 Let q be u(8). Let o = q - 10. Factor -1/2*p**2 + 1/4*p + 0*p**3 + 1/2*p**4 + 0 - 1/4*p**o.
-p*(p - 1)**3*(p + 1)/4
Suppose -7*p + 11*p - 8 = 0. Factor -3*h**4 + 12*h**4 - 6*h - 2 + p*h**3 + 4*h**5 - 8*h**2 + 1.
(h - 1)*(h + 1)**3*(4*h + 1)
Suppose 23*k**3 - 21*k**2 - 3*k**2 - 21*k**4 + 34*k**3 - 12*k = 0. What is k?
-2/7, 0, 1, 2
Let f be 6*6/144*8/6. Factor f + 2*w**2 + 25/3*w**4 - 8/3*w + 40/3*w**3.
(w + 1)**2*(5*w - 1)**2/3
Let f(s) = -s - 11. Let z be f(-14). Suppose -6*o = -o + 25, o = 5*v - 25. Factor -v*n**3 - n**2 + 4*n**z + n**3.
n**2*(n - 1)
Let o(k) = -4*k - 2 - k**2 + 2. Suppose 0 = 5*l + 1 + 4. Let j(w) = w. Let z(y) = l*o(y) - 4*j(y). Solve z(u) = 0.
0
Let c(b) = b**3 - 7*b - 3. Let w be c(-2). Let g(j) be the second derivative of 0*j**2 - 1/6*j**w + 4*j + 0 - 1/12*j**4. Determine l, given that g(l) = 0.
-1, 0
Suppose 3*u - 2*u - 3 = 0. Suppose -5 - 10 = -3*z. Factor -4*k**2 - 2 + 8*k - z*k**2 + u*k**2.
-2*(k - 1)*(3*k - 1)
Let q be 31*(-14)/(-108) - 4. Let w(m) be the second derivative of 0*m**3 + q*m**4 - 1/9*m**2 + 2*m + 0. Solve w(n) = 0.
-1, 1
Let g(u) = 29*u**4 - 41*u**3 - 31*u**2 + 113*u + 17. Let r(m) = 10*m**4 - 14*m**3 - 10*m**2 + 38*m + 6. Let o(s) = 6*g(s) - 17*r(s). Let o(x) = 0. Calculate x.
-2, 0, 2
Let x be (-68)/260*(-35)/(-6). Let q = -5/26 - x. Find r, given that -2/3*r**2 + 0 + q*r**3 - 2/3*r**4 + 0*r = 0.
0, 1
Let o be (28/(-12))/(42/(-36)). Factor 7/5*i + i**o + 2/5.
(i + 1)*(5*i + 2)/5
Suppose 5*u - f - 15 = 4*f, -4*u + 2*f = -6. Let z(v) be the third derivative of v**2 + 1/150*v**5 - 1/15*v**3 + u*v + 0*v**4 + 0. Factor z(m).
2*(m - 1)*(m + 1)/5
Let a(l) = l**3 - 3*l**2 + 2*l - 2. Let r be a(3). Solve 4/9*k**2 - 4/9*k**3 + 2/3*k - 2/3*k**r + 2/9 - 2/9*k**5 = 0.
-1, 1
Let a = -519 + 521. Solve -6/5*m**2 - 2/5 - 18/5*m**3 + a*m = 0 for m.
-1, 1/3
Let t(k) be the first derivative of 1 + 0*k**4 + 1/18*k**3 + k**2 - 1/180*k**5 + 0*k. Let j(f) be the second derivative of t(f). Factor j(l).
-(l - 1)*(l + 1)/3
Let y(b) be the second derivative of b**7/231 + 2*b**6/55 + b**5/10 + b**4/33 - 4*b**3/11 - 8*b**2/11 + 24*b. What is q in y(q) = 0?
-2, -1, 1
Factor 0 + 3/5*t - 3/5*t**2.
-3*t*(t - 1)/5
Let r(n) be the second derivative of n**9/15120 + n**4/6 + 3*n. Let v(g) be the third derivative of r(g). Factor v(h).
h**4
Suppose 27/4 + 9/4*k + 3/4*k**3 - 15/4*k**2 = 0. Calculate k.
-1, 3
Let w(a) be the first derivative of -a**4/2 + 12*a**3 - 108*a**2 + 432*a + 14. Factor w(h).
-2*(h - 6)**3
Let u(w) = -w**2 - 11*w + 17. Let l be u(-12). Suppose l*g - 8 = 3*g. Let -4/7*q**3 + 2/7*q**g + 4/7*q**5 + 0 - 2/7*q**2 + 0*q = 0. Calculate q.
-1, -1/2, 0, 1
Suppose -6*x + 2*x = 0. Factor x*w + 1/3 - 1/3*w**2.
