
-2*y**2*(y - 1)/15
Let w(q) be the first derivative of -1/5*q**3 + 6/5*q - 3/10*q**2 + 2. Determine s so that w(s) = 0.
-2, 1
Let v be 21/(-14)*(-4)/6. Let r be -4 + v/(9/48). Let 0 - 2/3*u - 2/3*u**3 - r*u**2 = 0. What is u?
-1, 0
Let v be 3 + 1/4*-6 - 1. Let k(m) be the second derivative of -1/10*m**5 + 0 + 3*m + v*m**4 + m**2 - m**3. Suppose k(q) = 0. What is q?
1
Factor 0*c**3 + 0 - 1/3*c**4 + 1/3*c**2 - 1/6*c + 1/6*c**5.
c*(c - 1)**3*(c + 1)/6
Let u(d) be the third derivative of -1/270*d**5 + 0 - 1/27*d**3 + d**2 + 0*d + 1/54*d**4. Factor u(m).
-2*(m - 1)**2/9
Let g(o) = -3*o - 2. Let b(q) = -q**2 + 7*q - 2. Let u be b(7). Let w be g(u). Suppose 2*y - w + 4*y - y**2 - 2*y = 0. Calculate y.
2
Let s(j) be the first derivative of j**6/6 + j**5/5 - j**4/2 - 2*j**3/3 + j**2/2 + j + 13. Factor s(r).
(r - 1)**2*(r + 1)**3
Suppose -6*x = -4*x - 6. Find w such that 2*w**2 + 5*w - 1 - 3*w**2 - x*w = 0.
1
Let m = -20 - -17. Let s be (m - (-34)/12)*-2. Factor s*f - 1/3*f**2 + 1/3 - 1/3*f**3.
-(f - 1)*(f + 1)**2/3
Let h(d) = -18*d**2 - 3*d + 30. Let r(f) = -f**2 - f + 1. Let k(y) = h(y) - 15*r(y). What is b in k(b) = 0?
-1, 5
Let x(h) = -h**2 + 1. Let b(q) = -15*q**3 - 12*q**2 + 6. Suppose 2*m = -p + 8, -4*m + 2 - 4 = -p. Let y(z) = p*x(z) - b(z). Suppose y(o) = 0. What is o?
-2/5, 0
Let q(g) be the first derivative of g**4/6 - 4*g**3/9 + g**2/3 - 10. Let q(k) = 0. What is k?
0, 1
Let 3/4*b**2 - 3/4*b**4 - 1/4*b**5 + 1/2*b + 0 - 1/4*b**3 = 0. What is b?
-2, -1, 0, 1
Let u = 414 + -927/2. Let j = u + 51. Factor 7/2*x**5 + 0 - 6*x**4 + x**2 + 0*x + j*x**3.
x**2*(x - 1)**2*(7*x + 2)/2
Let q = -1/30 - -23/90. Factor 0 - q*i - 2/9*i**2.
-2*i*(i + 1)/9
Let t(y) be the third derivative of 3*y**5/20 - 5*y**4/8 + 2*y**3 - 5*y**2. Let p(s) = -17*s**2 + 29*s - 23. Let r(a) = 6*p(a) + 11*t(a). Factor r(c).
-3*(c - 2)*(c - 1)
Let x(p) be the second derivative of p**7/5880 + p**6/210 + 2*p**5/35 + 3*p**4/4 - 10*p. Let t(u) be the third derivative of x(u). Factor t(a).
3*(a + 4)**2/7
Let a(j) = j**2 + 6*j - 4. Let y be a(-7). Suppose -5*b + 3 = -3*r - 14, -5*r + 17 = 3*b. Factor -y*o**b - 11*o**2 + 5*o**4 + 9*o**2.
2*o**2*(o - 1)*(o + 1)
Let h be (-1)/(3*10/(-2)). Let p(u) be the second derivative of 0*u**2 + h*u**6 - 2*u + 0*u**4 + 0*u**3 + 1/10*u**5 + 0. Find s, given that p(s) = 0.
-1, 0
Let i(a) = a**4 - a**3 - a - 1. Let h(q) = 4*q**4 - 3*q**3 - 3*q - 3. Let w(b) = -h(b) + 3*i(b). Factor w(n).
-n**4
Let u = 8 + 63. Let a = u + -51. Factor 2*x**4 - 4*x**3 + 8*x + a*x**2 - 8*x**2 + 2 + 12*x**3.
2*(x + 1)**4
Let p be (-22)/(-30) - 6/15. Factor 0 - p*r - 5/3*r**2 - 4/3*r**3.
-r*(r + 1)*(4*r + 1)/3
Let h(f) = 6*f + f**2 - 6*f**2 - f**2 + 4*f - 8. Let a(y) = y**2 - y + 1. Let i(t) = -4*a(t) - h(t). Factor i(j).
