + 1)
Let o(c) = 2*c**2 + 3*c. Let l(x) = x. Let j(z) = -5*l(z) + o(z). Find w, given that j(w) = 0.
0, 1
Factor 4*a**2 - 10 - 3*a**2 + 0*a + 11 - 2*a.
(a - 1)**2
Suppose -4*m + 4 = -2*m. Let 228*j - 266*j**3 + 6 + 277*j**m - 9 + 14 + 49*j**4 + 25 = 0. What is j?
-2/7, 3
Factor 0 - 4/15*x + 2/15*x**3 - 2/15*x**2.
2*x*(x - 2)*(x + 1)/15
Let a be -1*15/3*2. Let g be (-2)/5 + (-24)/a. Let -1 - 3*c**4 + 8*c + 9*c**3 - 2*c - 5*c**3 - 12*c**g + 6*c**3 = 0. Calculate c.
1/3, 1
Let g be (-4)/(-22) + (-28)/(-693). Factor 0*p**3 + 2/9*p**4 - 4/9*p**2 + g + 0*p.
2*(p - 1)**2*(p + 1)**2/9
Let t(q) be the first derivative of -q**6/120 - q**5/36 - q**4/36 + 3*q**2 - 10. Let s(v) be the second derivative of t(v). Let s(r) = 0. What is r?
-1, -2/3, 0
Let c(x) be the third derivative of -x**8/588 - 4*x**7/735 - x**6/210 - 9*x**2. Factor c(i).
-4*i**3*(i + 1)**2/7
Let v = -527/6 - -88. Let n(d) be the first derivative of -1/9*d**3 + v*d**2 - 2 + 1/3*d - 1/12*d**4. Factor n(i).
-(i - 1)*(i + 1)**2/3
Let h(p) be the first derivative of -p**4/2 + 4*p**3/3 - p**2 - 8. Determine n so that h(n) = 0.
0, 1
Suppose -9 = -4*b - 3*p, -2*b + 1 = 2*p - 5. Let x(k) be the second derivative of 0 + b*k**3 + 0*k**5 + 0*k**2 + 0*k**4 - 1/120*k**6 - 3*k. Factor x(y).
-y**4/4
Let s(d) be the second derivative of 1/135*d**6 - 3*d + 0 + 0*d**2 + 1/45*d**5 - 2/27*d**3 - 1/54*d**4. Let s(g) = 0. What is g?
-2, -1, 0, 1
Let t(q) be the second derivative of 0 - 1/30*q**5 + 2/3*q**2 + 1/9*q**3 - 1/9*q**4 + 9*q. Factor t(w).
-2*(w - 1)*(w + 1)*(w + 2)/3
Let u = 1 - -1. Find n such that 0*n**u - 3*n**2 + 2*n + 2*n - n = 0.
0, 1
Let a(t) = 13*t**2 - 12*t - 4. Let c(k) = -105*k**2 + 96*k + 33. Let o(w) = -33*a(w) - 4*c(w). Factor o(z).
-3*z*(3*z - 4)
Let u(m) be the first derivative of -3*m**4/4 + m**3 + 3*m**2/2 - 3*m + 9. Factor u(n).
-3*(n - 1)**2*(n + 1)
Let v(x) be the second derivative of x**4/6 - 4*x**2 - 7*x. Find i such that v(i) = 0.
-2, 2
Factor 1 + 14*r**2 + 67*r**2 + 36*r + 3.
(9*r + 2)**2
Suppose -3*c + 24 = -2*k + 6*k, 5*c + 3*k = 29. Let f be 3 - (3 + c/(-14)). Let -2/7*d + 2/7*d**3 - f*d**2 + 0 + 2/7*d**4 = 0. Calculate d.
-1, 0, 1
Let k(p) be the third derivative of -8/45*p**5 - 2/9*p**3 - 1/4*p**4 - 2/105*p**7 + 0*p + 4*p**2 - 1/504*p**8 + 0 - 7/90*p**6. Factor k(l).
-2*(l + 1)**4*(l + 2)/3
Let h(g) = -2*g**2 - 4*g + 6. Let u(i) = -6*i**2 - 12*i + 18. Let l(n) = 10*h(n) - 3*u(n). Suppose l(x) = 0. What is x?
-3, 1
Let j(a) be the first derivative of a**3/12 - a/4 - 2. Find d, given that j(d) = 0.
-1, 1
Let g be 1/2*2/3. Let q = -276 - -829/3. Let -2/3*o - q - g*o**2 = 0. What is o?
-1
Let q(b) be the second derivative of -b**6/6 - 3*b**5/2 - 25*b**4/12 + 21*b + 1. What is i in q(i) = 0?
-5, -1, 0
Let w(l) be the third derivative of l**7/70 + 7*l**6/120 + l**5/12 + l**4/24 - 5*l**2. Find q such that w(q) = 0.
-1, -1/3, 0
Let m be (3 + -6)*10/(-105). Factor 6/7 + m*p**2 + 8/7*p.
2*(p + 1)*(p + 3)/7
Let r = -173/210 + 6/7. Let b(x) be the third derivative of 2*x**2 + 1/24*x**4 - r*x**5 + 0*x + 1/120*x**6 + 0 + 0*x**3. Find l, given that b(l) = 0.
0, 1
Find k, given that -3/7*k - 10/7 + 1/7*k**2 = 0.
-2, 5
Suppose 45*d**2 + 349*d**4 - 20*d + 351*d**4 - 695*d**4 - 30*d**3 = 0. What is d?