-(w - 1)*(w + 1)/3
Let c(z) = -z**2 + 51. Let d be c(-7). Let k(p) be the first derivative of -8/15*p**5 - d + 2/3*p**3 + 5/3*p**2 + 2/3*p - 5/6*p**4. What is g in k(g) = 0?
-1, -1/4, 1
Suppose 2*p = 8 + 2. Solve -l**4 + 2*l**5 + l**2 - 5*l**p + 2*l**5 + l**3 = 0 for l.
-1, 0, 1
Factor -2/9*o + 2/9*o**3 + 0 + 0*o**2.
2*o*(o - 1)*(o + 1)/9
Let n(l) be the third derivative of -l**5/120 + 11*l**4/24 - 121*l**3/12 + 2*l**2 - 5*l. Find a, given that n(a) = 0.
11
Let i(l) be the second derivative of -l**9/1512 + l**8/840 + l**7/420 - l**6/180 + l**3/6 - 2*l. Let r(j) be the second derivative of i(j). Factor r(q).
-2*q**2*(q - 1)**2*(q + 1)
Let k(w) = -w + 10. Let s be k(6). Factor 16 + s*b**2 - 16 - 8*b.
4*b*(b - 2)
Let i(b) be the third derivative of b**9/211680 - b**8/70560 - b**5/20 - 3*b**2. Let q(z) be the third derivative of i(z). Solve q(r) = 0 for r.
0, 1
Let p = 1 - -2. Factor h**3 + h**4 + 0 + 0 - 4*h**4 + p*h**2 - h.
-h*(h - 1)*(h + 1)*(3*h - 1)
Let q(f) be the first derivative of -f**4/8 + f**2 + 9. Factor q(o).
-o*(o - 2)*(o + 2)/2
Let a be (-10)/4*(-24)/30. Suppose -g - 2 = -a*g. Factor q + q**3 + g*q + 0*q - 4*q.
q*(q - 1)*(q + 1)
Let r be (-4)/(-18) + (-185)/(-18). Let y = -10 + r. Suppose 0 + 0*q + y*q**3 - q**2 = 0. What is q?
0, 2
Factor 3*d**3 + 21/5*d**2 + 0 + 6/5*d.
3*d*(d + 1)*(5*d + 2)/5
Let x = 14 - 9. Factor -31*m**2 + 1 + 29*m**2 - x - 6*m.
-2*(m + 1)*(m + 2)
Let j = -12 + 12. Let z(c) be the first derivative of 0*c**3 + 7/24*c**6 + j*c + 0*c**2 - 1/8*c**4 - 1 - 1/4*c**5. Determine p so that z(p) = 0.
-2/7, 0, 1
Let l(z) be the second derivative of 21*z**5/20 + 4*z**4 + 11*z**3/2 + 3*z**2 - 18*z. Let l(q) = 0. Calculate q.
-1, -2/7
Let o be ((-24)/18)/(4/6). Let i be 4*(o + 15/6). Solve i + l - 2 + 2 - l**2 - 1 - l**3 = 0 for l.
-1, 1
Let t(a) be the third derivative of -6*a**2 + 0*a + 0*a**4 - 3/200*a**6 + 0*a**3 + 1/350*a**7 + 1/50*a**5 + 0. What is k in t(k) = 0?
0, 1, 2
Factor -27/4*o - 45/4*o**2 + 0 - 3/4*o**4 - 21/4*o**3.
-3*o*(o + 1)*(o + 3)**2/4
Suppose u - 13 + 2 = 0. Let o = u - 11. Factor o + 0*y - 5/3*y**3 - 2/3*y**2.
-y**2*(5*y + 2)/3
Let j = -267 - -1105/4. What is a in -21/4*a**3 + j*a**2 + 1 + a**4 - 6*a = 0?
1/4, 1, 2
Let b(f) be the third derivative of -f**8/336 - f**7/70 - f**6/60 + f**5/30 + f**4/8 + f**3/6 + 40*f**2. Factor b(w).
-(w - 1)*(w + 1)**4
Let y(g) = -g**3 + 6*g**2 - 5*g + 2. Let k be y(5). Solve -3*o**5 + 3*o**3 - o**5 + o**3 + 2*o**5 - k*o = 0.
-1, 0, 1
Let d = -195 + 607/3. Solve -2*h**4 - 4/3 - 38/3*h**2 + 26/3*h**3 + d*h = 0.
1/3, 1, 2
Let z(d) be the first derivative of -7*d**4/54 + 5*d**3/27 + 2*d**2/9 + d + 1. Let t(y) be the first derivative of z(y). Determine i so that t(i) = 0.
-2/7, 1
Let u(t) be the second derivative of -t**8/6720 + t**7/420 - t**6/60 + t**5/15 + t**4/4 + t. Let j(p) be the third derivative of u(p). Factor j(f).
