**2/2
Factor -1/4 + 3/8*t**3 - 3/8*t + 1/8*t**2 + 1/8*t**4.
(t - 1)*(t + 1)**2*(t + 2)/8
Factor 1/4*q**3 + 2*q - 1 - 5/4*q**2.
(q - 2)**2*(q - 1)/4
Suppose 2*j = m + 3*j - 1, m - 7 = 2*j. Let c(d) be the first derivative of 0*d - 1 + 2/5*d**5 + 0*d**2 + 0*d**m + 4/3*d**6 + 0*d**4. Factor c(q).
2*q**4*(4*q + 1)
Let c(u) = u**2 + 2*u - 3. Let h(g) = -2*g**2 - 4*g + 7. Let w(j) = 9*c(j) + 4*h(j). Factor w(o).
(o + 1)**2
Let o(c) = -5*c**2 - 18*c - 7. Let j(n) = n - 1. Let z(y) = 3*j(y) + o(y). Find h, given that z(h) = 0.
-2, -1
Let p = 1581/5 - 316. Factor -p*l**2 + 1/5*l + 0.
-l*(l - 1)/5
Let f = -128 - -513/4. Determine d so that 0 + f*d**3 + 0*d**2 - 1/4*d = 0.
-1, 0, 1
Let r(z) = z**2 + 15*z + 9. Suppose 0 = -y - 3*q - 13, -3*y - 4*q + 1 = -3*q. Let l(c) = c. Let g(n) = y*r(n) - 18*l(n). Factor g(p).
2*(p + 3)**2
Suppose 11 = 2*t - 7. Suppose 4*d - t = d. Factor 30*k**2 - 11*k + 2 - 6*k**2 - d*k.
2*(3*k - 1)*(4*k - 1)
Factor 57 - 6*q**2 - 22 - 26 - 15*q.
-3*(q + 3)*(2*q - 1)
Determine v so that -2/3 + 2/9*v**2 - 4/9*v = 0.
-1, 3
Suppose 0 - 68/9*k**3 + 56/9*k**2 - 2/3*k**5 - 16/9*k + 34/9*k**4 = 0. What is k?
0, 2/3, 1, 2
Factor -7*b - 6*b + 2*b**3 + 6*b**2 + 17*b.
2*b*(b + 1)*(b + 2)
Let d(n) be the second derivative of n**7/13860 + n**6/3960 + n**4/3 - 3*n. Let x(z) be the third derivative of d(z). Find m such that x(m) = 0.
-1, 0
Let c(k) be the second derivative of -k**6/180 - k**5/60 + k**3/18 + k**2/12 - 18*k. Factor c(q).
-(q - 1)*(q + 1)**3/6
Factor 147/2 + 21*j + 3/2*j**2.
3*(j + 7)**2/2
Let -42/13*m**3 + 0 - 98/13*m**4 - 8/13*m + 48/13*m**2 = 0. What is m?
-1, 0, 2/7
Let q(i) = i**3 - 16*i**2 + 16*i - 13. Let l be q(15). Factor 0 - h**4 - 5/4*h**3 + 0*h - 1/4*h**l.
-h**2*(h + 1)*(4*h + 1)/4
Factor 8*q - 20*q**2 + 5*q**3 + 12*q + 28 - 28.
5*q*(q - 2)**2
Let j = 1053 + -1050. Factor 0*y**j + 0*y - 3/7*y**4 - 3/7 + 6/7*y**2.
-3*(y - 1)**2*(y + 1)**2/7
Factor 0*d**2 - 5*d**2 - 56*d + 71*d - 10.
-5*(d - 2)*(d - 1)
Let p(a) be the third derivative of a**5/150 + 48*a**2 - 2. Let p(d) = 0. What is d?
0
Let a(r) = -10*r**2 - 8*r + 11. Suppose -3*l + 23 = -4*v - 10, 3*l = -v + 3. Let g = v - -8. Let q(n) = n**2 + n - 1. Let b(f) = g*a(f) + 18*q(f). Factor b(w).
-2*(w - 2)*(w + 1)
Let i(m) = -m**2 + m. Let v(y) = -3*y**2 + y - 1. Let c(s) = -10*i(s) + 4*v(s). Factor c(k).
-2*(k + 1)*(k + 2)
Let v = -273 - -1095/4. Find w, given that 0*w - 3/4*w**4 + 0*w**3 - v*w**5 + 0*w**2 + 0 = 0.
-1, 0
Let s(d) = -d + 6. Let x be s(0). Suppose -6 - x = -4*m. Factor -o**3 + 3*o**2 + 1 - m + 3 - 3*o.
-(o - 1)**3
Let w(v) = v - 5. Suppose -2*f + 30 = 4*h, -2*f - f = h - 20. Let r be w(h). Factor 1/2*p - 1/4*p**2 + r.
