**2 - 21*f. Let t(y) = y**2 + y. Let z(d) = g(d) + 15*t(d). Suppose z(i) = 0. What is i?
0, 2/3
Let f = 140 - 137. What is q in 1/4*q**f - 1/4*q**4 + 0 + 0*q**2 + 0*q = 0?
0, 1
Let w(t) be the first derivative of 0*t**3 + 3/4*t**4 + 1/2*t**6 + 0*t**2 + 6/5*t**5 + 0*t + 4. Determine n, given that w(n) = 0.
-1, 0
Suppose r + 6*s = 3*s + 113, -467 = -4*r + 3*s. Let o = -338/3 + r. Factor 0 - 4/3*b + 6*b**2 - 8*b**3 + o*b**4.
2*b*(b - 1)**2*(5*b - 2)/3
Factor -4 + 4*m**2 + 3*m**3 - m**3 - 4 + 2*m**2.
2*(m - 1)*(m + 2)**2
Factor 264 + 3*t - 3*t**3 - 264.
-3*t*(t - 1)*(t + 1)
Factor 5/6*d + 1/6*d**2 + 1.
(d + 2)*(d + 3)/6
Let g(z) be the first derivative of 1/2*z**2 + 5/12*z**3 + 3 + 1/4*z + 1/8*z**4. Factor g(a).
(a + 1)**2*(2*a + 1)/4
Suppose -15 = -3*z - 9. Factor -9*k + 9*k + k**z.
k**2
Let m(t) = -t**2 - 14*t - 13. Let l be m(-13). Suppose -1/2*y**3 - 2/3*y**2 + l - 1/6*y = 0. Calculate y.
-1, -1/3, 0
Suppose -4*h + 3*t = -25, 0 = -0*h + 3*h + 3*t - 3. Let s(k) be the first derivative of -1 + 0*k**2 + 2/15*k**5 + 0*k + 2/3*k**h + 8/9*k**3. Factor s(v).
2*v**2*(v + 2)**2/3
Let y(l) = l**3. Let n(x) be the first derivative of 7*x**4/4 + 10*x**3/3 + 3*x**2 - 18*x + 4. Let i(z) = n(z) - 5*y(z). Suppose i(m) = 0. What is m?
-3, 1
Let n = 24 - 22. Let y(q) be the first derivative of 3/2*q**4 + q**n + 0*q - 8/3*q**3 - 3. Solve y(u) = 0 for u.
0, 1/3, 1
Suppose 4*b - 3 = 5. Suppose b*r + r = 9. Determine l so that 6*l - r*l + l - 2*l**2 = 0.
0, 2
Let n(k) be the second derivative of 3*k**5/100 + k**4/10 - k**3/10 - 3*k**2/5 - k. Suppose n(x) = 0. What is x?
-2, -1, 1
Let u be ((-2)/(-2))/((-8)/(-24)). Factor 16*h**u - 5*h**2 + 44*h**2 + 4*h**4 - 23*h**2.
4*h**2*(h + 2)**2
Suppose -5*s - 131 - 9 = 0. Let a be -2*(-2 - s/16). Factor -1/4 + 0*o**2 - 1/2*o + a*o**3 + 1/4*o**4.
(o - 1)*(o + 1)**3/4
Let x(a) be the third derivative of a**5/270 - a**4/36 + 6*a**2. Let x(c) = 0. What is c?
0, 3
Let y(z) be the second derivative of -z**7/42 - 11*z**6/90 - z**5/4 - z**4/4 - z**3/9 - 6*z. Factor y(k).
-k*(k + 1)**3*(3*k + 2)/3
Let o(l) = 3*l**3 - 3*l**2 - 6*l. Let r(q) = 2*q**3 - 3*q**2 - 5*q. Let t(x) = -3*o(x) + 4*r(x). Factor t(y).
-y*(y + 1)*(y + 2)
Let p(h) be the third derivative of 0 + 2*h**2 + 0*h**3 + 0*h + 1/60*h**5 - 1/36*h**4 - 1/360*h**6. Factor p(o).
-o*(o - 2)*(o - 1)/3
Let g be 5/(-4) + (-8)/(-32). Let c be (-12)/15*g/2. Find q such that -c*q**2 + 2/5*q**3 + 2/5 - 2/5*q = 0.
-1, 1
Suppose 3*g - 5 = 7*g + p, 0 = 2*g - 5*p + 19. Let k be -1*(g - 21/(-12)). Determine s, given that 1/2*s**2 + k*s**5 + 0*s**3 + 0 - 1/2*s**4 - 1/4*s = 0.
-1, 0, 1
Let a(u) be the second derivative of -u**4/4 - 2*u**3 + 15*u**2/2 - 10*u + 1. Factor a(c).
