Factor -11/3*t - 2 + 1/3*t**3 - 4/3*t**2.
(t - 6)*(t + 1)**2/3
Suppose 2*q = 4*q - 10. Find z, given that -q*z - z - 2*z + 2*z + 3 + 3*z**2 = 0.
1
Let w = 14 + -12. Factor -6*z**w - 3*z + 5*z + 40*z**3 + 6 + z - 43*z**3.
-3*(z - 1)*(z + 1)*(z + 2)
Let p(a) = a - 7. Let w be p(3). Let c be (-68)/(-16) - (-1)/w. Let v**3 + 0 + 0 - v**2 - v + v**c = 0. Calculate v.
-1, 0, 1
Factor -s**5 - 259*s**3 - 16*s**2 + 255*s**3 + 16*s**4 + 5*s**5.
4*s**2*(s - 1)*(s + 1)*(s + 4)
Let h be 0 + 8/(-10) - (-904)/565. Determine v so that 2/5*v**3 + 4/5 - 2/5*v - h*v**2 = 0.
-1, 1, 2
Let z be (-4)/18 - (-870)/1485. Let -2/11 - 2/11*k**2 - z*k = 0. Calculate k.
-1
Let v(x) be the third derivative of x**5/15 + x**4/3 + 2*x**3/3 - 4*x**2. Determine g so that v(g) = 0.
-1
Let p be (150/(-180))/(0 + -5). Let f(b) be the second derivative of 1/3*b**3 - p*b**4 - 1/5*b**5 + 0 + 0*b**2 - 3*b. Factor f(s).
-2*s*(s + 1)*(2*s - 1)
Suppose -13*g = 15*g - 504. Solve 16/3 - g*r**4 - 36*r**2 + 54*r**3 - 8/3*r = 0.
-1/3, 2/3, 2
Let i(y) be the first derivative of 3*y**2 - y**3 + 3 - 2*y**3 - 4*y**3. Suppose i(c) = 0. Calculate c.
0, 2/7
Factor -6*p + 4*p**3 + 40 - 4*p**2 - 42 + 6*p**4 - p**5 + 3*p**5.
2*(p - 1)*(p + 1)**4
Let t = -4 - -4. Let r(b) be the third derivative of 0*b + 1/105*b**7 + 0 + 1/15*b**6 + 3*b**2 + t*b**3 + 2/15*b**5 + 0*b**4. Factor r(g).
2*g**2*(g + 2)**2
Factor -4/7 - 2/7*k**2 - 6/7*k.
-2*(k + 1)*(k + 2)/7
Let c = -5352/125 - -465973/12375. Let u = c - -69/11. Suppose 0 - 14/3*b**3 + 34/9*b**4 - 4/9*b + 22/9*b**2 - u*b**5 = 0. What is b?
0, 2/5, 1
Factor -1/4 + 1/4*b**2 + 0*b.
(b - 1)*(b + 1)/4
Let z = -2/27 + 176/189. Factor 2/7*f**2 - 8/7*f + z.
2*(f - 3)*(f - 1)/7
Factor -4/3*w + 4/3*w**3 + 0*w**2 - 2/3 + 2/3*w**4.
2*(w - 1)*(w + 1)**3/3
Let p = 342 - 8209/24. Let c = p + 11/8. Determine h so that 8/3*h**2 - c*h**4 + 2/3*h**5 - 4/3 - 4/3*h**3 + 2/3*h = 0.
-1, 1, 2
Let v(q) = -q**3 - 1. Let h(g) = -8*g**3 + 2*g**2 + g - 9. Let w(u) = 4*h(u) - 36*v(u). Suppose w(m) = 0. Calculate m.
-1, 0
Determine g, given that -10*g - 6*g**2 + 8*g**3 - 1 + 2*g**2 + 2 - 5 + 8*g**4 + 2*g**5 = 0.
-2, -1, 1
Suppose -g = -34 - 2. Let b = g - 143/4. Factor -b*r - 1/4*r**2 + 0.
-r*(r + 1)/4
Let y(x) be the second derivative of x**7/3780 - x**6/360 + x**5/90 - x**4/3 + 2*x. Let d(h) be the third derivative of y(h). Factor d(m).
2*(m - 2)*(m - 1)/3
Let -18/5*d**3 + 12/5*d + 6/5*d**5 - 22/5*d**4 + 38/5*d**2 - 16/5 = 0. Calculate d.
-1, 2/3, 1, 4
Solve -8/3 + 4/3*c**3 + 2*c**2 - 2/3*c**4 - 8/3*c = 0 for c.
-1, 2
Let v be (-240)/(-17) - (-26)/(-221). Factor -6*j**3 - 32/3*j + 8/3 + v*j**2.
-2*(j - 1)*(3*j - 2)**2/3
Let j(i) be the second derivative of -2*i**6 + 2*i + 7/2*i**3 + 0 - 111/20*i**5 - 3*i**4 + 3*i**2. Find q such that j(q) = 0.