0, 1, 4
Factor 16*b - 2*b + 5*b**2 + 10 + b.
5*(b + 1)*(b + 2)
Let p = -45 - -64. Let r be p/4 - (-3)/12. Let -r*w + 0*w + 3*w**2 + 10 - 7*w - 1 = 0. Calculate w.
1, 3
Determine w, given that -2/5*w - 2/5*w**4 + 2/5*w**3 + 2/5*w**2 + 0 = 0.
-1, 0, 1
Let q(w) = 4*w**3 + 6*w**2 + 10*w. Let l(y) = y**3 - y**2 + y. Let k(h) = -4*l(h) + 2*q(h). Factor k(s).
4*s*(s + 2)**2
Solve -7*n - 16*n**4 - 18*n + 10 + 5*n + 4*n**5 + 16*n**3 - 2 + 8*n**2 = 0.
-1, 1, 2
Let k be (-2 - 13/(-5))*5. Let v = 6 - k. Find i such that 2*i**2 + 2*i**5 + 2*i**v + i**5 - 2*i**4 - 5*i**5 = 0.
-1, 0, 1
Suppose 4*f + f = 150. Factor -29*d**3 + 10*d**2 + f*d + 18 - d**2 + 31*d**3 + 5*d**2.
2*(d + 1)*(d + 3)**2
Let s(z) be the first derivative of 6*z + 0*z**3 - 4 + 9/2*z**2 - 3/4*z**4. Solve s(j) = 0.
-1, 2
Let j(y) = 7*y**2 - 11*y + 1. Let h be (2/(6/(-9)))/(-1). Let n(p) = 13*p**2 - 21*p + 3. Let l(v) = h*n(v) - 5*j(v). Suppose l(r) = 0. What is r?
1
Let x(z) = -12*z**3 + 8*z**2 - 12*z + 16. Let c(b) = 4*b**3 - 3*b**2 + 4*b - 5. Let s(m) = 16*c(m) + 5*x(m). Factor s(n).
4*n*(n - 1)**2
Let j = -11 + 15. Suppose -j*k + 5*k = 2. Solve -3*d**2 - d**k + 2*d**4 + 2 + 0*d**2 = 0 for d.
-1, 1
Let m be (-16)/12 - (2 + -4). Let g be 4/(-2)*((-22)/(-6) - 4). What is q in m*q - 2/3*q**3 + g*q**2 + 0 - 2/3*q**4 = 0?
-1, 0, 1
Factor -1/2*o**2 + 7/2 + 3*o.
-(o - 7)*(o + 1)/2
Let c(w) be the third derivative of -3*w**2 + 1/240*w**5 + 0*w**3 + 0 - 1/96*w**4 + 0*w. Determine j, given that c(j) = 0.
0, 1
Let b = 187 - 3926/21. Let m(t) be the second derivative of 0*t**2 + b*t**3 + 0 - 2*t - 1/21*t**4 + 1/70*t**5. Factor m(i).
2*i*(i - 1)**2/7
Suppose 0 = -3*v + 2*v + 5. Let a(x) = 2*x - 4. Let j be a(3). Factor -5*r**3 + v*r**3 - j*r**5.
-2*r**5
Let r(h) be the second derivative of 0 - 1/8*h**2 + 1/48*h**4 - 3*h - 1/80*h**5 + 1/24*h**3. Factor r(n).
-(n - 1)**2*(n + 1)/4
Let w(q) be the third derivative of q**7/630 + q**6/360 - q**5/180 - q**4/72 + 10*q**2. Factor w(n).
n*(n - 1)*(n + 1)**2/3
Let x(a) be the third derivative of -a**7/630 + a**6/540 + a**5/135 - a**4/108 - a**3/54 + 9*a**2. Solve x(r) = 0 for r.
-1, -1/3, 1
Let p(k) be the third derivative of 0*k**3 + 0 + 0*k**4 + 0*k + 1/120*k**6 + 1/30*k**5 - 2*k**2. Suppose p(s) = 0. Calculate s.
-2, 0
Let m be (7/(-21))/(2/(-20)). Solve 0 + 0*i - 2*i**4 - 4/3*i**2 - m*i**3 = 0 for i.
-1, -2/3, 0
Let a be -1*1*2/(-6). Suppose 21 - 9 = 4*d. Solve -1/3*z**4 + 0*z**d + 0*z + 0 + a*z**2 = 0 for z.
-1, 0, 1
Let z = 38 + -38. Let a(b) be the third derivative of z - 1/105*b**7 + 0*b**3 - 1/20*b**6 - 1/12*b**4 + b**2 + 0*b - 1/10*b**5. Factor a(o).
-2*o*(o + 1)**3
Let v(q) be the first derivative of -q**2/2 + 7*q - 3. Let s be v(5). Factor 2*w**3 - 4*w + 0*w + 0*w + 2*w**s.
2*w*(w - 1)*(w + 2)
Let x = 1 + 5. What is l in 45*l - 7*l**2 - 18 + x*l + l**2 - 9*l**2 = 0?
2/5, 3
Find o such that -9*o - 13*o**2 + 12*o**2 + 4*o**2 = 0.
0, 3
Let -25*b + 15*b - 2*b**4 - 12*b**2 - 3 + b**4 + 4*b**3 - 10*b**3 = 0. What is b?
-3, -1
Let x(c) be the third derivative of -5*c**2 - 1/75*c**5 + 1/20*c**4 + 0*c + 2/15*c**3 + 0 - 1/10