-3*(c - 1)*(c + 5)
Let x(z) be the second derivative of 0*z**3 + 0*z**2 - 1/60*z**5 + 1/126*z**7 + 1/90*z**6 + 0 - 3*z - 1/36*z**4. Suppose x(o) = 0. What is o?
-1, 0, 1
Let t(m) be the second derivative of -1/30*m**4 + 2*m + 0 + 1/25*m**5 + 0*m**2 + 0*m**3 - 1/75*m**6. Factor t(s).
-2*s**2*(s - 1)**2/5
Let l(r) be the second derivative of r**6/210 + r**5/210 - r**4/84 - 2*r**2 - 3*r. Let a(o) be the first derivative of l(o). Factor a(b).
2*b*(b + 1)*(2*b - 1)/7
Let u(g) be the third derivative of 4*g**2 + 0*g - 3/490*g**7 + 1/784*g**8 + 0*g**4 + 3/280*g**6 + 0 - 1/140*g**5 + 0*g**3. Factor u(o).
3*o**2*(o - 1)**3/7
Let m = 191/9660 + -1/322. Let n(g) be the second derivative of 1/18*g**3 - 1/6*g**2 + 1/36*g**4 + 2*g - m*g**5 + 0. Factor n(t).
-(t - 1)**2*(t + 1)/3
Find s, given that 0 + 3/7*s**3 + 0*s + 6/7*s**2 = 0.
-2, 0
Let o(x) be the second derivative of 1/15*x**3 - 1/30*x**4 + 0*x**2 - 2*x + 0 + 1/75*x**6 - 1/50*x**5. Let o(l) = 0. Calculate l.
-1, 0, 1
Let k(h) be the third derivative of 0 + 0*h**3 + 1/420*h**7 + 0*h**4 - 3*h**2 + 1/120*h**6 + 0*h + 1/120*h**5. Factor k(s).
s**2*(s + 1)**2/2
Suppose 0 = -5*y + 112 - 102. Let d(i) be the third derivative of -1/8*i**4 + 3*i**y + 0 + 0*i + 0*i**3 + 1/40*i**6 + 0*i**5. Let d(v) = 0. What is v?
-1, 0, 1
What is p in 0 - p - 3*p**2 + 2 + 0 = 0?
-1, 2/3
Let q(p) be the third derivative of 2*p**6/25 - 3*p**5/25 + p**3/10 - 3*p**2. Determine u, given that q(u) = 0.
-1/4, 1/2
Let t(c) = -3*c**4 + 9*c**3 + 3. Let g(q) = -6*q**4 + 17*q**3 - q**2 + 5. Let d(k) = 3*g(k) - 5*t(k). Factor d(f).
-3*f**2*(f - 1)**2
Suppose -3*x = 3, 0 = -2*f - x - 1 - 0. Let v = -26/7 + 144/35. Find j such that 2/5*j - v*j**2 + f = 0.
0, 1
Factor -w - 3*w**2 - w + 4*w**3 - 5 - 2*w**3 + 8.
(w - 1)*(w + 1)*(2*w - 3)
Suppose 0 = -3*o - 2*o - 4*i + 8, 0 = -5*o - 2*i + 4. Let g(x) be the second derivative of -1/27*x**3 + o + 3*x + 2/9*x**2 - 1/27*x**4 + 1/90*x**5. Factor g(b).
2*(b - 2)*(b - 1)*(b + 1)/9
Let v(p) be the second derivative of 2/27*p**3 - 1/54*p**4 + 0*p**2 + 0 - 2*p. Suppose v(l) = 0. Calculate l.
0, 2
Let a = 1633/12 - 136. Let l(r) be the second derivative of r - 1/2*r**2 - 1/3*r**3 - a*r**4 + 0. Determine n, given that l(n) = 0.
-1
Factor 0*b + 0 - 4*b**2 + 4/5*b**3.
4*b**2*(b - 5)/5
Let n(l) = l**3 + 7*l**2 + 2*l + 2. Let r be n(-6). Factor -9*x**3 - r*x + 0*x**3 - 4 - 40*x**2 - 9*x**3.
-2*(x + 1)**2*(9*x + 2)
Let j(t) be the second derivative of 4/21*t**3 - 4/7*t**2 - 1/42*t**4 + 0 + t. Suppose j(o) = 0. Calculate o.
2
Let g = 4 + 8. Let p be ((-8)/g)/((-4)/3). Determine z, given that -p*z + z**3 + 1/2*z**4 - 1/2*z**5 - z**2 + 1/2 = 0.
-1, 1
Let i(k) = 5*k**4 - 16*k**3 + 11*k**2 - k. Let z(q) = q**4 - q**2 - q. Let d(j) = i(j) - z(j). Suppose d(a) = 0. Calculate a.