-1, -1/4, 2/5
Let l(d) be the first derivative of d**5/150 + d**4/10 + 3*d**3/5 + 3*d**2/2 - 5. Let b(p) be the second derivative of l(p). Let b(a) = 0. What is a?
-3
Let t(q) = 5*q**3 + q**2 - 5*q + 5. Let j(y) = 11 + 3*y**2 - 3*y - 2*y + 11*y**3 - 6*y. Let h(w) = 3*j(w) - 7*t(w). Suppose h(u) = 0. What is u?
-1, 1
Let j be 213618/(-210) - 3/(-7). Let d = j - -1024. Factor 16/5 + 2/5*t**4 + 8*t + 14/5*t**3 + d*t**2.
2*(t + 1)*(t + 2)**3/5
Suppose 8 = 5*v - 12. Suppose q = v*q - 150. Solve 32 - 98*m**5 - 188*m**4 - 249*m + 25*m + 368*m**2 + 160*m**3 - q*m**4 = 0 for m.
-2, 2/7, 1
Let j = -4/37 + 110/333. Factor 0 + 2/9*k**2 + 2/9*k - j*k**3 - 2/9*k**4.
-2*k*(k - 1)*(k + 1)**2/9
Let q(w) = 8*w**3 - 21*w**2 + 11. Let o(b) = -4*b**3 + 10*b**2 - 6. Let l(j) = 11*o(j) + 6*q(j). Factor l(p).
4*p**2*(p - 4)
Let t(h) be the first derivative of 2*h**3/9 + 4*h**2/3 - 10*h/3 - 2. Factor t(z).
2*(z - 1)*(z + 5)/3
Let a(c) be the first derivative of 2*c**3/15 + 4*c**2/5 + 8*c/5 + 25. Suppose a(v) = 0. Calculate v.
-2
Let r(x) be the third derivative of x**6/540 + x**5/270 - x**4/108 - x**3/27 - 3*x**2. Factor r(i).
2*(i - 1)*(i + 1)**2/9
What is t in -8*t**2 - t + 0*t**4 + 5*t - t**4 + 5*t**3 + 0*t**3 = 0?
0, 1, 2
Let j(r) be the third derivative of r**2 + 1/8*r**4 + 0 + 1/2*r**3 - 1/10*r**5 + 0*r. Let j(k) = 0. What is k?
-1/2, 1
Let i be -1*2/3*(-240)/180. Let p(r) be the second derivative of -4/3*r**2 - i*r**3 + 0 + r + 1/6*r**4 + 3/10*r**5. Find n, given that p(n) = 0.
-2/3, 1
Suppose 0 = -3*x + 2*x + 2. Solve 4 + 2*u**2 - 1 - 2*u**2 - 3*u**x = 0.
-1, 1
Let w = 2/15 + 1/5. Suppose -13 = -5*l + 2. Suppose 1/3*r**4 + 0 - w*r**l + 0*r + 0*r**2 = 0. Calculate r.
0, 1
Let a(c) = 3*c**3 + c**2 - 1. Let y be a(1). Let t = -1 + y. Factor 2*s**3 - s**2 + 0*s**2 + 2*s**4 + 0*s**t - 3*s**4.
-s**2*(s - 1)**2
Factor 0 + 4/19*z**2 + 0*z + 2/19*z**3.
2*z**2*(z + 2)/19
Factor 3*t**4 + 56/3*t**2 + 32/3*t**3 + 16/3 + 1/3*t**5 + 16*t.
(t + 1)*(t + 2)**4/3
Let o(f) = -23*f - 3. Let b be o(-5). Solve 8 - b*z**3 - 5*z + 32*z**4 + 61*z + 36*z**2 + 30*z**2 = 0 for z.
-1/4, 2
Factor 8/5 + 16/5*r + 2*r**2 + 2/5*r**3.
2*(r + 1)*(r + 2)**2/5
Let o = 2 - 0. Let i = 13 - 8. Factor -i*u**2 + 0 + 11*u**2 - 4 - o*u.
2*(u - 1)*(3*u + 2)
Let k(a) be the third derivative of a**7/1120 - 7*a**6/2880 - a**5/240 - 7*a**4/24 - 8*a**2. Let u(q) be the second derivative of k(q). Factor u(c).
(c - 1)*(9*c + 2)/4
Let m be ((-9)/35)/(-3) - 27/(-135). Factor 22/7*z + m + 8*z**2.
2*(4*z + 1)*(7*z + 1)/7
Let u be 0*(1*4 + (-27)/9). Let u*k - 1/3*k**2 + 0 = 0. Calculate k.
0
Suppose 16*w - 8/3*w**3 - 44/3*w**2 + 4/3*w**4 + 48 = 0. What is w?
-2, 3
Let l = 215/981 + 1/327. Factor -2/9*k**2 + 0 + l*k.
