
Let z = 1 - -2. Suppose z*x - 4*a - 1 = 0, 3*x - a = -0*a + 7. Factor 0*l**4 - l**4 + 3*l**4 - 2*l**x.
2*l**3*(l - 1)
Let v(g) = -6*g**2 + 112*g + 78. Let u(f) = 6*f**2 - 113*f - 79. Let r(i) = -2*u(i) - 3*v(i). Factor r(o).
2*(o - 19)*(3*o + 2)
Let k(v) = v**2 - 5*v - 10. Let x be k(7). Suppose 3*t + 5 = x*t. Let 1/4*q**t + 1/2*q**3 + 1/4 - 3/4*q + 1/2*q**2 - 3/4*q**4 = 0. Calculate q.
-1, 1
Let w(r) be the second derivative of -r**6/30 + r**5/10 + r**4/4 - 4*r**3/3 + 2*r**2 + 17*r. Solve w(x) = 0 for x.
-2, 1, 2
Factor m**2 - m**3 + 1/2*m**5 - 1/2 + 1/2*m - 1/2*m**4.
(m - 1)**3*(m + 1)**2/2
Factor 28/9*s - 2/9*s**2 + 0.
-2*s*(s - 14)/9
Suppose 5*y - 195 = 10*y. Let i = -39 - y. Let -1/3*n**3 - 2/3*n + n**2 + i = 0. Calculate n.
0, 1, 2
Let s(u) be the third derivative of 1/240*u**6 + 1/16*u**4 - u**2 + 0 - 1/12*u**3 + 0*u - 1/40*u**5. Suppose s(d) = 0. What is d?
1
Let g(z) be the third derivative of 1/108*z**4 + 1/540*z**6 + 0 - 5*z**2 + 0*z**3 + 1/135*z**5 + 0*z. Factor g(i).
2*i*(i + 1)**2/9
Let s(w) be the first derivative of -2 - 54/5*w**5 + 0*w**2 - 5/2*w**6 + 0*w + 8*w**3 - 9*w**4. Solve s(o) = 0 for o.
-2, 0, 2/5
Let v(c) be the third derivative of c**7/735 - c**5/70 + c**4/42 + 4*c**2 + 1. What is k in v(k) = 0?
-2, 0, 1
Let b(c) = 6*c**3 - 3*c**2. Let p(r) = 11*r**3 - 6*r**2. Let f(w) = 5*b(w) - 3*p(w). Suppose f(y) = 0. What is y?
0, 1
Let l(o) be the second derivative of o**6/60 + o**5/30 - o**4/6 + 3*o**2/2 + 5*o. Let t(h) be the first derivative of l(h). Factor t(q).
2*q*(q - 1)*(q + 2)
Let z(b) be the third derivative of b**8/5040 - b**7/420 + b**6/90 - b**5/12 - 10*b**2. Let w(v) be the third derivative of z(v). Determine i so that w(i) = 0.
1, 2
Let k(j) = -j**2 - 1. Let n(o) = -9*o**2 - 32*o - 135. Let d(w) = -14*k(w) + 2*n(w). Factor d(r).
-4*(r + 8)**2
Let p = 37 - 109/3. Suppose 5*t - t = 0. Determine s, given that p*s**2 - 2/3 + t*s = 0.
-1, 1
Let k(c) be the third derivative of 1/18*c**3 - 1/180*c**5 + 0 + 5*c**2 - 1/240*c**6 + 1/48*c**4 + 0*c. Factor k(i).
-(i - 1)*(i + 1)*(3*i + 2)/6
Let z(l) = 6*l + 2. Let v be z(-1). Let y = v - -6. Factor n**3 - 9/5*n**y - 2/5 + 7/5*n - 1/5*n**4.
-(n - 2)*(n - 1)**3/5
Suppose -2*b + 5*g = -11, -4*g = b - 3*b + 10. Let k be b/(-6) + (-135)/(-110). Factor 0 - 8/11*w**2 - 2/11*w - 2/11*w**5 - k*w**4 - 12/11*w**3.
-2*w*(w + 1)**4/11
Suppose 4 = 3*v - 5*w + 17, 0 = 2*w - 10. Find f such that 102/7*f**3 - 48/7*f**2 + 8/7*f + 30/7*f**5 + 0 - 92/7*f**v = 0.
0, 2/5, 2/3, 1
Let s be 0*(21/6 + -4). Let g(o) be the second derivative of -3*o - 1/70*o**5 + 1/42*o**4 + 2/21*o**3 + 0 + s*o**2. Factor g(j).
-2*j*(j - 2)*(j + 1)/7
Solve 5*x**2 + 3*x + x + 1 - 5*x**3 + 7*x**3 = 0 for x.
-1, -1/2
Let s be 2587/(-8580) + 4/(-22). Let j = -1/12 - s. Factor -4/5*u**2 - j*u + 0 - 2/5*u**3.