2*(j - 2)*(j - 1)
Let t(u) be the first derivative of -1/15*u**2 + 0*u - 3 - 2/45*u**3. Find v, given that t(v) = 0.
-1, 0
Let p = -35/3 - -12. Let c(u) be the first derivative of 1/2*u**4 + 0*u**2 + 0*u + 2/3*u**3 - p*u**6 - 2/5*u**5 - 1. Factor c(d).
-2*d**2*(d - 1)*(d + 1)**2
Let n = 38 + -36. Suppose 0*x**4 - 2/7*x + 0 - 2/7*x**5 + 0*x**n + 4/7*x**3 = 0. Calculate x.
-1, 0, 1
Suppose v + 3*p = -2*v + 39, -58 = -5*v + 2*p. Suppose -l + 4*z - 7 = 0, 4*l + 8*z - v = 4*z. Solve f + l + 1/4*f**2 = 0 for f.
-2
Let k be -2 + 0 + 0 + 2. Suppose k + 2/11*u + 2/11*u**2 = 0. What is u?
-1, 0
Factor 13*v**3 - 4*v**3 + 15*v**5 + 9*v**4 - 3*v**2 - 12*v**5 + 6*v**2.
3*v**2*(v + 1)**3
Let p(c) be the third derivative of 0 + 1/8*c**4 - 1/3*c**3 + c**2 + 0*c - 1/60*c**5. Factor p(m).
-(m - 2)*(m - 1)
Let u(g) be the first derivative of 0*g**2 + 7 - 2/45*g**5 + 0*g - 4/27*g**3 - 1/6*g**4. Suppose u(p) = 0. Calculate p.
-2, -1, 0
Let c be (-2)/8 + 3/12 + 0. Let b(m) be the second derivative of 0*m**4 + c + 1/110*m**5 - 1/33*m**3 + 4*m + 0*m**2. Let b(g) = 0. Calculate g.
-1, 0, 1
Suppose -4 = b - 2*b. Suppose 2*n = 5*f + 16, -b*f = -4*n + f + 22. Factor -w**3 + 3*w**n - w - w**3.
w*(w - 1)*(w + 1)
Factor -30*m + 40*m**2 + 10 - 33 + 30*m**3 - 12 - 10 + 5*m**4.
5*(m - 1)*(m + 1)*(m + 3)**2
Let w(x) be the first derivative of -2*x**5/15 + x**4/6 - 5. Factor w(p).
-2*p**3*(p - 1)/3
Let b = 58/33 + -12/11. Solve 8/3*v - 2*v**3 + 0 + 0*v**2 + b*v**4 = 0.
-1, 0, 2
Let x(h) be the first derivative of -4*h - 1/30*h**3 - 1/5*h**2 + 2 + 1/60*h**4. Let y(t) be the first derivative of x(t). Factor y(d).
(d - 2)*(d + 1)/5
Let a = 22 + -22. Let w(r) be the first derivative of 1/11*r**4 + 0*r - 1/11*r**2 + 0*r**5 - 1 + a*r**3 - 1/33*r**6. Let w(k) = 0. Calculate k.
-1, 0, 1
Let o(x) be the first derivative of -2*x - 19/6*x**3 + 13/8*x**4 + 7/12*x**6 + 23/10*x**5 - 5*x**2 - 4. Suppose o(h) = 0. Calculate h.
-2, -1, -2/7, 1
Let o(x) = x**3 + 5*x**2 - 5*x + 6. Let d be o(-6). Let i be -2 - (d - 1) - -3. Factor i*s**4 + 1/2*s + 0 + 1/2*s**5 + 3*s**3 + 2*s**2.
s*(s + 1)**4/2
Let d(y) be the second derivative of -13*y**5/70 - y**4/21 + 17*y. Factor d(o).
-2*o**2*(13*o + 2)/7
Let q(p) = -2*p**3 + 4*p**2 - 6*p. Let w(h) = h**3 - h**2 + 1. Let m be 3/(12/4)*4. Let z(c) = m*w(c) + q(c). Factor z(g).
2*(g - 1)**2*(g + 2)
Let q be (-1 - 0)/((-4)/20). Let k = 7 - q. Factor -2*y**2 + y**k - y**2 + 2.
-2*(y - 1)*(y + 1)
Let f = -122/3 - -127/3. Solve y**3 - 5/3*y**2 + 1/3*y + 0 - 4/3*y**5 + f*y**4 = 0.
-1, 0, 1/4, 1
Let w(r) be the first derivative of -2*r**3/3 + 4*r**2 - 8*r + 6. Suppose w(i) = 0. Calculate i.
2
What is b in -2/13*b**3 - 6/13*b**2 + 2/13*b + 6/13 = 0?
-3, -1, 1
Let h be (-2)/(-8) + 35/(-140). Factor 4/9*g**3 + h*g - 2/9*g**2 + 0 - 2/9*g**4.
