3.
4*f*(f + 1)**2
Let o(r) = -r**3 - r**2 - 1. Let h be o(-2). Factor 3*q - q + q**2 - 2*q + q - q**h - q**4.
-q*(q - 1)*(q + 1)**2
Let k(u) be the third derivative of -u**7/350 - u**6/200 - 18*u**2. Factor k(x).
-3*x**3*(x + 1)/5
Let r(x) be the first derivative of 0*x**4 + 0*x**3 + 0*x + 0*x**2 + 1/18*x**6 - 1/15*x**5 - 1. Solve r(l) = 0 for l.
0, 1
Factor -1600*w**2 - 160/3*w**3 - 2/3*w**4 - 320000/3 - 64000/3*w.
-2*(w + 20)**4/3
Suppose -3*d + 5*o + 32 = 0, -5 = 3*d - 2*o - 25. Let z(f) be the first derivative of 7/2*f**2 + 2*f - f**d + 4/3*f**3 - 1. Suppose z(k) = 0. What is k?
-1/2, 2
Suppose d = -5*h + 5*d - 895, -4*h - 710 = -2*d. Let o = -1923/11 - h. Suppose 0 - 4/11*k**2 + 2/11*k**3 + o*k = 0. What is k?
0, 1
Solve -2/7*q**3 + 4/7*q**2 + 0 - 2/7*q = 0 for q.
0, 1
Let q(h) be the second derivative of -5/27*h**4 - 4/27*h**3 - 5/54*h**5 - h + 0 - h**2. Let b(z) be the first derivative of q(z). Let b(j) = 0. Calculate j.
-2/5
Let l be 4/(-6) + (-44)/(-12). Suppose 0 = -2*j + 2*p + 2, -j - 1 = -l*p + p. Determine g so that 4*g**3 + 2*g**4 + j*g**3 - 4*g - 2 - 3*g**3 = 0.
-1, 1
Let z(i) be the first derivative of 5*i**4/4 - 5*i**3/3 - 5*i**2/2 + 5*i - 9. Factor z(m).
5*(m - 1)**2*(m + 1)
Let a(f) be the third derivative of -2*f**2 + 1/6*f**4 + 0*f**3 + 0*f + 0 - 1/30*f**5. Solve a(s) = 0 for s.
0, 2
Let g(d) be the second derivative of -d**4/36 - 2*d**3/9 - d**2/2 - 5*d. Factor g(x).
-(x + 1)*(x + 3)/3
Let z(i) be the second derivative of 5*i**4/24 - i**3/2 + i**2/4 - i. Factor z(u).
(u - 1)*(5*u - 1)/2
Suppose 0 = 3*a - 3*w - 9, -2*a = 5*w + 1 - 0. Factor -6 - 6*u - 3*u + 2*u + 3*u**4 - 2*u + 9*u**3 + 3*u**a.
3*(u - 1)*(u + 1)**2*(u + 2)
Let g(q) be the second derivative of q**7/210 + q**6/60 - q**2/2 + q. Let z(p) be the first derivative of g(p). Factor z(c).
c**3*(c + 2)
Let a be (1*(-1)/(-2)*0)/1. Factor 2/7*h + a + 2/7*h**2.
2*h*(h + 1)/7
Let h(g) = -g + 10. Let a be h(7). Determine x, given that -4*x**5 + 12*x**4 - 2*x**4 - x + x**5 - 17*x**a + 5*x**3 + 6*x**2 = 0.
0, 1/3, 1
Let a(n) be the first derivative of n**7/560 - n**6/240 - 10*n**3/3 - 5. Let t(m) be the third derivative of a(m). Factor t(o).
3*o**2*(o - 1)/2
Suppose 2*k + k = 15. Suppose -k*z = -9 - 6. Factor 0 - 1/4*i**z + 0*i**2 + 0*i.
-i**3/4
Let m(f) be the second derivative of -f**5/80 - 5*f**4/48 - 7*f**3/24 - 3*f**2/8 + 7*f. Factor m(z).
-(z + 1)**2*(z + 3)/4
Let g(i) be the second derivative of i**7/112 - i**6/80 - 3*i**5/32 - 3*i**4/32 - 9*i. Factor g(l).
3*l**2*(l - 3)*(l + 1)**2/8
Factor 0*a**2 + 0*a + 1/3*a**3 + 0.
a**3/3
Suppose 0 = y - 6*y - 30. Let b be ((-2)/(-3))/((-2)/y). Find o, given that -4/5*o + 0 - 81/5*o**3 + 36/5*o**b = 0.
0, 2/9
Let c(m) be the third derivative of m**7/1365 - m**6/390 - m**5/390 + m**4/78 + 2*m**2. Find z, given that c(z) = 0.
