+ 4*g - 8 = 0, 0 = 2*g. Let q be 15 - (t/(-1))/1. Factor q*r**3 - 2*r**3 - 13*r + 5*r - 11*r**2 + 4.
(r - 1)*(3*r + 2)*(5*r - 2)
Let f(z) = z - 6. Suppose 0 = -0*g - 3*g + 30. Let n be f(g). Suppose 1/3*c - 4/3*c**5 + 5/3*c**n - 5/3*c**2 + c**3 + 0 = 0. What is c?
-1, 0, 1/4, 1
Let f = 6 - 4. Find k such that -k**3 - 3*k**2 + 5*k**3 - f*k**4 + k**4 - 4*k + 4 + 0*k**4 = 0.
-1, 1, 2
Suppose 2*a - 4*z - 20 = 0, -2*a - 2*z = -6*a + 22. Let m = 7 - a. Suppose 4/3*p**m - 2/3 + 2/3*p**4 + 0*p**2 - 4/3*p = 0. What is p?
-1, 1
Suppose 6*d - 3*d = -4*g - 7, 4*d + 30 = 5*g. Factor 3*x + 3*x - 2*x**g - 8*x.
-2*x*(x + 1)
Let p(m) = -m**2 - 10*m - 13. Let f be p(-8). Factor -4/7 + 0*j**2 - 6/7*j + 2/7*j**f.
2*(j - 2)*(j + 1)**2/7
Let g(u) be the first derivative of u**6/9 - 4*u**5/5 + 2*u**4 - 20*u**3/9 + u**2 + 10. Determine q so that g(q) = 0.
0, 1, 3
Suppose -3/2*z + 1/2*z**3 + 1 + 0*z**2 = 0. What is z?
-2, 1
Let u(j) = j**5 - j**4 - j**3 - j**2 + j - 1. Let f(i) = 3*i**5 - 9*i**4 - 6*i**2 + 6*i - 6. Let a(r) = f(r) - 6*u(r). What is y in a(y) = 0?
-2, 0, 1
Let g be 4 - (-1 + 2)/1. Determine a so that 3*a**5 - a**5 + 2*a + 2*a**3 + 8*a**2 + 8*a**4 + 10*a**g = 0.
-1, 0
Let b be 2/1*(-36)/(-81). Find q, given that 2/3*q + b*q**3 - 1/9 - 4/3*q**2 = 0.
1/2
Let c(w) be the first derivative of 2/3*w**3 + 0*w**2 + 0*w - 7 + 1/2*w**4. Factor c(z).
2*z**2*(z + 1)
Suppose -3*x = -9 - 0. Let -15*i**4 - 8*i**4 - i**4 + 31*i + 21*i**2 + 48*i**5 - 10*i + 3 - 69*i**x = 0. What is i?
-1, -1/4, 1
Let v(p) be the second derivative of p**4/108 - 7*p**3/27 + 49*p**2/18 - p. Factor v(l).
(l - 7)**2/9
Let i(j) be the first derivative of -1 - 1/4*j**2 - 1/12*j**3 + 0*j + 1/16*j**4. Find o such that i(o) = 0.
-1, 0, 2
Let i(d) be the first derivative of -d**3 + 1/40*d**5 + 0*d**2 - 1/280*d**7 + 0*d - 1 + 0*d**6 + 0*d**4. Let z(l) be the third derivative of i(l). Factor z(x).
-3*x*(x - 1)*(x + 1)
Let x(l) be the third derivative of 5*l**7/14 - 3*l**6/8 - 9*l**5/20 - l**4/8 - 2*l**2. Factor x(p).
3*p*(p - 1)*(5*p + 1)**2
Suppose -q = 3*f + q - 2, -f = -4*q - 10. Let r be 8 + -7 + f/(-6). Solve -4/3*l**3 - r*l**4 + 2/3 + 4/3*l + 0*l**2 = 0 for l.
-1, 1
Let r be 3/(-2)*20/(-15). Suppose 4*u - 6 = u. Factor -2*f - u*f**2 + f + f**r.
-f*(f + 1)
Let v(i) be the second derivative of 0 + 4*i**2 + 1/24*i**4 + 2/3*i**3 - 6*i. Let v(d) = 0. What is d?
-4
Let i(q) be the third derivative of -q**7/525 + q**6/300 + q**5/75 + q**2. Determine w, given that i(w) = 0.
-1, 0, 2
Let 2/7*i**2 + 12/7*i + 16/7 = 0. What is i?
-4, -2
Let i = 4 - 1. Let y = i - 1. Factor -8*l**3 - 4 + 4*l**3 + y - 10*l**2 - 8*l.
-2*(l + 1)**2*(2*l + 1)
Determine n so that 6/5*n**2 + 0*n**4 - 9/5*n - 3/5*n**5 + 12/5*n**3 - 6/5 = 0.
