y**3*(y + 1)**2/4
Suppose 21 = -2*g - 7. Let x(p) = -7*p**2 - 14*p + 2. Let c(u) = -21*u**2 - 43*u + 5. Let l(t) = g*x(t) + 4*c(t). Determine v, given that l(v) = 0.
-2, 2/7
Let v be (-20)/(-12)*(-64)/50. Let i = 7/3 + v. Factor 0*z - i*z**3 - 2/5*z**2 + 0.
-z**2*(z + 2)/5
Let c(m) be the first derivative of m**4/22 - 4*m**3/11 + 17. Find s, given that c(s) = 0.
0, 6
Let h(f) be the second derivative of f**7/2520 + f**6/180 + f**5/40 - f**4/12 + 2*f. Let n(j) be the third derivative of h(j). Factor n(l).
(l + 1)*(l + 3)
Let j(r) be the first derivative of 3*r**4/28 + 3*r**3/7 - 12*r/7 - 33. Let j(o) = 0. What is o?
-2, 1
Let v = -12 + 13. Let i be v - 0 - (-7)/(-7). Factor 0 + 1/5*x**4 - 1/5*x**2 + i*x + 0*x**3.
x**2*(x - 1)*(x + 1)/5
Factor 140*r - 155*r**2 + 16 - 36 - 150*r**3 - 165*r**3.
-5*(r + 1)*(7*r - 2)*(9*r - 2)
Let x(a) be the first derivative of -1/8*a**2 - 1/4*a**3 + 6 + 0*a. Let x(s) = 0. Calculate s.
-1/3, 0
Let x be ((-4)/130*-1)/((-2)/(-20)). Determine j so that 6/13*j**3 - 2/13*j**4 + 0*j + 0 - x*j**2 = 0.
0, 1, 2
Find l such that 2/5*l**2 - 12/5 - 2*l = 0.
-1, 6
Let r be -1 - -7 - 3/1. Factor -r*j**4 - j**4 - j**2 + 6*j**3 - 2*j**2 + j**4.
-3*j**2*(j - 1)**2
Let b(j) = 5*j**4 - 11*j**3 + j**2 - j + 6. Let r(f) = -10*f**4 + 23*f**3 - 3*f**2 + 3*f - 13. Let u(y) = 13*b(y) + 6*r(y). Let u(d) = 0. Calculate d.
-1, 0, 1
Factor 27*a - 2*a**3 - 33*a + 3 - 8*a**2 - 3.
-2*a*(a + 1)*(a + 3)
Solve -5*a + 3*a + 4*a**3 - 4*a**3 + 2*a**3 = 0.
-1, 0, 1
Let y(w) be the second derivative of 4*w - 2/15*w**2 - 1/45*w**6 + 17/150*w**5 + 11/45*w**3 - 7/30*w**4 + 0. Solve y(i) = 0.
2/5, 1
Let r(d) be the first derivative of -d**5/3 - 25*d**4/12 - 20*d**3/9 + 5. Factor r(g).
-5*g**2*(g + 1)*(g + 4)/3
Factor -8/3*l**5 - 8/3*l**4 - 4/3*l**2 + 14/3*l**3 + 0 + 0*l.
-2*l**2*(l + 2)*(2*l - 1)**2/3
Let y(k) be the first derivative of 4 + 3/2*k**2 - 3/5*k**5 + 0*k + k**3 - 3/4*k**4. Let y(m) = 0. Calculate m.
-1, 0, 1
Let i be (0 + -3 - -6)*1/12. Factor 1/4*d**2 - i*d**4 - 1/4*d**3 + 0 + 0*d + 1/4*d**5.
d**2*(d - 1)**2*(d + 1)/4
What is y in -320*y - 35/2*y**4 - 105*y**2 + 235/2*y**3 - 80 = 0?
-1, -2/7, 4
Factor -10*s**2 - 8*s - 145*s**3 + 139*s**3 + 4*s + 2*s**5 + 2*s**4.
2*s*(s - 2)*(s + 1)**3
Suppose -5*n + 17 = -33. Let w = n - 6. Let -4*s**w + 5*s**4 - s**5 + 4*s**2 - 4*s**2 = 0. What is s?
0, 1
Suppose -3 = c - 7. Let v = 7 - c. Determine t so that -2*t**2 - v + t**2 + 3*t**3 - 5*t**2 + 9*t - 3*t**2 = 0.
1
Let i = -14 - -16. Factor -3*u**3 + 6*u**2 + u**5 - 2*u**2 - i*u**2 + 0*u**5.
u**2*(u - 1)**2*(u + 2)
Suppose -2*p = 3*p - 20. Let b(w) = -w**2 + 1. Let k(q) = 4*q**3 + q**2 + q + 4. Let g(l) = p*b(l) - k(l). Let g(s) = 0. Calculate s.