-2*u*(u + 1)**2/5
Determine l, given that 30 - 516*l + 581*l + 15*l**2 - 40*l**2 = 0.
-2/5, 3
Let q(a) = 10*a**2 - a - 2. Let u be q(-2). Let w = u + -159/4. Factor 0*l - w*l**2 + 1/4.
-(l - 1)*(l + 1)/4
Suppose o + 4 = -3*z, 0 = -6*z + 3*z - 3*o + 6. Let p = 5 + z. Determine q, given that 5*q**2 - 3*q**p - q**3 - 4*q**2 - 2*q**4 - 3*q**3 = 0.
-1, 0
Let j(a) = 5*a. Let f be 0 - (-3 - 3/(-3)). Let h be j(f). Factor 8 - 18*w**2 + 2*w + 2*w + 4*w - 8*w**2 + h*w**3.
2*(w - 2)*(w - 1)*(5*w + 2)
Let j(i) be the third derivative of -i**11/997920 + i**9/90720 - i**7/15120 + i**5/60 + 6*i**2. Let r(v) be the third derivative of j(v). Factor r(k).
-k*(k - 1)**2*(k + 1)**2/3
Let b = 2/179 - -1426/537. Let c(a) be the first derivative of -3 + 7/2*a**2 + 2*a + b*a**3 + 3/4*a**4. Find h such that c(h) = 0.
-1, -2/3
Let n(d) be the second derivative of d**5/70 + d**4/6 + 2*d**3/7 - 50*d. What is h in n(h) = 0?
-6, -1, 0
Suppose 0 = 7*o - 6*o - 6. Let k(t) be the third derivative of -1/42*t**7 - 1/30*t**5 + 0*t - 7/120*t**o + 0*t**4 + 0 + 0*t**3 - t**2. Factor k(c).
-c**2*(c + 1)*(5*c + 2)
Let c(i) be the third derivative of i**6/360 - i**5/120 + i**3 - 4*i**2. Let d(g) be the first derivative of c(g). Determine j, given that d(j) = 0.
0, 1
Let t = 4842/575 + -12/575. Let 98/5*x**4 - 16/5 - 24*x - t*x**3 - 244/5*x**2 = 0. What is x?
-1, -2/7, 2
Let n(x) = -4*x**4 - 2*x**3 - 8*x**2 - 4*x + 6. Let y(a) = 6 + a**2 - a - a**4 - 2*a**2 - 5. Let u(m) = -n(m) + 6*y(m). Factor u(l).
-2*l*(l - 1)**2*(l + 1)
Let t(j) be the third derivative of j**6/70 + 3*j**5/140 - j**4/56 + 4*j**2. Factor t(k).
3*k*(k + 1)*(4*k - 1)/7
Let h(w) be the second derivative of w**9/24192 + w**8/13440 - w**7/6720 - w**6/2880 - w**3/6 - 6*w. Let m(g) be the second derivative of h(g). Factor m(q).
q**2*(q - 1)*(q + 1)**2/8
Suppose 29*n + 38 = 48*n. Suppose 0 - 2/9*x**4 + 0*x**n + 2/9*x**5 + 0*x + 0*x**3 = 0. What is x?
0, 1
Let z(a) be the second derivative of 49*a**6/45 + 21*a**5/5 + 10*a**4/3 + 8*a**3/9 + 6*a. Factor z(o).
2*o*(o + 2)*(7*o + 2)**2/3
What is d in 0*d + 2/7 - 2/7*d**2 = 0?
-1, 1
Suppose -1 + 7 = 2*q. Factor -2*l + 2*l - 4*l**4 + 4*l**q.
-4*l**3*(l - 1)
Factor 3/7*p**3 - 3/7*p**2 - 2/7*p + 2/7*p**4 + 0.
p*(p - 1)*(p + 2)*(2*p + 1)/7
Let j(x) = -9*x**3 + 45*x**2 + 9*x - 45. Let w(h) = 2*h**3 - 11*h**2 - 2*h + 11. Let g(o) = 5*j(o) + 21*w(o). Factor g(y).
-3*(y - 1)*(y + 1)*(y + 2)
Suppose 3*a - 47 + 23 = 0. Let z(n) be the third derivative of 0*n**3 + 4*n**2 + 0 + 0*n**7 - 1/120*n**5 + 0*n + 1/160*n**6 + 0*n**4 - 1/1344*n**a. Factor z(u).
-u**2*(u - 1)**2*(u + 2)/4
Let k = 113/4 + -28. Find z, given that -1/4*z**3 - 1/4*z**2 + k*z + 1/4 = 0.
-1, 1
Factor -1 - 3*y + 2*y + y**3 + 0*y + y**2.
