1
Let g(k) be the second derivative of k - 1/15*k**5 - 1/3*k**2 + 4/63*k**7 + 0 + 4/9*k**4 - 2/9*k**3 - 7/45*k**6. Determine q so that g(q) = 0.
-1, -1/4, 1
Let z = 474 - 3314/7. Let 0*t + 0 + z*t**3 + 0*t**2 - 2/7*t**5 - 2/7*t**4 = 0. Calculate t.
-2, 0, 1
Let b(y) = 2*y**3 + 2*y**2 - 1. Let u be b(1). Factor -25*k**3 + 9*k**4 + 22*k**u + 3*k - 10*k**2 + k**2.
3*k*(k - 1)*(k + 1)*(3*k - 1)
Let c(m) = m**2 - 3*m + 3. Let o be c(3). Suppose -o*x + 11 = -1. Let 9*y**3 - x*y**4 - 2*y**4 - 6*y**2 + 3*y**4 = 0. Calculate y.
0, 1, 2
Let z = 1258/7 - 180. Let d = 1/21 - z. Let -d*s + 0 - 1/3*s**2 = 0. Calculate s.
-1, 0
Solve 11 - 2*i - i**2 - 11 = 0.
-2, 0
Let g(m) be the first derivative of -1/3*m**3 + 0*m**2 + 1/4*m**4 + 0*m + 3. Factor g(o).
o**2*(o - 1)
Let 2/3*d**3 - 20/3*d**2 - 64/3 + 64/3*d = 0. What is d?
2, 4
Let p(t) be the third derivative of t**8/112 + 2*t**7/35 + t**6/10 - t**5/10 - 5*t**4/8 - t**3 + 12*t**2. Factor p(w).
3*(w - 1)*(w + 1)**3*(w + 2)
Let v(n) be the third derivative of n**5/120 - n**4/12 - 5*n**3/12 - 9*n**2. Determine z, given that v(z) = 0.
-1, 5
Let j = -274 - -276. Suppose -1/5*l**4 + 0*l - 1/5 + 2/5*l**j + 0*l**3 = 0. Calculate l.
-1, 1
Let d = 35 + -33. Factor -4/5*o + 2/5 + 2/5*o**d.
2*(o - 1)**2/5
Find o, given that -o**5 - o**3 - 8*o**4 + 5*o**4 - 2*o**3 - o**2 = 0.
-1, 0
Let k(v) be the second derivative of 2/21*v**4 - 5*v + 0 - 2/105*v**6 - 2/7*v**2 - 2/35*v**5 + 2/21*v**3 + 2/147*v**7. Let k(a) = 0. Calculate a.
-1, 1
Let u(o) be the third derivative of -o**8/3360 - o**4/4 - 3*o**2. Let y(s) be the second derivative of u(s). Find j such that y(j) = 0.
0
Suppose l = 5*l + 100. Let z be l/10*8/(-35). Solve 2/7*y + 0 + 2/7*y**3 + z*y**2 = 0 for y.
-1, 0
Suppose 3*c - 28 = -b, 5*b - c - 60 = -0*b. Let p = -37/3 + b. Determine w, given that -p - 1/3*w**2 - w = 0.
-2, -1
Let w(b) be the first derivative of b**7/210 + b**6/40 + b**5/20 + b**4/24 + 3*b**2 - 9. Let i(p) be the second derivative of w(p). Factor i(z).
z*(z + 1)**3
Let p(v) be the second derivative of -1/14*v**4 + 0*v**3 + 4/7*v**2 + 2*v + 0 + 1/70*v**5. Factor p(z).
2*(z - 2)**2*(z + 1)/7
Let d(p) = p**4 - 5*p**3 - 3*p**2 - 3*p + 3. Let s(w) = w**4 - 4*w**3 - 2*w**2 - 2*w + 2. Let m(j) = 4*d(j) - 6*s(j). Let m(k) = 0. What is k?
0, 2
Factor 0 - 2/5*d**3 - 2/5*d**4 + 2/5*d + 2/5*d**2.
-2*d*(d - 1)*(d + 1)**2/5
Let r(u) be the third derivative of -1/180*u**6 - 2*u**2 + 0*u + 0*u**3 + 1/90*u**5 + 0 + 0*u**4. Factor r(c).
-2*c**2*(c - 1)/3
Let z(i) = -i**5 - i**3 - i**2. Let f(k) = 12*k**5 - 66*k**4 + 68*k**3 - 36*k**2 + 4*k. Let l(v) = f(v) - 6*z(v). Determine a so that l(a) = 0.
0, 1/3, 1, 2
Let v(f) = f**3 - 5*f**2 + 7*f - 10. Let i be v(4). Suppose -2/7*w**i + 0 + 2/7*w = 0. Calculate w.