-1, 0, 1, 2
Let i(o) = 9*o**2 + 60*o + 24. Suppose 3*u + 2*x - 3 = 4*x, u + 4 = -x. Let r(a) = a**2 + a. Let b(n) = u*i(n) - 6*r(n). What is p in b(p) = 0?
-4, -2/5
Let b(p) = 3*p + 1. Let f be b(1). Factor -2*l**5 + 12*l**f - 18*l**3 - 2*l**5 + 45*l**2 + l**5 - 33*l**2 - 3*l.
-3*l*(l - 1)**4
Determine g, given that 0 - 6/17*g**2 + 4/17*g = 0.
0, 2/3
Let u = 1467889/44 + -33363. Let l = -18/11 - u. Determine s so that s**2 + s + l*s**3 + 0 = 0.
-2, 0
Let u(k) = k**2 + k. Let n be u(0). Let j(t) be the second derivative of -1/8*t**2 - 1/3*t**4 + 1/3*t**3 + t + n. Solve j(w) = 0 for w.
1/4
Suppose -4*t - 10 = t. Let g be (t/6)/(8/(-12)). Factor -3/2*j**4 - 1/2*j**5 - j**3 + j**2 + 3/2*j + g.
-(j - 1)*(j + 1)**4/2
Let b be (1 - 11)*(-3)/8. Let i = 143/36 - b. Find k, given that 2/9*k + 0 - i*k**2 = 0.
0, 1
Let i(q) = q + 6. Let a be i(-3). Let n be (60/50)/(18/20). Factor -n - 8/3*m**2 + 10/3*m + 2/3*m**a.
2*(m - 2)*(m - 1)**2/3
Let d(w) be the second derivative of 3*w**5/20 + 3*w**4/4 + w - 4. Determine f so that d(f) = 0.
-3, 0
Let k be ((-30)/63)/(-2) - 3/(-7). Find b, given that -2/3*b + k*b**2 - 4/3 = 0.
-1, 2
Let o(p) = -2*p**4 + 11*p**3 + 2*p**2 + 11*p - 11. Let t(z) = -z**4 + 6*z**3 + z**2 + 6*z - 6. Let v(f) = -6*o(f) + 11*t(f). Find k, given that v(k) = 0.
-1, 0, 1
Factor 10*y**4 - y**2 - 4*y**3 - 3*y**4 + 4*y**3 - 2*y**3 - 4*y**5.
-y**2*(y - 1)**2*(4*y + 1)
Let j(x) be the second derivative of 54*x**4 + 12*x**3 + x**2 + 25*x. Solve j(i) = 0 for i.
-1/18
Let k = -1/2600 - -111/18200. Let t(l) be the third derivative of 0*l**5 + 0 - 3/200*l**6 + 0*l**3 + 1/40*l**4 + 0*l - k*l**7 - 2*l**2. Factor t(s).
-3*s*(s + 1)**2*(2*s - 1)/5
Let l = 6435/7 - 919. Factor 0*z - 2/7*z**2 + l.
-2*(z - 1)*(z + 1)/7
Suppose 5*v + 7 = 3*f - 1, -3*f = -v + 8. Let c(q) = q + 6. Let y be c(f). Factor -2/7*z**y + 0 - 4/7*z.
-2*z*(z + 2)/7
Factor 5*m**2 - 1/2*m - 2*m**3 - 4*m**4 + 5/2*m**5 - 1.
(m - 1)**3*(m + 1)*(5*m + 2)/2
Let d(c) be the third derivative of c**5/150 + 7*c**4/60 - 8*c**3/15 - 33*c**2. Let d(k) = 0. Calculate k.
-8, 1
Factor 5*t**2 + 25/4*t**4 - 10*t**3 - 5/4*t**5 + 0*t + 0.
-5*t**2*(t - 2)**2*(t - 1)/4
Let w(i) be the third derivative of 0 + 0*i**3 + 7/30*i**5 - 1/6*i**4 + 1/35*i**7 + i**2 + 0*i - 2/15*i**6. Factor w(t).
2*t*(t - 1)**2*(3*t - 2)
Suppose -4*t - t + x = -11, -10 = -4*t + 2*x. Factor 2/7*g + 0 - 2/7*g**t.
-2*g*(g - 1)/7
Let z = 19 - 16. Factor 2*c**5 + 2*c**2 + 4*c**4 - 4*c**z - 6*c**2 + 2*c**5.
4*c**2*(c - 1)*(c + 1)**2
Let v be (3/(-9))/((-4)/6). Factor -1/4*b**2 + v*b - 1/4.
-(b - 1)**2/4
Let r(v) = -7*v**4 + 6*v**3 - 9*v**2 + 5*v. Let d(x) = -6*x**2 - 4*x**2 - 8*x**4 + 10*x + 6*x**3 - 4*x. Let m(j) = 5*d(j) - 6*r(j). Find p, given that m(p) = 0.