-1, -1/4, 0
Let s(h) be the first derivative of h**8/224 - h**6/80 + 3*h**2/2 - 3. Let y(a) be the second derivative of s(a). Factor y(j).
3*j**3*(j - 1)*(j + 1)/2
Let l(g) be the second derivative of -g**4/16 - 2*g. Factor l(z).
-3*z**2/4
Let h = -162 + 4375/27. Let m(c) be the first derivative of -h*c**6 - 8/45*c**5 - 1/9*c**2 + 0*c - 1/3*c**4 + 1 - 8/27*c**3. Factor m(l).
-2*l*(l + 1)**4/9
Let s = 14 + -12. Suppose 4*p + s + 10 = 0, 0 = -4*m - 4*p - 12. Find v, given that m*v + 2/9*v**4 + 0*v**2 + 2/9*v**3 + 0 = 0.
-1, 0
Let x(i) be the first derivative of i**3/3 + i**2 - 4*i + 2. Let q be x(-4). Solve 5*y**3 - q*y**3 - 3*y + 2*y = 0.
-1, 0, 1
Let i = -17 - -25. Suppose -9 = i*s - 11*s. Factor 0*r + 2/9*r**4 + 0*r**s - 2/9*r**2 + 0.
2*r**2*(r - 1)*(r + 1)/9
Let o be 133/5700*(-1)/(-7). Let f(j) be the third derivative of 3*j**2 + 0*j - 2/15*j**3 + 0 - o*j**5 - 1/30*j**4. What is w in f(w) = 0?
-2
Let y be (2*1/(-2))/(-84). Let n = 163/420 + y. Determine q so that 2/5 - 4/5*q + n*q**2 = 0.
1
Let a = -9712 - -39095/4. Let j = 62 - a. Factor j*h**2 + 1 - h.
(h - 2)**2/4
Let m(v) be the first derivative of -1 + 8/7*v - 62/21*v**3 + 18/7*v**5 + 4/7*v**2 - 2/7*v**4 - 6/7*v**6. What is t in m(t) = 0?
-2/3, -1/3, 1/2, 1, 2
Factor 4*p**2 + 5 - 7 - 22*p**2 - 10*p - 2*p.
-2*(3*p + 1)**2
Solve 26*t**2 + 3*t - 51*t**3 - 11*t**2 - 23*t**4 - 3 - 25*t**4 + 36*t**2 + 48*t**5 = 0 for t.
-1, -1/4, 1/4, 1
Let f(v) be the first derivative of -v**3/9 + v**2/6 + 2*v + 7. Let f(m) = 0. Calculate m.
-2, 3
Let h(l) be the first derivative of -l**8/168 - l**7/60 - l**6/90 - 2*l**3/3 - 2. Let k(j) be the third derivative of h(j). Factor k(v).
-2*v**2*(v + 1)*(5*v + 2)
Let j(r) = 8*r**4 + 11*r**3 - 24*r**2 - 5*r. Let n(c) = -20*c**4 - 28*c**3 + 60*c**2 + 12*c. Let k(d) = 12*j(d) + 5*n(d). Solve k(b) = 0 for b.
-3, 0, 1
Let n(p) be the second derivative of 0 + 1/12*p**3 + 0*p**2 + 4*p + 1/40*p**5 - 1/12*p**4. Factor n(h).
h*(h - 1)**2/2
Suppose -4 = b + b. Let r be b/5 + 9/10. Suppose 3/2*m**2 + r*m**3 + 3/2*m + 1/2 = 0. What is m?
-1
Let h be 1/3*(7 + -1). Factor -3*l + 3*l**2 + 2*l**2 - 4*l**h + 2*l + l**3 - l**4.
-l*(l - 1)**2*(l + 1)
Suppose -5 = 2*v + 3. Let a = -2 - v. Factor -6/7*c - 2/7*c**3 - 6/7*c**a - 2/7.
-2*(c + 1)**3/7
Let p(n) be the second derivative of 2*n**6/45 - 7*n**5/15 + 5*n**4/9 + 14*n**3/9 - 4*n**2 - 25*n. Let p(y) = 0. What is y?
-1, 1, 6
Let m be (-2 - 1)/(3/2). Let q = m + 6. Determine r, given that 0*r**2 + q*r - r**2 - 5*r = 0.
-1, 0
Let f(g) = -4*g - 2. Let r be f(-1). Let j(o) be the first derivative of 0*o**r + 1/4*o**4 + 0*o**3 + 0*o + 1. Factor j(a).
a**3
Factor 0*p - 2/9*p**5 + 0 - 2*p**4 - 6*p**2 - 6*p**3.
-2*p**2*(p + 3)**3/9
Factor -5*c**2 - c + 3*c**2 - 2*c**2 + 6*c**2 - c**3.
-c*(c - 1)**2
Let s be (-11)/(-5) - (-1)/(-5). Suppose -5*t = -s*v - 16, -v + 6 = -0*t + t. Factor v*i**3 + 4/5*i**2 + 8/5*i**4 + 2/5*i**5 + 0*i + 0.
