 - 7*c. Let r be y(0). Suppose -1/3*m**3 + 0*m**2 + 0 + r*m = 0. Calculate m.
0
Let w(n) = -n**3 - 2*n**2 + 3*n + 4. Let a be w(-3). Determine s so that 59*s**a - 39*s**4 + 39*s**2 + 21*s**5 + 81*s**3 + 49*s**4 + 6*s = 0.
-1, -2/7, 0
Suppose 80 - 3 = w. Let n = w + -72. Factor 2/3*h**n + 0*h**3 - 2/3*h + 4/3*h**2 + 0 - 4/3*h**4.
2*h*(h - 1)**3*(h + 1)/3
Let i(o) be the third derivative of o**8/336 - o**7/210 - o**6/120 + o**5/60 + 42*o**2. Factor i(q).
q**2*(q - 1)**2*(q + 1)
Suppose -w = -3*x + 14, 0 = -2*x - 3*w - 11 + 2. Suppose 0 = 3*r - x*a - 19 + 1, 2*r - 15 = 3*a. Factor -r*l**2 + 9*l - l**3 - 3 + 4*l**3 - 5*l**2 - l**2.
3*(l - 1)**3
Let v(b) be the first derivative of -2*b**3/15 - 31*b**2/5 + 289. Let v(h) = 0. Calculate h.
-31, 0
Let 7/8 + 1/8*l**4 + 3*l**2 - 5/4*l**3 - 11/4*l = 0. What is l?
1, 7
Suppose -255*y + 1272 = -43*y. Determine f so that -3/2*f**4 + 3/4*f**5 - 21/4*f - 3/2*f**3 + 3/2 + y*f**2 = 0.
-2, 1
Let s(u) = 6*u**2 - 38*u - 3. Let d(g) = 13*g**2 - 75*g - 6. Let w(y) = 2*d(y) - 5*s(y). Let c be w(10). Factor 1/5 - z**2 + 3/5*z**c + 1/5*z.
(z - 1)**2*(3*z + 1)/5
Suppose 130*k**3 + 128*k - 242*k**3 + 108*k**3 - 34*k**2 - 90*k**2 = 0. What is k?
-32, 0, 1
Let c(b) be the first derivative of -b**7/42 - b**6/15 + b**5/10 + b**4/3 - b**3/6 - b**2 + 10*b + 2. Let p(r) be the first derivative of c(r). Factor p(y).
-(y - 1)**2*(y + 1)**2*(y + 2)
Let f(h) be the second derivative of 0*h**3 - 2/105*h**6 - 4/21*h**4 - 4/35*h**5 - 7*h + 0 + 0*h**2. What is a in f(a) = 0?
-2, 0
Let b(t) be the second derivative of 1/3*t**3 - 1/10*t**5 - 28*t + 0 - 2*t**2 + 1/3*t**4. Factor b(p).
-2*(p - 2)*(p - 1)*(p + 1)
Let k(q) be the first derivative of -q**4/16 - 7*q**3/12 - 5*q**2/4 + 147. Solve k(m) = 0.
-5, -2, 0
Let z(r) be the first derivative of r**5/20 + 5*r**4/8 + 11*r**3/4 + 5*r**2 + 4*r + 66. Suppose z(d) = 0. What is d?
-4, -1
Let y(g) be the third derivative of -g**5/15 + 3*g**4/8 + 13*g**3/6 - 25*g**2. Let d(j) = -5*j**2 + 8*j + 13. Let q(w) = -5*d(w) + 6*y(w). Factor q(u).
(u + 1)*(u + 13)
Suppose 2*h - 3 - 3 = 0. Suppose -3*c + 9 = h*w, 0 = -10*w + 5*w + 5. Determine g, given that 4 + 8*g - 3 - 19*g**2 + 11*g**c - 3 = 0.
1/2
Let f(y) = 13*y - 20. Let o be f(3). Suppose -4*v = o - 39. Suppose 0*m - 3/4*m**3 - 27/4*m**v + 9/2*m**4 + 0*m**2 + 0 = 0. What is m?
0, 1/3
Suppose 5*u = 10, 0*k - 4 = 2*k - 5*u. Let v be 1*(-14)/((-2)/1) - 3. Determine d, given that 5*d**k - 8*d + 5*d**3 - 3*d**v + d**4 + 0*d**4 + 16 - 12*d**2 = 0.
-1, 2
Factor 17/6*y + 1/3*y**2 + 4/3 - 5/3*y**4 - 1/6*y**5 - 8/3*y**3.
-(y - 1)*(y + 1)**3*(y + 8)/6
Let d(f) = -f**3 - f**2 - f + 4. Let v(u) = 2*u**3 - 26*u**2 - 2*u + 8. Let z(t) = -2*d(t) + v(t). Factor z(i).
4*i**2*(i - 6)
Let l(v) be the third derivative of 1/9*v**3 + 1/72*v**4 - 15*v**2 - 23/180*v**5 + 1/18*v**6 + 0*v + 0. Determine r, given that l(r) = 0.
-1/4, 2/5, 1
Let g(a) be the first derivative of -42 - 1/2*a - 1/2*a**3 - 3/4*a**2 - 1/8*a**4. Factor g(i).
-(i + 1)**3/2
Suppose -q + 5*w = -88, -2*q - 3*w = -0*w - 137. Factor -8*t + 16 + 75*t**2 - 147*t**2 + q*t**2.
(t - 4)**2
Let p = 1/82028 + -103519357/1722588. Let i = -346/7 - p. Factor -2/3 - i*w**2 + 16/3*w.