0, 1
Let t(m) be the first derivative of m**4/7 + 4*m**3/7 - 16*m/7 - 7. Factor t(x).
4*(x - 1)*(x + 2)**2/7
Suppose 3 + 0 = -w. Let y be (w - 0)*4/(-6). Let y*d + d + d**2 - 6*d + 4*d = 0. What is d?
-1, 0
Let q be (46/(-44) + -22 + 23)*-20. Factor 0 + 4/11*z + 8/11*z**3 - q*z**2 - 2/11*z**4.
-2*z*(z - 2)*(z - 1)**2/11
Let u(g) be the third derivative of -4*g**7/455 + 23*g**6/780 - g**5/30 + g**4/78 + 3*g**2. Suppose u(d) = 0. What is d?
0, 1/4, 2/3, 1
Let l(a) = -2*a**2 - 2*a + 2. Let k(p) = 6*p**2 + 6*p - 7. Let t = 15 + -29. Let c(n) = t*l(n) - 4*k(n). Suppose c(z) = 0. Calculate z.
-1, 0
Let x(h) be the first derivative of 0*h**2 + 0*h**3 + 0*h + 2/15*h**5 - 2 + 0*h**4. Suppose x(i) = 0. Calculate i.
0
Let b = -40 + 40. Let s(y) be the third derivative of -y**2 - 1/240*y**5 - 1/240*y**6 + 0*y**3 - 1/840*y**7 + b*y**4 + 0*y + 0. Factor s(j).
-j**2*(j + 1)**2/4
Let x be 27/(-36) - (-142)/40. Let y = 207 - 1031/5. Let 0 - x*b**4 + 4/5*b**5 + 14/5*b**3 + 0*b - y*b**2 = 0. Calculate b.
0, 1/2, 1, 2
Let b(y) be the third derivative of 0*y - 3/5*y**4 + 1/5*y**5 - y**2 + 8/15*y**3 - 7/300*y**6 + 0. Let b(v) = 0. Calculate v.
2/7, 2
Let v(h) be the second derivative of 0*h**2 - 1/15*h**3 + 0 + 4*h - 1/30*h**4. What is a in v(a) = 0?
-1, 0
Suppose 5*m - 2*r + 10 = 3*r, -5*m = 5*r - 10. Let u(p) be the first derivative of -1 + m*p**2 + 1/16*p**4 + 1/12*p**3 + 0*p. Solve u(v) = 0.
-1, 0
Let 2/9*h**2 + 0 - 4/9*h = 0. What is h?
0, 2
Let i(y) be the first derivative of -2*y**3/15 + 3*y**2/5 + 4*y - 23. Solve i(b) = 0.
-2, 5
Let o = 8 - 5. Let k(x) be the second derivative of 1/21*x**o - 1/21*x**4 - x + 1/70*x**5 + 0 + 0*x**2. Factor k(d).
2*d*(d - 1)**2/7
Let p(w) be the first derivative of w**5/5 + 5*w**4/4 + 8*w**3/3 + 2*w**2 + 8. Factor p(g).
g*(g + 1)*(g + 2)**2
Solve -20*o**2 + 4 - 8 + 4 + 20*o**3 - 5*o**4 = 0 for o.
0, 2
Let t(p) be the second derivative of -p**7/147 + p**5/70 - 14*p. Factor t(f).
-2*f**3*(f - 1)*(f + 1)/7
Let x(k) be the third derivative of -k**8/1176 - k**7/147 - k**6/42 - k**5/21 - 5*k**4/84 - k**3/21 + 4*k**2. Factor x(n).
-2*(n + 1)**5/7
Factor -4/7 + 4/7*x**4 + 2*x - 2/7*x**5 + 4/7*x**3 - 16/7*x**2.
-2*(x - 1)**4*(x + 2)/7
Let p = 28 + -21. Let l(f) be the third derivative of 2*f**2 + 0*f**3 + 0*f + 0*f**4 + 1/504*f**8 + 0*f**5 + 1/180*f**6 + 2/315*f**p + 0. Factor l(t).
2*t**3*(t + 1)**2/3
Let i(m) = -5*m**4 - 9*m**3 - m**2 + 9*m + 5. Let g(f) = -f**3 + f**2 + f. Let c(v) = -g(v) - i(v). Suppose c(u) = 0. What is u?
-1, 1
Factor 0 + 0*z - 3/4*z**2 + 3/4*z**3.
3*z**2*(z - 1)/4
Let q be (-4 - -3)*1*1/(-5). Factor 0*i + q*i**2 + 0.
i**2/5
Let i(z) = z**2 + 6. Let t be i(3). Let c = t - 15. Solve k**2 - k**3 + 1/3*k**4 + c - 1/3*k = 0.
