 + 1)**2*(q + 2)/3
Let k = 0 + 2. Factor -k*a + a**3 + 0*a**2 - 2*a**3 + 3*a**2.
-a*(a - 2)*(a - 1)
Let t(b) be the first derivative of 2/5*b**3 + 1/10*b**4 + 2/5*b + 3/5*b**2 - 4. Solve t(p) = 0 for p.
-1
Factor 0 + 1/4*n + 1/4*n**5 + 0*n**4 - 1/2*n**3 + 0*n**2.
n*(n - 1)**2*(n + 1)**2/4
Suppose 2*j + j = 6. Let n(f) be the second derivative of 0 + 1/60*f**4 + 0*f**3 - 1/10*f**2 - j*f. Let n(v) = 0. What is v?
-1, 1
Let o be (23/(-9) + 2)*(-60)/50. Factor 0 + 0*i - 4/3*i**2 + o*i**3 + 2/3*i**4.
2*i**2*(i - 1)*(i + 2)/3
Find b such that 2/5*b**4 + 8/5*b + 0 + 2*b**3 + 16/5*b**2 = 0.
-2, -1, 0
Let w(b) be the third derivative of b**6/160 - 31*b**5/240 + 85*b**4/96 - 25*b**3/24 + 2*b**2. Suppose w(r) = 0. Calculate r.
1/3, 5
Let q be (35/21)/((-5)/(-6)). Let h be (-1 + q)*(-2)/(-6). Factor -4/3*r**3 + h*r**4 + 0*r + 0 + 4/3*r**2.
r**2*(r - 2)**2/3
Let i(h) = 7 + 3*h - 7*h**2 - 3 + 4*h - h. Let s(w) = 8*w**2 - 5*w - 4. Let t(y) = -3*i(y) - 2*s(y). Let t(l) = 0. What is l?
-2/5, 2
Let s be 9/12*(-1 + 25). Let q = s - 13. Find t, given that -2*t**3 - 2*t**3 + 3*t**4 - q*t**4 + 0*t**2 - 2*t**2 = 0.
-1, 0
Let w(s) = -s**4 - s**3. Suppose -4 = -2*c + 4. Let g(i) = -7*i + 12*i**2 + 0 - i + 2 - 6*i**3 + c*i**4. Let r(q) = -g(q) - 2*w(q). Factor r(y).
-2*(y - 1)**4
Let l(j) be the first derivative of -2*j**3/3 - 2*j**2 - 2*j - 2. Factor l(k).
-2*(k + 1)**2
Let k(c) be the first derivative of -2*c**5/5 + 3*c**4/2 - 2*c**3 + c**2 + 24. Factor k(d).
-2*d*(d - 1)**3
Let q be (-23)/(-15) + (-76)/57. What is t in 0 + 2/5*t + 1/5*t**5 + q*t**2 - 1/5*t**4 - 3/5*t**3 = 0?
-1, 0, 1, 2
Let y(m) = m**2 + 9*m - 4. Let i be y(-9). Let g be (-17)/(-36) + 1/i. Factor 0 - g*q**2 + 2/9*q.
-2*q*(q - 1)/9
Let w = 23 - 113/5. Let -w + 1/5*l**2 + 1/5*l = 0. Calculate l.
-2, 1
Let i(u) = -u**3 + 7*u**2 - 7*u + 8. Let y be i(6). Suppose -y*b - 5 = o, 6*o - 31 = o + 4*b. Determine z so that 5/2*z**2 - 1/2 + 3/2*z**o + 1/2*z = 0.
-1, 1/3
Let g = 56 + -54. Let s(v) be the second derivative of 3/20*v**5 + 0 - 3*v + 1/6*v**3 + 0*v**g + 1/4*v**4 + 1/30*v**6. Factor s(y).
y*(y + 1)**3
Let j(n) = 7*n**3 - 21*n**2 + 15*n - 1. Let v(d) = 15*d**3 - 43*d**2 + 31*d - 3. Let o(f) = -10*j(f) + 6*v(f). Suppose o(l) = 0. What is l?
2/5, 1
Let o(j) = 5*j**3 - 9*j**2 - 11*j + 3. Let l(a) = -4*a**3 + 8*a**2 + 10*a - 2. Let k(b) = -6*l(b) - 4*o(b). Factor k(t).
4*t*(t - 4)*(t + 1)
Let c = 46 - 42. Factor 8/7*p**3 + 8/7*p + 12/7*p**2 + 2/7 + 2/7*p**c.
2*(p + 1)**4/7
Let p be (-28)/16 - (-1)/(-4). Let m = 5 + p. Solve -v**2 + 10 + m - 13 - v = 0 for v.
-1, 0
Let z be (-1)/(-3)*(-21)/(-63). Let n(m) be the second derivative of -z*m**3 + 3*m + 0 + 0*m**2 - 1/18*m**4. Determine i, given that n(i) = 0.