-p*(p - 2)/4
Let p(v) = -5*v**2 - 25*v + 5. Let r(u) = -5*u**2 - 24*u + 6. Let d(n) = -6*p(n) + 5*r(n). What is q in d(q) = 0?
-6, 0
Let a(b) be the third derivative of -7/120*b**6 + 0 + 7/24*b**4 - 1/42*b**7 - b**2 + 0*b + 1/20*b**5 + 1/3*b**3. What is j in a(j) = 0?
-1, -2/5, 1
Factor 2/7*x**3 + 0 - 2/7*x**5 + 0*x**4 + 0*x**2 + 0*x.
-2*x**3*(x - 1)*(x + 1)/7
Suppose 5*c - 2 = 7*c, u - 1 = -2*c. Suppose 3 + 3/4*o**2 - u*o = 0. Calculate o.
2
Let m = -9 + 11. Let b(a) be the third derivative of 0*a + 3/4*a**4 - 7/30*a**5 - 2/3*a**3 + 0 + 2*a**m. Determine o, given that b(o) = 0.
2/7, 1
Suppose 2*q**3 - q + 7/2*q**2 + 0 = 0. What is q?
-2, 0, 1/4
Let s(d) be the third derivative of d**6/360 - d**5/60 + d**4/24 + d**3/6 + 2*d**2. Let t(j) be the first derivative of s(j). Factor t(c).
(c - 1)**2
Let d(x) = x**3 - 2*x**2 + x. Let r be d(1). Let m(o) be the second derivative of 0*o**3 + r + 1/2*o**2 - 1/12*o**4 + o. Let m(t) = 0. Calculate t.
-1, 1
Let t(i) be the third derivative of i**5/270 + i**4/36 - 4*i**3/27 + 37*i**2. Find o such that t(o) = 0.
-4, 1
Suppose 0 = -5*z + 5*u, 4*z + 4 = -4*u + 20. Factor 2/7*a**z + 2/7 + 4/7*a.
2*(a + 1)**2/7
Let o(p) = 6*p**2 + 2*p - 8. Let n(q) = -7*q**2 - q + 8. Let t(l) = -4*n(l) - 5*o(l). Let t(a) = 0. What is a?
-4, 1
Suppose 13 = 2*n - 5. Suppose j**2 + n*j**2 - 6*j**2 - 4*j = 0. What is j?
0, 1
Factor 1/5*f**2 + 169/5 - 26/5*f.
(f - 13)**2/5
Let w(z) be the first derivative of -4*z + 1/20*z**5 + 0*z**2 + 0*z**4 - 2 + 0*z**3. Let d(f) be the first derivative of w(f). Factor d(c).
c**3
Let b be (4/12)/((-1)/(-3)). Determine j, given that 11*j**2 - b - 13*j**2 + 3 = 0.
-1, 1
Let b(v) be the first derivative of v**6/120 - 3*v**5/80 + v**4/16 - v**3/24 + 3*v - 3. Let c(w) be the first derivative of b(w). Suppose c(f) = 0. Calculate f.
0, 1
Factor 16/9*c + 0 - 2/9*c**2.
-2*c*(c - 8)/9
Let j(z) be the first derivative of -2*z**3/27 + z**2/9 + 4*z/9 + 12. Factor j(h).
-2*(h - 2)*(h + 1)/9
Let c(g) be the second derivative of -g**5/6 - 2*g**4/3 - 4*g**3/9 - 3*g - 3. Factor c(l).
-2*l*(l + 2)*(5*l + 2)/3
Let l(u) = 3*u**2 - 10*u. Let w(j) = 1. Let i(x) = -3*l(x) + 24*w(x). Factor i(a).
-3*(a - 4)*(3*a + 2)
Factor 2*h**2 - 83*h**5 + 6*h**3 + 81*h**5 - 6*h**2.
-2*h**2*(h - 1)**2*(h + 2)
Solve -2*i**2 + 8*i + 8*i**2 - 8 - 2*i**4 + 0*i**3 - 4*i**3 = 0 for i.
-2, 1
Let z(a) = -6*a**3 - 42*a**2 - 90*a - 54. Let f(n) = -4*n**3 - 28*n**2 - 60*n - 36. Let x(c) = 7*f(c) - 5*z(c). Factor x(r).
2*(r + 1)*(r + 3)**2
Determine l, given that l**2 - 3*l - 3*l - 5*l**2 - 2*l = 0.
-2, 0
Let p(f) be the third derivative of -8*f**7/105 - f**6/10 + f**5/3 + f**4/2 - 2*f**3/3 - 12*f**2. Find v such that p(v) = 0.
-1, 1/4, 1
Let f(o) be the first derivative of 0*o**2 + 1/4*o**4 + 3*o - 1/3*o**3 - 1/20*o**5 - 1. Let r(t) be the first derivative of f(t). Determine n so that r(n) = 0.