-2*g**2*(g - 1)**2/9
Let y(j) be the third derivative of -j**9/12600 + j**8/2400 - j**7/1260 + j**6/1800 + j**4/8 - 5*j**2. Let g(o) be the second derivative of y(o). Factor g(f).
-2*f*(f - 1)**2*(3*f - 1)/5
Let s be (1 + (-88)/(-10))*(-15)/(-9). Let r = 423 + -1249/3. Factor -4/3 - s*z**4 - r*z + z**2 + 70/3*z**3.
-(z - 1)**2*(7*z + 2)**2/3
Let j be (-286)/(-66) + (-2)/6. Let 4/9*l**3 + 2/9*l**j - 4/9*l + 0*l**2 - 2/9 = 0. What is l?
-1, 1
Let b be (0/(-3))/(-5 - -2). Suppose 1 = z - 3. Factor -s**z + 3*s**4 + b*s**5 + 2*s**5.
2*s**4*(s + 1)
Let y be 3/(2/(24/(-9))). Let i be (y/(-3))/(4/6). Factor 2/3*k**i + 0*k - 2/3.
2*(k - 1)*(k + 1)/3
Find i, given that 2*i**2 + 2/3*i**3 - 2/3*i - 2 = 0.
-3, -1, 1
Let a(s) = -4*s**2 + 11*s - 7. Let g(i) = 4*i**2 - 12*i + 8. Let d(v) = -4*a(v) - 3*g(v). Suppose d(y) = 0. Calculate y.
1
Let b(q) be the first derivative of -q**3/3 + q**2 + 2. Let s be b(2). Factor 2*c - 3*c + c**2 + s*c.
c*(c - 1)
Let v(m) = -m**3 - m**2. Let q(f) = f**2 - 4 + 1 - 5*f + 1 + 4*f**3. Let a = 14 - 11. Let r(j) = a*q(j) + 15*v(j). Factor r(l).
-3*(l + 1)**2*(l + 2)
Let c(l) be the third derivative of -l**7/315 + l**5/45 - l**3/9 - 23*l**2. Factor c(g).
-2*(g - 1)**2*(g + 1)**2/3
Let l be (-4)/(16/6) - (-169)/78. What is s in -4/3*s**2 + l*s**4 + 0*s + 0*s**3 + 2/3 = 0?
-1, 1
Suppose w = -4*w + 2*t + 10, -2*w = 2*t - 4. Find y such that y**3 + 12*y + y**3 + 12*y**w + y**3 = 0.
-2, 0
Factor -15/4*h**4 - 3*h**2 + 0 - 6*h**3 + 0*h - 3/4*h**5.
-3*h**2*(h + 1)*(h + 2)**2/4
Let x(z) = z**2 - 7*z + 9. Let s be x(6). Determine k, given that 8*k + 3*k**2 - k - s + 5 - 7*k**3 - 5*k**4 = 0.
-1, -2/5, 1
Let v be (-2)/3 - 48/9. Let c be v/(-15) - 16/(-10). Factor -c + 5*m**2 + 7*m + 0*m + 4*m**2.
(m + 1)*(9*m - 2)
Let w(k) = k**2 - 17*k + 5. Let c(j) = j**2 - 9*j + 3. Let a(s) = 5*c(s) - 3*w(s). Solve a(v) = 0.
-3, 0
Let p be (2 + (-16)/10)*5. Factor 10*i**3 + 2 + 10*i**3 + 15*i**4 + p*i**5 + 10*i + 19*i**2 + i**2 - 5*i**4.
2*(i + 1)**5
Let b be ((-3)/(-5))/((-42)/20 - -3). Let -2/3*y**2 + 0 + b*y = 0. Calculate y.
0, 1
Let h(u) = -36*u**2 + 4*u + 21. Let g(p) = -7*p**2 + p + 4. Let c(b) = -33*g(b) + 6*h(b). Solve c(j) = 0.
-2/5, 1
Let n = -129 + 134. Suppose -2*l**4 + 4/7*l**n + 12/7*l**3 - 4/7*l + 0 + 2/7*l**2 = 0. What is l?
-1/2, 0, 1, 2
Let i be (6/3 - 2) + 2. Solve 4*s + 0*s + i*s**2 + 0*s**2 = 0 for s.
-2, 0
Factor -f**2 + 0*f**2 + 3 + 3*f**3 + 25*f - 28*f - 2*f**2.
3*(f - 1)**2*(f + 1)
Let h(p) = -2*p**3 - p**2 + 2*p - 1. Let i be h(1). Let y be (-2 + (-1 - i))*-3. Let 14*j**y - 3 + 18*j**2 + 3 + 4*j = 0. What is j?
-1, -2/7, 0
Suppose -17*q = -47*q + 90. Factor 2/9*r**q - 2/9*r**2 + 2/9 - 2/9*r.
2*(r - 1)**2*(r + 1)/9
Let o(b) = 5*b - 