0, 1
Let s(z) be the second derivative of 3*z**8/80 + z**7/280 - z**6/60 + z**3/3 + 3*z. Let b(w) be the second derivative of s(w). Factor b(t).
3*t**2*(3*t + 1)*(7*t - 2)
Suppose 3 - c**5 + 53*c**3 - 12*c**2 - 5*c**5 - 47*c**3 + 9*c**4 = 0. What is c?
-1, -1/2, 1
Let k(h) = -h + 2. Let u be k(-2). Suppose -u*v + 5*m + 3 + 3 = 0, -2*m = 4*v - 20. Factor -v + 3 + 0*t - 2*t - t**2.
-(t + 1)**2
Let p(n) be the third derivative of 5*n**8/336 + 3*n**7/35 + n**6/10 - 2*n**5/15 + 16*n**2. Find h such that p(h) = 0.
-2, 0, 2/5
Let f(j) be the second derivative of 2/135*j**6 + 0*j**3 + 0 + 0*j**4 - j + 0*j**2 + 0*j**5 + 1/21*j**7. Factor f(c).
2*c**4*(9*c + 2)/9
Let z(i) be the second derivative of -i**4/3 - 2*i**3/3 - 10*i. Factor z(c).
-4*c*(c + 1)
Let i(u) be the third derivative of -u**8/1680 - u**7/1050 + u**6/300 - 8*u**2. Factor i(r).
-r**3*(r - 1)*(r + 2)/5
Let r(u) be the third derivative of -u**11/166320 + u**9/15120 - u**7/2520 - u**5/20 - 3*u**2. Let w(z) be the third derivative of r(z). Factor w(x).
-2*x*(x - 1)**2*(x + 1)**2
Let h(c) be the third derivative of -5*c**2 - 1/504*c**8 + 0*c - 1/45*c**5 + 0*c**4 + 0*c**3 - 4/315*c**7 - 1/36*c**6 + 0. Solve h(v) = 0.
-2, -1, 0
Let p(h) be the first derivative of h**5/5 + 5*h**4/4 + 8*h**3/3 + 2*h**2 + 19. Let p(b) = 0. Calculate b.
-2, -1, 0
Let l(w) be the first derivative of 3*w**5/5 - 9*w**4/4 + 3*w**3 - 3*w**2/2 + 7. Let l(r) = 0. Calculate r.
0, 1
Let x(k) = -8*k**3 - 20*k**2 + 9*k - 14. Let t(p) = 3*p**3 + 7*p**2 - 3*p + 5. Let j(r) = 11*t(r) + 4*x(r). Let j(w) = 0. Calculate w.
1
Let i = 795 + -59624/75. Let r(g) be the second derivative of 0 - 1/15*g**3 - 2*g - i*g**6 - 1/10*g**4 + 0*g**2 - 3/50*g**5. Factor r(f).
-2*f*(f + 1)**3/5
Let y = 283/2 + -141. Let u(l) = l**3 - 6*l**2 - l + 6. Let t be u(6). Suppose -1/2*r**5 + 0 + t*r**4 + r**3 + 0*r**2 - y*r = 0. What is r?
-1, 0, 1
Let z(c) = c**3 + 19*c**2. Let a be z(-19). Factor a - 2/5*h**5 + 2/5*h**3 + 0*h + 2/5*h**4 - 2/5*h**2.
-2*h**2*(h - 1)**2*(h + 1)/5
Determine k so that -9/2*k**3 + 0 - 13/2*k**4 + k + 1/2*k**2 - 5/2*k**5 = 0.
-1, 0, 2/5
Let l(c) be the second derivative of c**5/60 - c**4/12 + 2*c**2/3 + c. Factor l(t).
(t - 2)**2*(t + 1)/3
Let n = -2 - -7. Suppose 15 = b - 4*b, n*b = -5*r. Factor -1/4*m**2 + 0 - 1/4*m**r + 0*m + 1/4*m**4 + 1/4*m**3.
-m**2*(m - 1)**2*(m + 1)/4
Let m be ((-3)/(-10))/((-4)/(-10) + 2). Let c(b) be the third derivative of 0*b + 1/120*b**6 - 1/20*b**5 + m*b**4 + 0 - 1/6*b**3 - b**2. Factor c(k).
(k - 1)**3
Let d(j) be the third derivative of j**5/80 + j**4/48 - j**3/24 - 5*j**2. Factor d(a).
(a + 1)*(3*a - 1)/4
Let a(i) = i. Let g(v) = -3*v**3 - 6*v**2 + 3*v. Let z(o) = -6*a(o) + g(o). Suppose z(l) = 0. What is l?
-1, 0
Let f(q) be the third derivative of -q**5/150 + q**4/1