0, 1, 2
Let d(t) be the first derivative of -2*t**3/21 - 8*t**2/7 - 32*t/7 - 2. Let d(h) = 0. Calculate h.
-4
Let r(z) be the third derivative of -z**6/420 + z**5/210 + z**4/42 - 10*z**2. Factor r(d).
-2*d*(d - 2)*(d + 1)/7
Let b(g) be the second derivative of g**5/20 + g**4/3 + 5*g**3/6 + g**2 + 3*g. Suppose b(j) = 0. What is j?
-2, -1
Let c(t) = t**5 - t**3 + t**2 - t + 1. Let x(i) = 5 + 10*i**5 + 8*i**2 - 10*i + 7 + 2*i**4 + 2*i**4 - 12*i**3. Let j(r) = 12*c(r) - x(r). Factor j(d).
2*d*(d - 1)**3*(d + 1)
Let f(z) be the first derivative of 4*z**3/3 + 12*z**2 + 36*z - 5. What is t in f(t) = 0?
-3
Let y = 63 + -61. Determine f, given that -24/7*f**y - 12/7*f**4 + 2/7*f**5 + 26/7*f**3 + 8/7*f + 0 = 0.
0, 1, 2
Let p(w) be the second derivative of -w**6/30 + w**5/20 + 4*w. Suppose p(y) = 0. What is y?
0, 1
Let d be ((-4)/10)/((-21)/45). Let g be (-12)/56 + 2/4. Factor -g*b - d*b**3 + 0 - 6/7*b**2 - 2/7*b**4.
-2*b*(b + 1)**3/7
Factor 4*t**5 - 13*t**4 + 7*t**4 + 3*t**3 - t**5.
3*t**3*(t - 1)**2
Let t(k) = -k + 15. Let h be t(13). Factor 0 - 6/11*y**h + 4/11*y + 2/11*y**3.
2*y*(y - 2)*(y - 1)/11
Let k(x) = x**3 + x**2 - x. Let h(c) = 3*c**4 - 21*c**3 + 6*c**2 + 3*c. Suppose 9 = -r + 2*r. Let b(v) = r*k(v) + h(v). Factor b(g).
3*g*(g - 2)*(g - 1)**2
Let s(h) be the first derivative of 0*h + 3 + 0*h**2 - 1/2*h**4 + 1/3*h**3 + 1/5*h**5. Suppose s(z) = 0. Calculate z.
0, 1
Let g(w) be the second derivative of -1/98*w**7 - 3/70*w**6 + 0*w**2 - 9/140*w**5 + 0*w**3 - 3*w + 0 - 1/28*w**4. Suppose g(q) = 0. Calculate q.
-1, 0
Let f(g) = -4*g - 32*g**4 + 9*g + 36*g**2 - 8*g**3 + 15*g. Let c(i) = -97*i**4 - 25*i**3 + 107*i**2 + 59*i. Let k(r) = 4*c(r) - 11*f(r). Factor k(b).
-4*b*(b - 1)*(3*b + 2)**2
Let j be 2/3 + 14/6. Let z be -8 + 6 + (j - 1). Factor s**2 + z + 0*s**2 - 1 + 0.
(s - 1)*(s + 1)
Let q = 263/524 - 1/524. Suppose -4*d + d**3 + 2 - q*d**4 + 3/2*d**2 = 0. Calculate d.
-2, 1, 2
Let j(q) be the second derivative of -1/60*q**6 + 7/12*q**3 + 1/8*q**5 + 0 - 3/8*q**4 - 1/2*q**2 + 3*q. Find o, given that j(o) = 0.
1, 2
Factor -6/7*b + 0 - 2/7*b**2.
-2*b*(b + 3)/7
Suppose 2*d + 4 = 4*a, 2*a + 4*d = -11 + 23. Solve 14/3*t**4 + 22/3*t**a + 4/3*t + 32/3*t**3 + 0 = 0.
-1, -2/7, 0
Let n(q) be the third derivative of 2*q**7/105 - q**6/15 + q**5/15 - 3*q**2. Factor n(m).
4*m**2*(m - 1)**2
Let z = 119 - 117. Let y(s) be the first derivative of 0*s - 1/2*s**z - 4 - 2/3*s**3. What is u in y(u) = 0?
-1/2, 0
Let k(z) be the third derivative of z**6/540 - 2*z**5/135 + 5*z**4/108 - 2*z**3/27 - 6*z**2. Factor k(m).
2*(m - 2)*(m - 1)**2/9
Factor 0*k + 6/5*k**4 + 4/5*k**2 + 2*k**3 + 0.
2*k**2*(k + 1)*(3*k + 2)/5
Let s(o) = o**2. Suppose 4*h + h = 0. Let j be s(h). Find p, given that