-1, 0
Let a = 2/667 + 661/2001. What is o in a*o**3 + 2/3 - 1/3*o - 2/3*o**2 = 0?
-1, 1, 2
Factor 0*s - 16/7*s**3 + 0 + 4/7*s**4 + 16/7*s**2.
4*s**2*(s - 2)**2/7
Factor -2/13 + 10/13*a + 14/13*a**3 - 4/13*a**4 - 18/13*a**2.
-2*(a - 1)**3*(2*a - 1)/13
Let w be 1/(-1)*(-6 + 4). Suppose w*l + 3*l = 10. Let 0*q**3 + 0 + 0*q - 2/3*q**4 + 2/3*q**l = 0. What is q?
-1, 0, 1
Suppose 6*u + 4 - 10 = 0. Suppose -2*t - s + 6*s - 1 = 0, -t + 3*s = u. Factor 0 + 0*v - 2/7*v**5 + 0*v**t - 2/7*v**4 + 0*v**3.
-2*v**4*(v + 1)/7
Let f(c) be the third derivative of -c**5/330 + c**4/66 - 10*c**2. Factor f(t).
-2*t*(t - 2)/11
Find i, given that 3/5*i**2 - 21/5*i + 18/5 = 0.
1, 6
Suppose -11 = 2*o + 3*n, 5*o - 18 = o + 2*n. Let -2/7*v**o + 0 - 2/7*v**4 + 0*v + 4/7*v**3 = 0. What is v?
0, 1
Let z(n) be the third derivative of n**8/1176 - n**6/420 + 21*n**2. Determine j so that z(j) = 0.
-1, 0, 1
Let w(r) be the second derivative of -1/11*r**2 + 3*r - 1/22*r**4 + 0 - 1/110*r**5 - 1/11*r**3. Factor w(c).
-2*(c + 1)**3/11
Let l(o) be the first derivative of -o**6/105 + 7*o + 8. Let i(k) be the first derivative of l(k). Factor i(p).
-2*p**4/7
Let j(k) = 5*k**2 + 3*k + 2. Let c = 1 - 5. Let m(n) = -4*n**2 - 3*n - 2. Let v(g) = c*m(g) - 3*j(g). Factor v(f).
(f + 1)*(f + 2)
Suppose 5*j = 4 + 11. Let t(p) be the first derivative of -7/9*p**6 - 6/5*p**5 + 5/6*p**4 + 2/3*p**2 + 1 + 2*p**j + 0*p. Let t(b) = 0. What is b?
-1, -2/7, 0, 1
Let t(h) = -2*h**2 - 28*h + 32. Let s be t(-15). Let p(r) be the second derivative of 0*r**s + 0 - 1/36*r**3 + 5/72*r**4 + 3*r. Suppose p(i) = 0. Calculate i.
0, 1/5
Suppose 15 - 11 = 2*k. Let h(n) be the second derivative of 1/147*n**7 + 0*n**3 + 1/70*n**5 + 0*n**4 + 0 + 2/105*n**6 - k*n + 0*n**2. Factor h(q).
2*q**3*(q + 1)**2/7
Let b be (8/20 + -1)*(-80)/16. Factor 3/2*r**3 - 3/2*r + b*r**2 - 3.
3*(r - 1)*(r + 1)*(r + 2)/2
Let b(y) be the third derivative of 1/30*y**5 + 2*y**2 - 1/60*y**6 + 0 + 0*y**3 + 0*y + 0*y**4. Factor b(w).
-2*w**2*(w - 1)
Suppose 0 = -0*w - 4*w. Factor 1/2*y + 1/2*y**2 + w.
y*(y + 1)/2
Suppose -5*u = -2*m + 24, -6 - 6 = 4*m. Let i be 3*u/(-45)*1. Factor 2/5 - 2/5*j**2 + 2/5*j - i*j**3.
-2*(j - 1)*(j + 1)**2/5
Let a be 1*(-2 + (-10)/(-2)). Let k be (0 - 0) + (2 - 0). What is s in 1/3*s**4 - 4/3*s - s**k + 2/3*s**a + 4/3 = 0?
-2, 1
Let p(q) = q**2 + 8*q - 6. Let o be p(-7). Let c = o + 16. Determine b so that 3/4*b**5 + 3/2*b**4 - 9/4*b**c + 3*b + 0 - 3*b**2 = 0.
-2, 0, 1
Let g(t) = -5*t**3 + 10*t**2 + 10*t - 10. Let n(b) = -5*b**3 + 9*b**2 + 9*b - 9. Let w(p) = -4*g(p) + 5*n(p). Factor w(q).
-5*(q - 1)**2*(q + 1)
Let d(f) be the third derivative of -2*f**7/105 - f**6/30 + f**5/15 + f**4/6 + 3*f**2. Factor d(a).
-4*a*(a - 1)*(a + 1)**2
Let m = 92 - 89. Let n(b) be the first derivative of -4*b + 1 + 0*b**2 + 1/3*b**m. Let n(h) = 0. What is h?
