t).
(t - 1)**2*(t + 1)/4
Suppose 6 = 3*v - 3*p, -v + 4*p + 1 = -1. Find w such that -3*w + 4*w + 3*w + v*w**2 - 2 - w = 0.
-2, 1/2
Let u be 50/135*1*(-15)/(-25). Solve u*r**2 + 2/9*r + 0 = 0.
-1, 0
Let f be (-4)/10 - 81/(-15). Factor 4*s**4 + 2*s**5 + s**5 + 2*s + 3*s**f - 4*s**2 - 8*s**5.
-2*s*(s - 1)**3*(s + 1)
Let f = 993/8 + -124. Let s(x) be the first derivative of f*x**2 - 1/12*x**3 + 2 + 1/2*x. Determine g so that s(g) = 0.
-1, 2
Let p be (-4)/10 - (-12)/(-20). Let f be 2 - 0*p/2. Factor 0*y - 3*y**2 - 3*y + f - 2*y**2.
-(y + 1)*(5*y - 2)
Let w(k) be the third derivative of k**6/90 + 2*k**5/15 + k**4/2 - 11*k**2. Factor w(g).
4*g*(g + 3)**2/3
Find o such that 0 - 4/9*o**2 - 2/3*o**3 + 0*o + 4/9*o**4 = 0.
-1/2, 0, 2
Solve 3/8*a**3 + 3/4 + 9/8*a**2 - 3/8*a**4 - 15/8*a = 0.
-2, 1
Let k(p) be the third derivative of -p**6/60 - p**5/30 + p**4/12 + p**3/3 + 7*p**2. Let k(l) = 0. What is l?
-1, 1
Let z(d) be the second derivative of 1/42*d**4 + 0 + 2/21*d**3 + 5*d - 3/7*d**2. Factor z(v).
2*(v - 1)*(v + 3)/7
Let c(b) = -11*b**3 - 11*b**2 + b + 6. Let i(y) = 6*y**3 + 6*y**2 - 3. Let t(q) = 3*c(q) + 5*i(q). Factor t(d).
-3*(d - 1)*(d + 1)**2
Let u(v) be the third derivative of v**7/420 + v**6/144 + v**5/180 - 5*v**2. Factor u(z).
z**2*(z + 1)*(3*z + 2)/6
Let g(z) be the first derivative of -1 + 1/9*z**3 - 1/3*z**2 + 1/3*z. Factor g(d).
(d - 1)**2/3
Let h = -61/7 + 9. Let x be (-69)/(-21) + (-3 - 0). Factor 2/7 - x*c**3 - 2/7*c**2 + h*c.
-2*(c - 1)*(c + 1)**2/7
Let w(l) be the first derivative of -2*l**3/3 + 8*l - 5. Suppose w(x) = 0. What is x?
-2, 2
Suppose 0 = 5*k - 3*w - 11 - 6, 5*k - 22 = -2*w. Let d(g) = -g**3 + 4*g**2 + 2*g - 2. Let f be d(k). Factor 2 - v**3 - 1 + f*v**2 - 3*v - 3*v**2.
-(v - 1)**3
Let i(q) = 2*q - 10. Let w(p) = -p**3 - p**2 + 3*p - 3. Let z be w(-3). Let a be i(z). Let 1/3*v + 0 - 1/3*v**a = 0. Calculate v.
0, 1
Factor -1/4*k**3 + 1/4*k**2 + 0 + 1/4*k - 1/4*k**4.
-k*(k - 1)*(k + 1)**2/4
Let x be (-6)/(-2) + (-12)/(-3). Let s be x/14 - (-1 + 1). Factor s*g - 1/4*g**2 - 1/4.
-(g - 1)**2/4
Let l(x) be the first derivative of 5*x**4 - 8*x**3/3 - 3. Factor l(w).
4*w**2*(5*w - 2)
Let v(r) be the second derivative of r**9/7560 + r**8/3360 + r**4/4 + 3*r. Let x(o) be the third derivative of v(o). Determine i so that x(i) = 0.
-1, 0
Factor 0*i**5 + 4*i**5 - 9*i**5 + 3*i**5.
-2*i**5
Let l(u) be the first derivative of -u**3/4 + 6*u**2 + 32. Solve l(f) = 0 for f.
0, 16
Let n(l) = -l**3 - 2*l**2 - 3*l + 2. Let q(y) = 2*y**3 + 3*y**2 + 3*y - 2. Let b(m) = 3*n(m) + 2*q(m). Factor b(x).
(x - 1)**2*(x + 2)
Let c(p) = p**2 - p - 1. Let g be c(0). Let k = g - -4. Factor 3 + k*u**2 - 5 - u**2.
2*(u - 1)*(u + 1)
Let i(m) be the second derivative of m**7/2940 + m**6/1260 - m**3/2 + 3*m. Let r(l) be the second derivative of i(l). Factor r(y).