-2*k*(k - 1)/9
Let s = -952 + 954. Factor 4/3*n**3 + 2/3*n**s + 2/3*n**4 + 0 + 0*n.
2*n**2*(n + 1)**2/3
Let f(x) be the third derivative of 0*x**3 - 1/60*x**5 + 0 + 0*x + 6*x**2 + 0*x**4. Let f(s) = 0. What is s?
0
Let y be (-3)/(63/2)*837/(-62). Suppose -s - 15/7*s**2 - y*s**3 - 1/7 = 0. Calculate s.
-1, -1/3
Let w(k) be the third derivative of k**6/300 - k**5/50 + k**4/30 + 6*k**2. Let w(s) = 0. What is s?
0, 1, 2
Let u(a) = a**2 - 2*a + 2. Let l be u(2). Find m, given that 4*m**4 - l*m**2 + m**2 + 0*m**4 - 3*m**4 = 0.
-1, 0, 1
Let r(y) be the first derivative of 2/5*y**3 - 2 + 7/5*y**2 + 4/5*y. Factor r(f).
2*(f + 2)*(3*f + 1)/5
Suppose -n**3 - 5*n**2 + 3*n**2 + 4*n**2 - n**2 + 2*n = 0. Calculate n.
-1, 0, 2
Let l(h) be the second derivative of h**5/60 - h**4/36 - h**3/9 - 12*h. What is k in l(k) = 0?
-1, 0, 2
Suppose -3*a**4 - 28*a**3 + 16*a**2 + 28*a**3 - 12 - a**2 = 0. Calculate a.
-2, -1, 1, 2
Let u(x) be the second derivative of x**7/10080 - x**5/480 - x**4/4 + 2*x. Let w(g) be the third derivative of u(g). Factor w(i).
(i - 1)*(i + 1)/4
Let d be 0/3 - (3 + -3). Let n(m) be the first derivative of -2 + 0*m**2 + 1/16*m**4 - 1/12*m**3 + d*m. Factor n(f).
f**2*(f - 1)/4
Suppose 0 = 3*o + o + 3*z - 23, 2*o - 14 = -2*z. Let b = o + 2. Factor f**5 - 2*f**b + 2 - 2.
f**4*(f - 2)
Suppose 3*q + 17 - 47 = 0. Let -7*g + q*g - g**2 - 6*g = 0. What is g?
-3, 0
Find c, given that 26*c**3 + 4*c**5 + 25*c - 80*c**2 + 7*c + 69*c**3 - 28*c**4 - 23*c**3 = 0.
0, 1, 2
Let q(o) = -11*o**3 + 19*o**2 - 25*o - 1. Let y(m) = 5*m**3 - 9*m**2 + 12*m. Let n(w) = 4*q(w) + 9*y(w). Suppose n(l) = 0. What is l?
1, 2
Let y(k) = 3*k + 6. Let b be y(8). Suppose 5*j + 0 = b. Factor -5*x - 2 - 4*x**2 + 6*x + j*x**2 - x**3.
-(x - 2)*(x - 1)*(x + 1)
Let d(c) be the second derivative of -c**7/21 + 2*c**6/15 + 2*c**5/5 - 4*c**4/3 + 7*c. Factor d(q).
-2*q**2*(q - 2)**2*(q + 2)
Let k(l) = l**2 + 7*l - 15. Let d be k(-9). Suppose 0*p - p**d + 0 + 2/3*p**2 + 1/3*p**4 = 0. Calculate p.
0, 1, 2
Let u be 56/10 - 16/(-40). Suppose 0 = 4*i, 2*v + 3*i - u = -0*i. Suppose -10*j**2 - 2/3 - 10/3*j**4 - 13/3*j - 29/3*j**v = 0. Calculate j.
-1, -1/2, -2/5
Factor 2/7 - 1/7*b**3 - 5/7*b + 4/7*b**2.
-(b - 2)*(b - 1)**2/7
Let z be -6 + 13 + (-6)/2. Let 4*d - 2*d**4 - 2 + 4*d**4 + 0*d**z - 4*d**3 = 0. Calculate d.
-1, 1
Let a(g) = -g + 2. Let c be a(6). Let z = c - -4. Factor 0 - 2/5*s**3 + z*s**2 + 2/5*s**4 + 0*s.
2*s**3*(s - 1)/5
Factor -18*o**2 + 7*o**3 - o**3 - 6*o + 21*o**4 + 9*o**5 - 5 - 9*o + 2.
3*(o - 1)*(o + 1)**3*(3*o + 1)
Let s be ((-47)/(-846))/(1/4). Suppose -2/3*o - s*o**2 - 4/9 = 0. What is o?
-2, -1
Let f(z) = 2*z**4 - 3*z**3 - 3*z**2 - 3. Let w(j) = j**4 - j**3 - j**2 - 1. Let a = 15 - 9. Let i(p) = a*w(p) - 2*f(p). Factor i(g).
2*g**4
Suppose