-2, 2
Let k(s) be the third derivative of s**9/272160 - s**5/60 + 2*s**2. Let w(n) be the third derivative of k(n). Factor w(f).
2*f**3/9
Factor -2/9*w**4 + 0 - 2/3*w**2 + 0*w + 8/9*w**3.
-2*w**2*(w - 3)*(w - 1)/9
Let s be (-200)/(-48) + -2*2. Let i = -42 + 253/6. Find f, given that -s*f**3 + 0*f + i*f**2 + 0 = 0.
0, 1
Let z(c) = -2*c**2 + 4*c + 10. Let d(h) = h**2 - 5*h - 9. Let n(w) = -4*d(w) - 3*z(w). Factor n(k).
2*(k + 1)*(k + 3)
Factor 2*p - 35*p**3 - 1 + 10*p**4 - 9 + 3*p + 30*p**2.
5*(p - 2)*(p - 1)**2*(2*p + 1)
Let z(r) be the first derivative of -8/35*r**5 + 1/21*r**6 - 3/7*r**2 + 8/21*r**3 + 10 + 1/7*r**4 + 0*r. Suppose z(m) = 0. Calculate m.
-1, 0, 1, 3
Suppose -3*f + 15 = 2*f. Find q, given that -3*q - 5*q**2 + 2*q**2 + q**f + 2*q**3 + 3*q**4 = 0.
-1, 0, 1
Let y = 8 - 6. Determine i so that -y - i - 2*i**3 + 2 + 3*i = 0.
-1, 0, 1
Let z(o) = -15*o**2 + o + 2. Let y(r) = -r**2 - r + 1. Let g(d) = 4*y(d) - 2*z(d). Factor g(t).
2*t*(13*t - 3)
Let c = -141 - -141. What is z in 1/3*z + c - 1/3*z**2 = 0?
0, 1
Factor g**5 + 15/7*g - 40/7*g**2 + 50/7*g**3 - 30/7*g**4 - 2/7.
(g - 1)**4*(7*g - 2)/7
Let i = 2922 - 5697/2. Let r(z) be the first derivative of -686/15*z**5 - 1 + i*z**4 - 140/9*z**3 - 12*z**2 + 16/3*z. Suppose r(s) = 0. Calculate s.
-2/7, 2/7, 1
Let z(d) be the second derivative of -d**7/273 - 2*d**6/195 + d**5/65 + 2*d**4/39 - d**3/39 - 2*d**2/13 - 17*d. Determine b so that z(b) = 0.
-2, -1, 1
Solve 15*s**3 + 11*s**3 - 2*s - 7*s**2 - 35*s**3 - s**5 - 5*s**4 = 0.
-2, -1, 0
Let k = 3 - 8/3. Find m, given that 0*m - k*m**3 + 1/3*m**5 + 1/3*m**2 + 0 - 1/3*m**4 = 0.
-1, 0, 1
Let x be 3/5*(14 + -9). Factor 1/4*n**x + 3/4*n + 1/4 + 3/4*n**2.
(n + 1)**3/4
Let y(n) = n**3 - n**2 - n. Let t(o) = 55*o**3 - 125*o**2 - 86*o - 12. Let p(x) = t(x) - 6*y(x). Factor p(k).
(k - 3)*(7*k + 2)**2
Determine t, given that 3/4*t**4 + 0 + 3/2*t + 0*t**3 - 9/4*t**2 = 0.
-2, 0, 1
Let h(b) = b**3 - 6*b**2 - b + 7. Let y be h(6). Let j(o) be the first derivative of -2/3*o**3 - y + 0*o + 1/2*o**4 + 0*o**2. Solve j(q) = 0.
0, 1
Let g(k) = -k**3 + k**2 + 4*k. Let m be g(3). Let h = -6 - m. Find u such that 0*u + h*u + 4*u**5 - 6*u**5 + 2*u + 4*u**2 - 4*u**4 = 0.
-1, 0, 1
Suppose 0*o + 3*m = 2*o + 15, 3*m - 15 = -o. Let 1/3*x**5 + 1/3*x**3 + x**4 - 2/3*x + o - x**2 = 0. Calculate x.
-2, -1, 0, 1
Let y(n) = 2*n**3 - 4*n**2 - 6*n. Let z(p) = -18*p**3 + 36*p**2 + 54*p. Let r(o) = -52*y(o) - 6*z(o). Factor r(k).
4*k*(k - 3)*(k + 1)
Suppose -p + 2 + 1 = 0. Factor 5/4*t**4 - 1/4*t**2 + 3/4*t**p - 1/4*t + 0 + 1/2*t**5.
t*(t + 1)**3*(2*t - 1)/4
Let p(n) be the third derivative of 0*n**4 + 1/60*n**6 + 0*n + 0*n**3 + 1/75*n**5 + 4/525*n**7 + 5*n**2 + 0 + 1/840*n**8. Fact