2*y**2*(y + 1)/7
Suppose 4*j - u = 18, 4*j - 2*u = 8*j - 12. Factor -8/3*p**2 - 8/3*p**3 - 2/3*p**j + 0 + 0*p.
-2*p**2*(p + 2)**2/3
Let w(f) be the third derivative of 0*f - 1/15*f**5 - f**2 + 0 + 1/3*f**4 + 0*f**3. Factor w(k).
-4*k*(k - 2)
Let x = 833/309 + -3/103. Solve -x*o**2 - 8/3*o**4 - 4*o**3 - 2/3*o**5 - 2/3*o + 0 = 0 for o.
-1, 0
Let t(n) = n**3 + 4*n**2 + n + 7. Let z be t(-4). Factor 2/7*f**z + 0*f - 2/7*f**4 + 0 + 4/7*f**2.
-2*f**2*(f - 2)*(f + 1)/7
Let f be 2 - (-6 - 6/(-2)). Let p(s) = -6*s**2 - 32*s - 24. Let i(b) = 4*b**2 + 21*b + 16. Let t(u) = f*p(u) + 8*i(u). Solve t(o) = 0.
-2
Let 3/7*m**2 + 0*m + 0 = 0. What is m?
0
Let v be 2*(1 - 17)*-1. Let q be ((-2)/(-5))/(v/40). Let -q + y**2 - 1/2*y**4 + 0*y + 0*y**3 = 0. What is y?
-1, 1
Let v(g) be the first derivative of 3*g**4/4 - 2*g**3 + 3*g**2/2 + 1. Determine m so that v(m) = 0.
0, 1
Let v(d) be the third derivative of d**6/150 + d**5/15 + 4*d**4/15 + 8*d**3/15 + 13*d**2. Factor v(q).
4*(q + 1)*(q + 2)**2/5
Let o(p) = 10368*p**4 + 6903*p**3 + 1719*p**2 + 183*p + 17. Let b(h) = 5184*h**4 + 3452*h**3 + 860*h**2 + 92*h + 8. Let u(w) = 9*b(w) - 4*o(w). Factor u(l).
4*(6*l + 1)**4
Let d(i) be the first derivative of -i**3/9 - 2*i**2/3 - 4*i/3 + 3. Factor d(c).
-(c + 2)**2/3
Factor -2/11*b + 2/11*b**2 - 4/11.
2*(b - 2)*(b + 1)/11
Suppose -r + 4 - 2 = 0. Let m be ((-6)/10)/(r/(-10)). Factor 1/3*v**m + 1/3*v**2 + 0*v + 0.
v**2*(v + 1)/3
Suppose -18*f**3 - 26*f**3 + 61*f**3 + 28*f + 34*f**2 + 3*f**4 + 8 = 0. Calculate f.
-2, -1, -2/3
Determine i, given that -110/3*i**2 - 5/3*i**4 - 15 + 40*i + 40/3*i**3 = 0.
1, 3
Let l = -54 - -57. Let k be (-12)/14*(-4)/12. Solve -k*u**4 + 0 - 6/7*u**l - 2/7*u - 6/7*u**2 = 0.
-1, 0
Let z(m) = -2*m**4 - 8*m**3 + 6*m**2 + 4*m. Let b(t) = -4*t**4 - 15*t**3 + 11*t**2 + 8*t. Let o(q) = -4*b(q) + 7*z(q). Solve o(l) = 0.
-2, -1, 0, 1
Factor 3/2*h + 0 + 1/2*h**2.
h*(h + 3)/2
Let p(k) be the third derivative of k**6/300 - 2*k**5/75 + k**4/12 - 2*k**3/15 - 13*k**2. Solve p(t) = 0.
1, 2
Let v(r) be the first derivative of r**8/4200 + r**7/1050 + 2*r**3 + 4. Let l(x) be the third derivative of v(x). What is k in l(k) = 0?
-2, 0
Suppose 2*z = 5 - 1. Determine v so that 4*v**3 - 7*v + 4*v**5 + 8*v**4 - 10*v**2 - 2 + 4*v**z - v**5 = 0.
-1, -2/3, 1
Let j(o) = o**3 + o**2 + o + 2. Let v be j(0). Suppose a + 2 = -5*f, f = -v*f - 2*a - 4. Suppose -2/9 + 2/9*m**2 + f*m = 0. Calculate m.
-1, 1
Let r(x) be the second derivative of -x**7/210 - 2*x**6/75 + x**5/50 + x**4/5 - 3*x**3/10 + 6*x. Solve r(b) = 0.
-3, 0, 1
Let r(o) be the third derivative of -o**10/453600 + o**8/60480 + o**5/30 + o**2. Let m(q) be the third derivative of r(q). Let m(d) = 0. What is d?
-1, 0, 1
Let m be (6 + -3)*2/3. Factor 8*g - m*g**3 - 8*g.