-1, 1, 2
Let w be 66/231 + 0 + (-146)/(-28). Let -w*r + 3/2*r**2 + 3 = 0. Calculate r.
2/3, 3
Let b(p) be the second derivative of -p**7/30 - 2*p**6/25 - 3*p**5/100 + p**4/30 - 34*p. Factor b(g).
-g**2*(g + 1)**2*(7*g - 2)/5
Let z(p) = -4*p**4 + 27*p**3 - 51*p**2 + 32*p + 3. Let v(k) = -20*k**4 + 136*k**3 - 256*k**2 + 160*k + 16. Let t(d) = -3*v(d) + 16*z(d). Solve t(q) = 0 for q.
0, 2
Suppose -2*a = -2508 - 338. Let o = 15669/11 - a. Let 2*y**3 + 4/11*y**2 + 2/11*y**5 + 12/11*y**4 - o - 24/11*y = 0. Calculate y.
-2, -1, 1
Suppose 2*j - m - 12 + 3 = 0, -m = 5. Factor 2*h**2 - 6*h**j + 5*h**2 - h.
h*(h - 1)
Let t(q) = -3*q**3 - 2*q**2 - 3*q. Suppose -2*o - 2 - 10 = 0. Let b(x) = -19*x**3 - 12*x**2 - 19*x. Let r(f) = o*b(f) + 39*t(f). Let r(z) = 0. Calculate z.
-1, 0
Solve -4/3*m**3 - 2/3*m - 5/3*m**2 - 1/3*m**4 + 0 = 0.
-2, -1, 0
Let x be (242/(-33) + 9)*(-2 - -3). Suppose -f**2 + f**4 + 0 + x*f**3 - 1/3*f - 4/3*f**5 = 0. What is f?
-1, -1/4, 0, 1
Solve -4*v - 1 + 7/4*v**3 - 5/4*v**2 = 0.
-1, -2/7, 2
Factor -7*v**2 - 2 + 9*v**2 - v**3 + 2 + v - 2*v**4.
-v*(v - 1)*(v + 1)*(2*v + 1)
Suppose 0 = 7*m - 2*m - 10. Let s(a) be the first derivative of 1 - 1/10*a**4 - 2/5*a + 1/5*a**m + 2/15*a**3. Let s(r) = 0. What is r?
-1, 1
Let a(y) = -y**2 - 6*y + 2. Let z be a(-6). Let c(b) = b**2. Let x = 9 + -3. Let u(n) = -n**2 - n. Let i(d) = x*c(d) + z*u(d). Factor i(j).
2*j*(2*j - 1)
Factor 0*s + 4*s**4 + s**3 - 29*s**3 + 60*s**2 - 25*s - 11*s.
4*s*(s - 3)**2*(s - 1)
Let j = -80 + 80. Suppose 0 + 0*y + 2/9*y**4 + 2/9*y**3 + j*y**2 = 0. What is y?
-1, 0
Let a = 86/5 + -453/5. Let u = a - -1573/20. Let 1/2 - 9/4*o**4 - 13/4*o**2 + u*o**3 - 1/4*o = 0. Calculate o.
-1/3, 2/3, 1
Suppose 10 = -4*b + 9*b. Let r(v) be the second derivative of 0*v**b + 1/24*v**3 + 0 - 2*v + 1/48*v**4. Factor r(z).
z*(z + 1)/4
Let t = -2 + 5. Suppose 6 = -i - t*w - 2*w, -3*i = -2*w - 16. Factor -i + c**4 - 2 + 2*c**3 + c**2 + 6.
c**2*(c + 1)**2
Factor 4*p**2 - 5 + 12*p**2 - 4*p**3 - 9 + 4*p - 2.
-4*(p - 4)*(p - 1)*(p + 1)
Let r(i) be the third derivative of i**8/1008 - i**6/360 + 9*i**2. Factor r(l).
l**3*(l - 1)*(l + 1)/3
Find t, given that t**2 - 16*t - 4*t + 24 + 0*t**2 + 3*t**2 = 0.
2, 3
Let f(w) be the first derivative of 1/2*w**4 + 0*w - 2 + w**2 + 4/3*w**3. Factor f(s).
2*s*(s + 1)**2
Let k(w) be the second derivative of w**8/504 - w**2 + w. Let l(y) be the first derivative of k(y). Factor l(u).
2*u**5/3
Let t(o) be the second derivative of 1/15*o**6 + 0*o**2 - 1/6*o**3 - 1/6*o**4 + 3*o + 0 + 1/20*o**5. Solve t(j) = 0.
-1, -1/2, 0, 1
Let m(v) = v + 7. Let s be -1 - (-1)/(3/(-12)). Let a be m(s). Let 6/5*f**3 + 14/5*f + 4/5 + 16/5*f**a = 0. Calculate f.
-1, -2/3
Let u = 11 - 7. Suppose 5*p = u*t - 36, t - 5*p - 3 = 6. Factor n - 13 - 10*n - 3*n**3 - t*n**2 + 10.
