Let u = -10 - c. Determine y so that 1/4*y**u + 1/4 - 1/2*y = 0.
1
Let n(x) = -2*x. Suppose 3*v + 9 = 3. Let o be n(v). Factor f**o - 1 - 2*f**3 + 0*f**4 - 2*f + 2*f**3 + 2*f**3.
(f - 1)*(f + 1)**3
Let k(z) be the third derivative of -z**5/180 - z**4/72 + z**3/9 - 10*z**2. Let k(g) = 0. What is g?
-2, 1
Let c(f) = f + 5. Let y be c(-3). Suppose -14 = -4*j - 2*o, -y*j - 4*o + 20 = 2*j. Factor 0*w**j - w + 1 + w**2 + w + 2*w.
(w + 1)**2
Let r(w) = w**2 + 11. Let n be r(0). Suppose -5*p + p + 4*s + 12 = 0, 0 = -5*p + s + n. Let -2*g**p + 5*g + 2*g + 2*g**3 - 6*g - g**3 = 0. Calculate g.
0, 1
Let c(d) = -2*d**4 - 2*d**3 + d + 1. Let p(b) = b**4 + b. Let a(s) = -3*c(s) - 3*p(s). Factor a(h).
3*(h - 1)*(h + 1)**3
Let q be (-4)/(-30) - 35/(-300). Let u(f) be the first derivative of -1/3*f**3 + f + q*f**4 - 1/2*f**2 + 2. Factor u(x).
(x - 1)**2*(x + 1)
Suppose 2*v - 19 = -4*r + 5, v = 4*r - 36. Let y = -6 + r. Factor -7/4*g + 1/4*g**4 + 1/2 - 5/4*g**3 + 9/4*g**y.
(g - 2)*(g - 1)**3/4
Find h, given that 4 - 3*h**3 + 14 - 9*h + 9 - 15*h**2 = 0.
-3, 1
Let l = -6 - -8. Let b(r) be the second derivative of 1/12*r**4 + 0 + 1/6*r**3 + 1/60*r**5 + 1/6*r**l - 3*r. Factor b(h).
(h + 1)**3/3
Let n(j) be the third derivative of j**8/420 - 2*j**7/525 - j**6/150 + j**5/75 - 3*j**2. Suppose n(i) = 0. What is i?
-1, 0, 1
Suppose -5*l - 5 = 5*j, l = 5*j + 21 - 22. Let -4/9*g**4 + 2/9*g**3 + 0*g + 0*g**2 + 2/9*g**5 + j = 0. Calculate g.
0, 1
Let o(c) be the second derivative of 0 + 44/21*c**3 + 121/42*c**4 + 4*c + 4/7*c**2. Suppose o(k) = 0. What is k?
-2/11
Let r(j) be the second derivative of -j**7/231 - 4*j**6/165 - j**5/55 + 2*j**4/33 + j**3/11 + 15*j. Suppose r(c) = 0. Calculate c.
-3, -1, 0, 1
Let k(v) be the first derivative of -v**5/40 - v**4/16 - v**3/24 - 2. Suppose k(t) = 0. What is t?
-1, 0
Let d(f) be the first derivative of -4*f**6/15 + f**5/30 + f**4/2 + 2*f**3/9 - f - 3. Let t(x) be the first derivative of d(x). Let t(v) = 0. What is v?
-2/3, -1/4, 0, 1
Suppose -4*n - 1 = -0*n + i, -n - 1 = i. Factor 2/3*o + n - 2/3*o**2.
-2*o*(o - 1)/3
Let l(n) = -n - 2. Let z be l(-5). Let p(d) = -3*d - 32. Let m be p(-12). Factor 0*c**z + 2/5*c**5 - 4/5*c**m + 4/5*c**2 + 0 - 2/5*c.
2*c*(c - 1)**3*(c + 1)/5
Let d = 87/52 - 12/13. Let u(z) be the second derivative of 3/80*z**5 - 1/8*z**3 + d*z**2 + 0 - 4*z - 1/8*z**4. Let u(y) = 0. What is y?
-1, 1, 2
Let z be (-2)/6 + 24/(-9). Let g be (-3)/18*z*8. Suppose -3*n + 0 - n + 0*n**4 + 4*n**3 + 2*n**g - 2 = 0. Calculate n.
-1, 1
Let c(w) be the first derivative of 0*w**2 + 0*w + 4 + 5/2*w**6 - 9/5*w**5 + 0*w**3 - 3/2*w**4. What is n in c(n) = 0?
-2/5, 0, 1
Let y(f) be the first derivative of f**8/840 + f**7/210 + f**6/180 - 5*f**3/3 + 4. Let s(w) be the third derivative of y(w). Factor s(m).