0, 1, 3
Let b(f) be the third derivative of f**7/420 - f**6/240 - f**5/60 - 7*f**2. Factor b(n).
n**2*(n - 2)*(n + 1)/2
Let h(o) be the third derivative of -1/420*o**6 - 1/210*o**5 + 1/84*o**4 + 0*o**3 + 1/735*o**7 + 0 + 0*o - o**2. Solve h(k) = 0.
-1, 0, 1
Determine t, given that 2/7*t**2 - 2/7 + 2/7*t - 2/7*t**3 = 0.
-1, 1
Suppose 24 + 12 = 6*c. Factor 3/4*n**4 - 9/2*n**3 + 0 - c*n + 9*n**2.
3*n*(n - 2)**3/4
Suppose 0*z - 3*z = -4*x - 21, -3*x + 2*z = 15. Let f be (-2)/(-4) - x/(-12). Suppose 0*b + 0*b**3 - 1/4*b**4 + 0 + f*b**2 = 0. Calculate b.
-1, 0, 1
Let i = -47047/1828 + -6/457. Let l = i - -26. Factor 0*w + 0*w**2 + 0 - l*w**4 - 1/4*w**3.
-w**3*(w + 1)/4
Let y(s) be the second derivative of -s**6/16 - s**5/20 + 5*s**4/16 + s**3/2 + 5*s**2/2 + s. Let n(o) be the first derivative of y(o). Factor n(x).
-3*(x - 1)*(x + 1)*(5*x + 2)/2
Let i(x) = x**2 + x + 1. Let k(u) = 9*u**2 + 9*u - 3. Let t(a) = -5*i(a) + k(a). Factor t(v).
4*(v - 1)*(v + 2)
Let n(j) be the first derivative of 2*j**2 - 1/12*j**4 + 0*j + 3 - 1/15*j**5 + 1/3*j**3. Let l(s) be the second derivative of n(s). Solve l(g) = 0.
-1, 1/2
Let d(q) be the first derivative of q**4 - 8*q**3/3 - 8*q**2 + 32*q + 12. Solve d(n) = 0.
-2, 2
Let f(j) be the third derivative of 0*j + 0*j**5 + 0 - 1/3*j**3 + 1/8*j**4 - 1/120*j**6 - j**2. Factor f(w).
-(w - 1)**2*(w + 2)
Let y be ((-5)/20)/(2 - 15/6). Let a(w) be the first derivative of w + 1/12*w**3 + y*w**2 + 2. Factor a(q).
(q + 2)**2/4
Let p(j) be the second derivative of 10*j**7/21 - 3*j**6/2 + 3*j**5/2 - 5*j**4/12 - 11*j. Factor p(f).
5*f**2*(f - 1)**2*(4*f - 1)
Suppose -4*d - d + 10 = 0. Let f(h) be the first derivative of -218/9*h**3 - 8/3*h - 12*h**d - 21*h**4 - 1 - 98/15*h**5. Factor f(k).
-2*(k + 1)**2*(7*k + 2)**2/3
Solve 14*k + 0*k**2 - 14*k + 2*k**2 = 0 for k.
0
Let s(r) = 8*r**2 + 4*r - 4. Suppose -4*z - 16 = -0*z. Let m(g) = -7*g**2 - 4*g + 3. Let k(t) = z*s(t) - 5*m(t). Factor k(l).
(l + 1)*(3*l + 1)
Factor -3/5*j**3 + 0*j + 1/5*j**4 + 2/5*j**2 + 0.
j**2*(j - 2)*(j - 1)/5
Let v(b) = b**3 + b**2 + 1. Let s(t) = -4*t**3 - 34*t**2 - 105*t - 76. Let w(h) = -s(h) - v(h). Find l, given that w(l) = 0.
-5, -1
Find w such that -3 + w - 52*w**2 + 27*w**2 - w**3 + 28*w**2 = 0.
-1, 1, 3
Let k(q) = -5*q - 5. Let n(z) = -z - 4*z**2 - 24 + 23 + 5*z**2. Let t(f) = k(f) - n(f). Factor t(o).
-(o + 2)**2
Let q = -142 - -144. Find c such that -1/2 + c - 1/2*c**q = 0.
1
Let n(o) be the third derivative of o**6/540 - o**5/270 - o**4/108 + o**3/27 + 2*o**2. Find j, given that n(j) = 0.
-1, 1
Let k(r) be the first derivative of r**6/18 - 4*r**5/5 + 9*r**4/2 - 12*r**3 + 27*r**2/2 - 3. Determine c, given that k(c) = 0.
0, 3
Let z(o) be the second derivative of -o**4 + 2/5*o**5 - 1/15*o**6 + 4*o + 0 + 4/3*o**3 - o**2. Find q, 