-3*(n + 1)**3
Factor 631 - 623 - 28*l**2 + 2*l + 18*l.
-4*(l - 1)*(7*l + 2)
Let a(b) be the second derivative of -1/63*b**7 - 1/9*b**4 + 0*b**2 + 1/10*b**5 + 0*b**3 + b + 0*b**6 + 0. Let a(g) = 0. Calculate g.
-2, 0, 1
Factor -1/2*w**4 + 0 - 3/2*w**3 - 3/2*w**2 - 1/2*w.
-w*(w + 1)**3/2
Let f(a) = a**2 - 4*a + 5. Let y be f(4). Let n be (1/(-2))/((-1)/2). Factor 8*z**4 + 34*z**3 + 52*z**2 - 4*z**2 - n + 26*z + y.
2*(z + 1)**2*(z + 2)*(4*z + 1)
Let s(r) be the third derivative of r**8/30240 + r**7/2520 + r**6/540 - r**5/30 + 2*r**2. Let i(h) be the third derivative of s(h). Factor i(u).
2*(u + 1)*(u + 2)/3
Suppose 0 = 2*o - 6*o - 5*i - 1, 4*o = -4*i + 4. Suppose o*j = 2*j. Factor 2/5*k**2 - 2/5 + j*k.
2*(k - 1)*(k + 1)/5
Let a(c) = -c**3 + 11*c**2 + c - 7. Let x be a(11). What is j in -j**2 + 4 - 7 + x = 0?
-1, 1
Suppose 0 = 11*n - 8*n - 6. Let w(g) be the second derivative of 1/4*g**4 - 1/6*g**3 + 1/30*g**6 - 3/20*g**5 - 3*g + 0 + 0*g**n. Solve w(c) = 0.
0, 1
Let q(b) = 4*b**3 - 1. Let p be q(1). Let f be 8/p*2/2. Solve a**2 - f*a + 4/3 = 0.
2/3, 2
Suppose -5*z + 2*d + 19 = 0, -z - z + 5*d - 5 = 0. Factor 2*b**4 + 2/3*b**z + 0 + 0*b + 4/3*b**3 + 0*b**2.
2*b**3*(b + 1)*(b + 2)/3
Let d(k) = 9*k**4 + 3*k**3 + k**2 - 3*k. Let o(t) = -4*t**4 - t**3 + t. Let w be 3*1/((-3)/(-2)). Let x(c) = w*d(c) + 5*o(c). Solve x(i) = 0 for i.
-1, 0, 1/2, 1
Factor -8/17*f - 2/17*f**3 + 0 + 8/17*f**2.
-2*f*(f - 2)**2/17
Let n = -9 - -15. Let 2*r**4 + 4*r**2 - 3*r**4 - 2*r - n*r**3 - 10*r**2 - r**4 = 0. What is r?
-1, 0
Let t = -4 + 4. Factor 5 + t*u**2 + 2*u**2 - 5 - 2*u**3.
-2*u**2*(u - 1)
Let -92*s - 12*s**5 + 0*s**5 + 92*s - 8*s**4 = 0. Calculate s.
-2/3, 0
Suppose 13 = -l + 5*m, 3*m - 20 + 3 = -4*l. Factor -1/5*c**l - 2/5 - 3/5*c.
-(c + 1)*(c + 2)/5
Factor 3/5*u**2 + 9/5 - 12/5*u.
3*(u - 3)*(u - 1)/5
Let n = -121 + 121. Factor 0*l - l**3 - 1/2*l**4 - 1/2*l**2 + n.
-l**2*(l + 1)**2/2
Let o(l) be the second derivative of -l**8/3360 - l**7/1260 - l**4/6 + 5*l. Let g(i) be the third derivative of o(i). Factor g(p).
-2*p**2*(p + 1)
Let f be (-4)/3*9/(-66). Suppose -f*c + 0 - 2/11*c**2 = 0. What is c?
-1, 0
Let t(s) = -s**5 - s**4 + 2*s**3 + 2*s**2 - 5*s + 1. Let r(x) = x**5 - x**4 + x. Let f(v) = -4*r(v) - 2*t(v). Factor f(k).
-2*(k - 1)**4*(k + 1)
Let t(g) = -g + 8. Let o = 13 + -6. Let c be t(o). Factor -w**2 - w + c + w + w - w**3.
-(w - 1)*(w + 1)**2
Let u(p) be the second derivative of -p**8/336 - p**7/105 - p**6/120 - 3*p**2/2 + p. Let r(m) be the first derivative of u(m). Find q such that r(q) = 0.
-1, 0
Suppose 0*k + 3*t = -3*k + 12, 5*t - 10 = 0. Factor 2/3*h + 0 - 2/3*h**k.
-2*h*(h - 1)/3
Let i(b) be the first derivative of -5*b**4/4 + 10*b**3/3 - 50. Solve i(g) = 0.
0, 2
Let x(