2*m**2*(m + 1)**2
Factor 5*r - 3*r**4 + 4 - r**4 + 0*r**3 + 8*r**3 - 13*r.
-4*(r - 1)**3*(r + 1)
Let k = -119 - -121. Factor -1/5 + 2/5*l + 4/5*l**3 + 7/5*l**k.
(l + 1)**2*(4*l - 1)/5
Let c(i) be the second derivative of -i**5/100 + i**4/20 - i**3/15 + 25*i. Factor c(j).
-j*(j - 2)*(j - 1)/5
Let y = -1080 - -6481/6. Factor 2/3*b + 1/2*b**2 - 2/3*b**3 + y*b**4 - 2/3.
(b - 2)**2*(b - 1)*(b + 1)/6
Let h(s) be the third derivative of -5*s**6/24 + 17*s**5/12 - 10*s**4/3 + 10*s**3/3 - 14*s**2. Solve h(k) = 0 for k.
2/5, 1, 2
Let l(f) be the first derivative of -f**6/300 - f**5/50 + 4*f**3/15 + 3*f**2/2 - 4. Let c(g) be the second derivative of l(g). Suppose c(j) = 0. Calculate j.
-2, 1
Let p be (-5)/(-6)*1/(-10)*-8. Factor 2/3 + p*s**2 - 4/3*s.
2*(s - 1)**2/3
Let q(i) be the second derivative of i**5/390 - i**4/78 - 3*i**2/2 - 4*i. Let d(k) be the first derivative of q(k). Factor d(l).
2*l*(l - 2)/13
Let d(f) be the third derivative of 8*f**2 + 1/4*f**4 + 0*f + 1/70*f**7 - 1/20*f**5 + 1/112*f**8 + 0*f**3 + 0 - 3/40*f**6. Find m, given that d(m) = 0.
-2, -1, 0, 1
Let c(w) = -w**3 - 2*w**2 + 3*w. Let b = 20 - 25. Let h(v) = 2*v**3 + 5*v**2 - 7*v. Let q be 3*(-2 - 8/(-6)). Let t(z) = b*c(z) + q*h(z). Factor t(i).
i*(i - 1)*(i + 1)
Let h(a) be the first derivative of 3*a**4/16 + a**3/2 + 3*a**2/8 - 17. Suppose h(k) = 0. Calculate k.
-1, 0
Let o(y) = -y**2 - 6*y + 94. Let b be o(-13). Factor 1/7*v**2 - 4/7 + 1/7*v**b - 4/7*v.
(v - 2)*(v + 1)*(v + 2)/7
Let i be (1 + -2)/((-1)/(-6)). Let l be i/(-12) + (-1)/4. Factor 0 + 0*p - 1/4*p**2 + l*p**3.
p**2*(p - 1)/4
Let b(x) be the first derivative of -x**6/90 - x**5/20 - x**4/12 - x**3/18 - x - 4. Let o(u) be the first derivative of b(u). Factor o(t).
-t*(t + 1)**3/3
Let h = -13 - -17. Suppose -h*g - 5*r = -23, -4*g - 3 = -5*r + 4. Solve -2/9*p**3 + 0 + 2/9*p + 0*p**g = 0.
-1, 0, 1
Factor -6/5*j**3 + 3/5 - 3/5*j**5 + 6/5*j**2 - 9/5*j**4 + 9/5*j.
-3*(j - 1)*(j + 1)**4/5
Suppose -75*b + 16*b**3 + b**2 + 11*b**2 - 18*b**5 - 12*b**4 + 77*b = 0. What is b?
-1, -1/3, 0, 1
Let f = -146 - -147. Let c(d) be the first derivative of -1/10*d**4 + 0*d + f - 1/5*d**2 - 4/15*d**3. Factor c(z).
-2*z*(z + 1)**2/5
Let t = -22/25 + 817/900. Let a(b) be the second derivative of 1/18*b**3 + t*b**4 - 1/3*b**2 + 0 + b. Factor a(j).
(j - 1)*(j + 2)/3
Let n(f) = 5*f**3 + f - 1. Let r be n(1). Suppose p - r = -2. Determine z so that -2/7*z**4 - 2/7*z**p + 0*z**2 + 0 + 0*z = 0.
-1, 0
Let r(m) be the second derivative of -m**5/30 + m**4/3 - 4*m**3/3 - 3*m**2/2 + 4*m. Let u(l) be the first derivative of r(l). Determine s, given that u(s) = 0.
2
Let q(b) be the first derivative of -4*b + 5/18*b**5 - 8/9*b**2 - 4/3*b**3 - 5/9*b**4 + 3. Let p(o) be the first derivative of q(o). Factor p(s).