-2*g**3
Let c(l) = -l - 5. Let h be c(-7). Factor -4*d**2 + 4*d**h - d**2.
-d**2
Suppose 0*u - 5*u = -3*j + 37, 4*j - 11 = -u. Factor -4*l**2 + 1/4*l**5 + 7/2*l**3 + 9/4*l - 1/2 - 3/2*l**j.
(l - 2)*(l - 1)**4/4
Let h be (41 - 3) + 1 + -3. Let y be h/24*2/15. Factor 2/5 + y*d**2 - 3/5*d.
(d - 2)*(d - 1)/5
Suppose -10 = 15*u - 17*u. Let b(i) be the first derivative of 0*i - 1/9*i**2 + 1/18*i**4 - 2/45*i**u + 2/27*i**3 + 1. Factor b(o).
-2*o*(o - 1)**2*(o + 1)/9
Let u = 20 + -15. Let b(m) be the third derivative of 1/3*m**3 + 0 - 1/60*m**6 + 1/10*m**u - 1/4*m**4 + 0*m + 2*m**2. Factor b(z).
-2*(z - 1)**3
Let s(n) = -4*n**3 - 2*n + 2. Let l be (9/6)/(3/4). Let c(a) = 21*a**3 + a**2 + 11*a - 11. Let z(y) = l*c(y) + 11*s(y). Find j, given that z(j) = 0.
0, 1
Let t(r) be the first derivative of 2*r**3/3 + r**2 + 12*r - 3. Let u be t(-6). Factor u*p**3 + 3/2 - 12*p**2 - 15/2*p.
3*(3*p + 1)*(4*p - 1)**2/2
Let g be 3 + 1 - (0 + 1). Suppose -r - 1 + g = 0. What is y in 2 - 4*y - 4*y + 0*y + 6*y**r = 0?
1/3, 1
Let r be 165/180*(-2)/(-11). Let -r + 5/3*j - 25/6*j**2 = 0. Calculate j.
1/5
Factor 2 + 9*z - 2*z - 3*z + 5*z**2 - 1 + 2*z**3.
(z + 1)**2*(2*z + 1)
Let b be (-7)/8 - (-9)/6. Let r(t) be the first derivative of 5/6*t**3 + 1/4*t - 3 - 5/8*t**4 - 1/24*t**6 - b*t**2 + 1/4*t**5. Suppose r(i) = 0. Calculate i.
1
Let f(r) be the third derivative of -r**10/30240 - r**9/5040 - r**8/2240 - r**7/2520 + r**4/24 - r**2. Let p(k) be the second derivative of f(k). Factor p(i).
-i**2*(i + 1)**3
Suppose 3*w + 3*f = 45, -5*w + 2*f = 6*f - 78. Let p be (-3)/w + (-25)/(-60). Find a such that p*a**3 - 3/2*a**2 + 3*a - 2 = 0.
2
Let j be (-2)/(-10)*30/12. Suppose -3*g + q + 7 = -q, 2 = -2*g + 3*q. Factor v**2 - 1/2*v**4 - 1/2*v - 1/2*v**g + v**3 - j.
-(v - 1)**2*(v + 1)**3/2
Factor 0*c + 1/4*c**3 + 5/4*c**2 + 0.
c**2*(c + 5)/4
Let b(u) be the second derivative of -8*u**6/35 - u**5/5 + u**4/3 + 4*u**3/21 + 8*u. What is z in b(z) = 0?
-1, -1/4, 0, 2/3
Let k be 6 + -3 - 6*1. Let y be k/(18/(-8)) - 1. Solve y*g**3 + 1/3 - 1/3*g**2 - 1/3*g = 0 for g.
-1, 1
Suppose 0 = 3*a - 2*a. Let m(t) be the third derivative of 0*t**4 - 1/30*t**5 + 1/84*t**8 + 0 - 1/21*t**7 + 0*t**3 + t**2 + a*t + 1/15*t**6. Factor m(w).
2*w**2*(w - 1)**2*(2*w - 1)
Suppose 3*l = 5*i + 7, -3*l + 4*l + i - 5 = 0. Let q = l + 0. Factor -4*x**q - 2*x**2 - 3*x**4 - 2*x**3 + 3*x**2 - 4*x**5.
-x**2*(x + 1)**2*(4*x - 1)
Factor -3/5*b - 1/5 - 3/5*b**2 - 1/5*b**3.
-(b + 1)**3/5
Let k = 2 - -1. Let 2 + i + 12*i**2 + 147*i**k + 7*i - 139*i**3 + 2*i**4 = 0. What is i?
-1
Let i be 6 + -2 - 476/126. Factor i*t**4 + 2/9 + 4/3*t**2 - 8/9*t - 8/9*t**3.
2*(t - 1)**4/9
Let y(c) = 7*c**3 + 36*c*