-(f - 2)**3
Let n(m) = -4*m**2 + 6*m. Let f(j) = j + 1. Let w(g) = 21*g**2 - 28*g + 3. Let d(q) = -3*f(q) + w(q). Let i(r) = 2*d(r) + 11*n(r). Factor i(u).
-2*u*(u - 2)
Let t(v) = -v**2 - 8*v - 9. Let f be t(-6). Let q = 5 - f. Solve -2 - q*o**2 + 3*o**2 + o**2 = 0 for o.
-1, 1
Let m(g) be the third derivative of g**6/210 + g**5/35 - 10*g**2. Factor m(f).
4*f**2*(f + 3)/7
Suppose 4 = 2*n - 0*n. Factor -r**3 - 5*r**n + 0*r**4 + r**4 - r**3 + 6*r**2.
r**2*(r - 1)**2
Let t(i) = -i**2 + 4*i + 1. Let s(h) = h**2 + 8*h + 1. Let y(j) = 2*j**2 + 9*j + 1. Let r(l) = -4*s(l) + 3*y(l). Let a(g) = 2*r(g) + 3*t(g). Factor a(z).
(z + 1)**2
Suppose 5*f + 7 - 17 = 0. Factor -1/2 + s - 1/2*s**f.
-(s - 1)**2/2
Let k = -1 - 2. Let n(b) = b**3 + b**2 - b + 1. Let s(h) = -5*h**3 + h**2 + h - 3. Let w(v) = k*n(v) - s(v). Solve w(p) = 0.
0, 1
Let l(o) be the second derivative of 135*o**7/7 + 438*o**6/5 + 3092*o**5/25 + 1256*o**4/15 + 464*o**3/15 + 32*o**2/5 - 20*o. Let l(d) = 0. Calculate d.
-2, -2/5, -2/9
Factor 5*j**4 - 2*j**2 + 50*j + 16*j**2 - 12*j**3 + 46*j**2 + 15 + 42*j**3.
5*(j + 1)**3*(j + 3)
Suppose 0*l + 8 = 2*l. Suppose 2*v = l*v - 8. Factor -16/7*q**3 + 0*q + 2/7 - 12/7*q**2 - 6/7*q**v.
-2*(q + 1)**3*(3*q - 1)/7
Let m(p) be the first derivative of -p**6/6 + p**5 - 2*p**4 + 4*p**3/3 - 6. Determine i, given that m(i) = 0.
0, 1, 2
Let i(p) = 6*p**3 - 11*p**2. Let y(o) = -2*o**3 + 4*o**2. Let z(s) = -4*i(s) - 11*y(s). Solve z(q) = 0 for q.
0
Let j(y) be the second derivative of y**4/12 + y**3/6 + y - 35. Suppose j(h) = 0. Calculate h.
-1, 0
Let h(z) = -2*z**3 - 4*z**2 - z + 1. Let u(a) = -3*a**3 - 5*a**2 - a + 1. Let t = 2 - 0. Suppose i + t*i = -9. Let b(l) = i*u(l) + 4*h(l). Factor b(q).
(q - 1)**2*(q + 1)
Let y(c) be the first derivative of c**9/3024 - c**8/840 + c**7/840 + c**3/3 + 1. Let h(b) be the third derivative of y(b). Factor h(o).
o**3*(o - 1)**2
Let i = -11 + 7. Let a be i/(-6)*-3*-1. Find n such that -4/3 - 2/3*n + 2/3*n**a = 0.
-1, 2
Let d(z) be the third derivative of 0*z**4 + 2*z**2 + 0 + 1/504*z**8 - 1/90*z**5 + 0*z - 1/180*z**6 + 1/315*z**7 + 0*z**3. Let d(j) = 0. What is j?
-1, 0, 1
Suppose -2*p = -3*p + 4. Suppose 0 = l - p*l. Factor -1/5*u + 1/5*u**4 + l + 1/5*u**3 - 1/5*u**2.
u*(u - 1)*(u + 1)**2/5
Suppose 6 = -2*f - f. Let t be (-6)/f*6/9. Let -2 + 6*z - 2*z - t*z**2 + 0*z = 0. What is z?
1
Let v(j) be the second derivative of -j**5/120 + j**3/36 - 13*j. Factor v(t).
-t*(t - 1)*(t + 1)/6
Let d = -882 + 3529/4. Factor 1/4 + 1/2*o + d*o**2.
(o + 1)**2/4
Factor 1/5*r - 1/5 + 1/5*r**2 - 1/5*r**3.
-(r - 1)**2*(r + 1)/5
Let h = -141 + 141. Let l(t) be the first derivative of 4/3*t**3 + 4 - 1/2*t**2 + 4/5*t**5 - 1/6*t**6 + h*