2*(s - 2)*(5*s + 2)**2/9
Let z(p) = 3*p**2 - p - 1. Let x be z(-1). Determine n, given that 0 - 3 - 3*n**2 + 6*n**4 - x*n**3 + 3 = 0.
-1/2, 0, 1
Let a(z) be the first derivative of -z**4/20 + 6*z - 2. Let u(l) be the first derivative of a(l). Factor u(w).
-3*w**2/5
Factor 6*b**2 - 25*b**3 - 6 - 3*b + 0*b**2 + 28*b**3.
3*(b - 1)*(b + 1)*(b + 2)
Let p(z) be the second derivative of 0 + 0*z**2 + 1/18*z**3 - z + 1/36*z**4. Factor p(a).
a*(a + 1)/3
Let a(t) be the second derivative of t**7/7 + 3*t**5/20 - t**4/6 - 7*t**3/6 - 7*t**2/2 + 5*t. Let o(y) = y**5 - y - 1. Let h(j) = 3*a(j) - 21*o(j). Factor h(g).
-3*g**2*(g - 1)**2*(g + 2)
Let g(w) be the first derivative of -1 + 1/3*w**3 - 1/2*w**2 + 1/3*w - 1/12*w**4. Factor g(v).
-(v - 1)**3/3
Let t be -1*(-34)/70 + 2/(-7). Suppose -t + 1/5*z**2 + 0*z = 0. What is z?
-1, 1
Suppose -3*d + 10*d = 14. What is l in 4/5*l - 2*l**4 + 2/5*l**5 + 0 + 18/5*l**3 - 14/5*l**d = 0?
0, 1, 2
Let q(o) = -o**2 + 4*o - 2. Let g(n) = n. Let d(h) = -5*g(h) + 5*q(h). Solve d(i) = 0 for i.
1, 2
Let o(h) be the second derivative of h**6/120 + h**5/20 + h**4/12 - 3*h**2/2 + 7*h. Let j(l) be the first derivative of o(l). Let j(f) = 0. What is f?
-2, -1, 0
Let n(x) = 3*x**2 - 3*x - 3. Let f be (3 + 2 + -2)*1. Let w(l) = -6*l**2 + 6*l + 7. Let z(h) = f*w(h) + 5*n(h). Factor z(o).
-3*(o - 2)*(o + 1)
Factor 93*a**3 + 152*a**3 + 91*a + 49*a - 40 + 160*a - 630*a**2.
5*(a - 2)*(7*a - 2)**2
Let p(g) = g**3 + g**2 + 1. Let k(j) = 3 + 26*j**2 - 27*j**2 + 3*j**3 + 3. Let s(b) = k(b) - 2*p(b). Factor s(f).
(f - 2)**2*(f + 1)
Let b(o) be the first derivative of o**9/1512 - o**7/420 - 4*o**3/3 - 5. Let n(r) be the third derivative of b(r). Factor n(m).
2*m**3*(m - 1)*(m + 1)
Let r(h) = h**3 - 3*h**2 - 4*h. Let y(a) = -4*a**3 + 8*a**2 + 12*a. Let i(s) = -8*r(s) - 3*y(s). Solve i(b) = 0.
-1, 0, 1
Let v(b) be the first derivative of 5*b**4/4 + 5*b**3 - 5*b**2/2 - 15*b + 18. Factor v(c).
5*(c - 1)*(c + 1)*(c + 3)
Let v(y) be the second derivative of -y**9/1008 - y**8/280 - y**7/280 - 5*y**3/6 + 3*y. Let o(z) be the second derivative of v(z). Suppose o(m) = 0. What is m?
-1, 0
Suppose 5*b + 113 = 113. Let d(p) be the second derivative of -1/6*p**4 + b + 0*p**2 - 4*p + 2/3*p**3. Factor d(q).
-2*q*(q - 2)
Let i = 76 - 76. Let m(p) be the second derivative of 0*p**3 - 1/63*p**7 + 1/30*p**5 + i*p**2 + 2*p + 0 + 0*p**4 + 0*p**6. Suppose m(l) = 0. Calculate l.
-1, 0, 1
Let b be ((-83)/(-332))/((-2)/(-20)). What is a in -12*a - b*a**5 - 27/2*a**4 - 53/2*a**2 - 2 - 55/2*a**3 = 0?
-2, -1, -2/5
Solve -24*p**4 - 9*p**3 - 70*p + 24*p**2 - 9*p**3 - 2*p**3 - 8 + 82*p = 0.
-1, 1/2, 2/3
Let n = -9 + 13. Find j, given that 3/2*j**n + 13/4*j**3 + 0 + 1/4*j**5 + j 