(y - 1)*(y + 1)**2
Solve 2 + 2*v + 1/2*v**2 = 0 for v.
-2
Let f(o) = o**5 + o**4 + o**2 - 1. Let m(d) = d**5 + 38*d**4 - 72*d**3 + 80*d**2 - 35*d. Let z(q) = 6*f(q) - m(q). Let z(u) = 0. What is u?
2/5, 1, 3
Let x = -11 + 13. Let p = -2 + x. Factor p*d + 2/5*d**2 + 0.
2*d**2/5
Suppose -5*s**2 + 3*s + 4*s**4 - s + 5*s**3 + s**4 - 7*s = 0. What is s?
-1, 0, 1
Let o(r) be the second derivative of -2/45*r**6 - 2/9*r**4 + 0*r**3 - 5*r + 0*r**2 + 0 + 1/5*r**5. Let o(l) = 0. What is l?
0, 1, 2
Let p = -1 + 3. Let k be 0*(7/(-2))/(-7). Factor 0*h + 1/2*h**p + k.
h**2/2
Find r, given that 0*r + 2/15*r**4 + 0 + 2/15*r**3 - 2/15*r**5 - 2/15*r**2 = 0.
-1, 0, 1
Let b(x) be the third derivative of -5*x**7/168 + x**6/72 + 2*x**5/15 + x**4/6 - x**3/6 - 2*x**2. Let p(t) be the first derivative of b(t). Factor p(y).
-(y - 1)*(5*y + 2)**2
Let h be 50/(-15) - (-4)/(-6). Let p be (13 - 5)*(-2)/h. Factor -3*v - 2*v**p - 1 + 27*v + 16*v**3 - 26*v**2 - 4*v**3 - 7.
-2*(v - 2)**2*(v - 1)**2
Let u(j) = j**3 + 8*j**2 + 6*j - 5. Let m be u(-7). Suppose -m = -2*g + 6. Factor 8 - 4*y**3 - 9 - 6*y**2 - y - 3*y - y**g.
-(y + 1)**4
Let o(u) = u**3 - 8*u**2 + 9*u - 2. Let i be o(7). Suppose -3*f = f - i. Solve -6*z**f + 2*z - 6*z + 2*z + 8*z**2 = 0 for z.
0, 1/3, 1
Let y = -1 + 2. Suppose -b - j + 2*j = 1, -3*b + y = -2*j. Solve k**b - 4*k + 5*k - 2*k = 0 for k.
-1, 0, 1
Suppose -d + q = 3, -q + 2*q = 3. Let c(h) be the second derivative of -1/9*h**2 + d + 2/27*h**3 - 1/54*h**4 - h. Factor c(g).
-2*(g - 1)**2/9
Let l(i) be the first derivative of -i**6/6 + i**5/3 - i**4/12 - i**3/9 - 7. Determine j so that l(j) = 0.
-1/3, 0, 1
Let n(d) = -d**3 - 3*d**2 + 3*d + 1. Let q be n(-3). Let x be q/24 - (-1)/3. Suppose -4/7*h - 2/7*h**3 - 6/7*h**2 + x = 0. What is h?
-2, -1, 0
Let t = -382/5 - -80. Solve -6/5*f**3 - t*f + 4/5 + 4*f**2 = 0 for f.
1/3, 1, 2
Factor 1/8*t**2 + 0 - 1/4*t.
t*(t - 2)/8
Factor 0 + 6/5*d - 3/5*d**2.
-3*d*(d - 2)/5
Solve 54/23*y - 20/23 - 10/23*y**2 = 0.
2/5, 5
Let g = -20 - -102/5. Factor g - 3/5*z + 1/5*z**2.
(z - 2)*(z - 1)/5
Let y(d) be the third derivative of 0*d**3 + 0*d - 1/168*d**8 + 0*d**4 + 1/60*d**6 - 2*d**2 - 1/105*d**7 + 1/30*d**5 + 0. Factor y(v).
-2*v**2*(v - 1)*(v + 1)**2
Let x(u) = -3*u - 12. Let a be x(-7). Suppose -10 = 4*m - a*m. Factor 1/4*p**m - 1/4*p + 0.
p*(p - 1)/4
Suppose 7*b + 4 = 3*b. Let h(s) = -4*s**3 - s**2 - s. Let z be h(b). Factor 1 - 2*g - 2*g**5 - 1 + z*g**3.
-2*g*(g - 1)**2*(g + 1)**2
Let a(k) be the first derivative of -1 - 1/6*k**4 - k**2 + 2/3*k**3 - 2*k. Let r(i) be the first derivative of a(i). Factor r(u).
-2*(u - 1)**2
Let i(k) be the second derivative of -1/24*k**4 + 0*k**2 + 2*k + 0 + 0*k**3 - 1/80*k**5 + 1/120*k**6. Factor i(n).
n**2*(