0, 1, 2
Let b(w) = w**5 + w**3 + w**2 + 1. Let i(m) = 15*m**5 + 12*m**4 + 30*m**3 + 24*m**2 + 3*m + 12. Let z(j) = -12*b(j) + i(j). Let z(u) = 0. What is u?
-1, 0
Let w(f) be the third derivative of -f**2 - 1/150*f**5 - 1/15*f**3 + 0 - 1/30*f**4 + 0*f. Factor w(z).
-2*(z + 1)**2/5
Let m(p) = -5*p**3 - 16*p**2 - 11*p. Let w(l) = 5*l**3 + 15*l**2 + 10*l. Let u(h) = 5*m(h) + 6*w(h). Factor u(i).
5*i*(i + 1)**2
Let c(s) be the second derivative of 5*s**4/12 - 17*s**3/6 + 3*s**2 + 12*s. What is k in c(k) = 0?
2/5, 3
Let p = 1187/2 + -593. Let p*l**2 + 0 + 1/2*l = 0. What is l?
-1, 0
Let m = -49 + 53. Find g, given that -2/5*g**2 + 0 + 9/5*g**3 - 7/5*g**m + 0*g = 0.
0, 2/7, 1
Let d(y) be the third derivative of -y**5/480 + 5*y**4/192 - y**3/12 - 4*y**2. Determine t, given that d(t) = 0.
1, 4
Factor 1 - 4/3*q + 1/3*q**2.
(q - 3)*(q - 1)/3
Let u = 43 - 38. Factor 0 - 2/5*b**u + 0*b + 0*b**3 - 2/5*b**4 + 0*b**2.
-2*b**4*(b + 1)/5
Suppose 12 = 2*q - 2*t + 4, t = 5*q - 12. Let p be 68/24 + (-1)/2. Factor 5/3*x**q + 0 + p*x**3 - 2/3*x.
x*(x + 1)*(7*x - 2)/3
Let h(j) be the first derivative of -j**5/10 + j**4/3 + 3*j + 4. Let r(x) be the first derivative of h(x). Let r(q) = 0. Calculate q.
0, 2
Let z(i) = -10*i**2 - 27*i + 28. Let v(b) = -52*b**2 - 136*b + 140. Let h(x) = 3*v(x) - 16*z(x). Solve h(y) = 0.
-7, 1
Let c(z) be the first derivative of -2/7*z - 2/21*z**3 + 2/7*z**2 + 3. Factor c(r).
-2*(r - 1)**2/7
Let f(d) be the second derivative of d**8/6720 + d**7/1680 - d**6/1440 - d**5/240 + d**3/3 - 4*d. Let b(j) be the second derivative of f(j). Factor b(p).
p*(p - 1)*(p + 1)*(p + 2)/4
Let q(s) = -2*s**3 - 2*s**2 - 4*s - 4. Let v(j) = j**2 + j. Let f be 2 - (0/(-1) + 3). Let i(l) = f*q(l) - 6*v(l). Factor i(y).
2*(y - 2)*(y - 1)*(y + 1)
Let -18 - 16*i**2 - 146*i**2 + 108*i + 79*i**3 + 2*i**3 - 6 = 0. Calculate i.
2/3
Let b(v) be the third derivative of v**8/588 + 4*v**7/245 + 2*v**6/35 + 8*v**5/105 + 3*v**2. What is g in b(g) = 0?
-2, 0
Let x = -31 - -21. Let y(j) = -j**3. Let l(u) = 12*u**3 + 2*u**2. Let n(q) = x*y(q) - l(q). Factor n(d).
-2*d**2*(d + 1)
Let b be 6/(-18)*1 - 20/(-6). Factor 80/7*w**4 + 34/7*w**b + 0*w + 32/7*w**5 + 0 + 4/7*w**2.
2*w**2*(w + 2)*(4*w + 1)**2/7
Let n = 2338911255/812 + -2880432. Let b = -1/116 + n. Factor 2/7*a**2 + b*a - 4/7*a**3 - 2/7.
-2*(a - 1)*(a + 1)*(2*a - 1)/7
Let s(o) be the second derivative of -o**7/42 - 11*o**6/120 - 9*o**5/80 - o**4/48 + o**3/24 + 6*o. Let s(g) = 0. What is g?
-1, 0, 1/4
Factor -t**2 + t**2 - 2*t**2.
-2*t**2
Let d(r) be the third derivative of r**6/420 + r**5/210 + r**2. Find j such that d(j) = 0.
-1, 0
Let i(h) be the second derivative of -1/84*h**4 + 0*h**2 + 0 - 1/6*h**3 - 1/1260*h**6 - h + 1