2*i**2*(i + 1)**2*(i + 2)/5
Let v(u) be the first derivative of -7*u**5 - 20*u**4 - 55*u**3/3 - 5*u**2 - 17. Factor v(k).
-5*k*(k + 1)**2*(7*k + 2)
Let p(z) = 4*z**5 + 4*z**4 - 4*z**3 + 2*z**2 - 3. Let q(b) = -3*b**5 - 3*b**4 + 3*b**3 - b**2 + 2. Let y(v) = 2*p(v) + 3*q(v). Factor y(u).
-u**2*(u - 1)*(u + 1)**2
Let h = 140 - 140. Let d(o) be the first derivative of -1/4*o**2 - 1/12*o**3 - 2 + 1/16*o**4 + h*o. Factor d(a).
a*(a - 2)*(a + 1)/4
Solve -3*d**2 - 22 + 20*d**4 - 2*d**3 + 4*d**5 + 6 - 32*d - d**2 + 30*d**3 = 0.
-2, -1, 1
Suppose 80/3*w**3 - 168*w**2 + 784/3*w + 1372/3 - 4/3*w**4 = 0. What is w?
-1, 7
Let r(m) be the first derivative of 1/10*m**2 - 2 + 1/5*m - 1/15*m**3 - 1/20*m**4. Factor r(w).
-(w - 1)*(w + 1)**2/5
Let r = -527 + 531. Let -8/3 + 2/3*p**5 + 38/3*p**3 - 50/3*p**2 - 14/3*p**r + 32/3*p = 0. What is p?
1, 2
Let i(r) be the third derivative of r**7/1155 + r**6/330 - r**4/66 - r**3/33 - 3*r**2. Factor i(n).
2*(n - 1)*(n + 1)**3/11
Let k(i) = -i**3 + 8*i**2 + 10*i - 4. Let t be k(9). Factor 4 - 4 + 3*h**2 + h**2 + 5*h**4 + 16*h**3 - 25*h**t.
-h**2*(h - 1)*(5*h + 2)**2
Let p(z) be the second derivative of 0*z**2 + 3*z - 1/30*z**6 - 1/42*z**7 + 0*z**5 + 0*z**4 + 0 + 0*z**3. Factor p(o).
-o**4*(o + 1)
Suppose h - 5*q - 17 + 51 = 0, -10 = -2*q. Let j be h + 6 + (-14)/(-4). Suppose 1/2 - j*m**3 + 3/4*m - 3/4*m**2 = 0. Calculate m.
-2, -1/2, 1
Let w(u) = -u**4 - u**2 - u + 1. Let o(k) = -k**5 + 7*k**4 + 3*k**3 + k**2 + 8*k - 6. Let n(z) = o(z) + 6*w(z). Factor n(q).
-q*(q - 1)**3*(q + 2)
Let s(a) be the second derivative of -4/15*a**3 + a + 0 - 1/30*a**4 - 4/5*a**2. Factor s(l).
-2*(l + 2)**2/5
Let q(v) be the third derivative of -v**5/55 - 5*v**4/44 + 3*v**3/11 - 31*v**2. Factor q(f).
-6*(f + 3)*(2*f - 1)/11
Solve 2/9*z**2 - 2/9*z**4 + 0 + 0*z**3 + 0*z = 0.
-1, 0, 1
Find y, given that 8 - 9*y + 27*y - 4 + 36*y**2 + 6*y = 0.
-1/3
Let c(p) be the third derivative of -p**5/160 + 3*p**4/64 - p**3/8 - 4*p**2. Factor c(r).
-3*(r - 2)*(r - 1)/8
Let z(x) be the second derivative of -x**4/6 + 2*x**3/3 - x**2 + 10*x. Factor z(p).
-2*(p - 1)**2
Let z be 2 - 5/((-5)/2). Suppose 2*m + 0 = z. Factor -8*h**3 - m*h**4 + 0*h**4 - h**4 - 7*h**2 - 2*h.
-h*(h + 1)**2*(3*h + 2)
Let h be (-1)/(-1)*3 - 0. Suppose -10*v + 14 = -3*v. Find g, given that -3*g**2 + h - 1 + g**v = 0.
-1, 1
Let p = 2936/99 + -292/11. Let v = p - 25/9. Factor -v - 2/3*z**3 + 0*z**2 + 1/3*z**4 + 2/3*z.
(z - 1)**3*(z + 1)/3
Let p be 1/((4/(-40))/1). Let n = 10 + p. Factor 0*b + 0*b**2 - 5/3*b**5 + 2/3*b**3 - b**4 + n.
-b**3*(b + 1)*(5*b - 2)/3
Let l(g) be the first derivative of 27/2*g**6 + 5 + 118*g**4 + 0*g - 160/