-2*(4*w - 1)**2/3
Let j(q) be the third derivative of -14*q**2 + 1/40*q**5 + 0*q + 0*q**3 - 1/4*q**4 + 0. Factor j(b).
3*b*(b - 4)/2
Let h(w) be the third derivative of -11*w**7/420 - 13*w**6/24 - 97*w**5/120 + 11*w**4/24 + 413*w**2 - w. Determine k, given that h(k) = 0.
-11, -1, 0, 2/11
Suppose 5*q + 664 = 4*b, -q + 101 = -4*b + 237. Let s = 134 + q. Suppose -1/2*r**s - r + 0 + 1/2*r**3 = 0. What is r?
-1, 0, 2
Let g(j) be the first derivative of 10 - j + 25/12*j**2 - 1/6*j**3 - 1/6*j**4. Solve g(l) = 0 for l.
-3, 1/4, 2
Let c = -97 - -89. Let d(m) = -m**2 - 1. Let k(j) = 2*j**3 - 16*j**2 - 8. Let h(i) = c*d(i) + k(i). Solve h(a) = 0.
0, 4
Determine o so that -16*o - o**2 + 41 - 3*o**2 - 9 - 12 + 0*o**2 = 0.
-5, 1
Factor -y**2 + 0 - 6/5*y + 1/5*y**3.
y*(y - 6)*(y + 1)/5
Suppose -2*l = 2*l - 3*i + 45, 0 = -3*l + 5*i - 31. Let s(g) = g**2 + 11*g - 7. Let w be s(l). Factor 8*r**4 - 3*r + 9*r**w - 12*r**3 + r - 11*r**5 + 8*r**2.
-2*r*(r - 1)**4
Let h(k) = 11*k**2 - 4*k + 20. Let f(i) = -4*i**2 + i - 7. Let p(r) = 8*f(r) + 3*h(r). What is b in p(b) = 0?
2
Factor 8998912/5*k - 129792/5*k**2 - 2/5*k**4 - 233971712/5 + 832/5*k**3.
-2*(k - 104)**4/5
Find u, given that 0 + 3/2*u - 1/2*u**3 + u**2 = 0.
-1, 0, 3
Let z(d) be the first derivative of 2/15*d**3 + 0*d + 33 - 2/5*d**2. Factor z(n).
2*n*(n - 2)/5
Let j(k) be the first derivative of k**5/45 + 19*k**4/18 + 4*k**3 + 53*k**2/9 + 35*k/9 - 41. Solve j(i) = 0 for i.
-35, -1
Let b be (1 + (-130)/150)/(6/27). Factor 9/5*q**3 + 3/5*q**4 + b*q + 0 + 9/5*q**2.
3*q*(q + 1)**3/5
Let v(j) be the third derivative of j**6/40 + j**5/2 - 17*j**4/8 - 33*j**3 + j**2 + 80*j. Suppose v(a) = 0. What is a?
-11, -2, 3
Let u = 771672239/1005 + -767833. Let b = 4/67 + u. Suppose 4/15*c - b*c**2 + 0 = 0. What is c?
0, 2
Let r(n) = -n**4 - 2*n**3 + 2*n**2 + 1. Let m(s) = -s**4 + 57*s**3 + 964*s**2 + 900*s + 2. Let w(z) = -m(z) + 2*r(z). Determine b, given that w(b) = 0.
-30, -1, 0
Let i(l) = 2*l**2 + 730*l - 26631. Let v(j) = j**2 + 730*j - 26633. Let y(c) = -6*i(c) + 7*v(c). Determine s so that y(s) = 0.
73
Let c(u) be the first derivative of u**4/8 - 7*u**3/2 + 147*u**2/4 - 343*u/2 - 43. Factor c(d).
(d - 7)**3/2
Factor 34/3*m**2 + 16 - 82/3*m.
2*(m - 1)*(17*m - 24)/3
Let t = 53 - 19. Let k = t + -30. Solve j**3 - 1/2*j**k - 1/2 - 1/2*j**5 - 1/2*j + j**2 = 0 for j.
-1, 1
Determine p, given that 155*p - 14*p**4 - 30 - 75*p**3 + 17*p**4 + 20*p**5 + 52*p**4 - 125*p**2 = 0.
-3, -2, 1/4, 1
Let r = -9 + 13. Let k(h) be the first derivative of 3/5*h**5 + 3 - 3*h**3 + 3*h**2 + 0*h**r + 0*h. Solve k(y) = 0 for y.
-2, 0, 1
Let y(c) be the third derivative of -c**8/896 - 9*c**7/560 - 11*c**6/160 + c**4/2 + 4*c**2 - 20*c. Suppose y(v) = 0. Calculate v.
-4, -2, 0, 1
Let t(j) be the first derivative of 0*j**2 - 7 + 6*j - 2/5*j**6 - 2/3*j**3 - 7/5*j**5 - 5/3*j**4. Let o(p) be the first derivative of t(p). Factor o(d).
-4*d*(d + 1)**2*(3*d + 1)
Let h(g) = 15*g**3 - 40*g**2 + 91*g - 54. Let z(n) = -18*n**3 + 41*n**2 - 92*n + 54. Let d(w) = -5*h(w) - 4*z(w). What is b in d(b) = 0?
1, 2, 9
Find i, given that 282*i**2 - 23 - 297*i**2 + 100*i - 135*i**3 + 3 = 0.
-1, 2/9, 2/3
Let p(i) be the first derivative of -i**5/15 + 2*i**4/3 + i**3 - 35. Factor p(l).
-l**2*(l - 9)*(l + 1)/3
Let v(x) = -x**4 + x + 3. Let r(m) = -m**5 - 3*m**4 + 3*m**3 + m**2 + 6. Let h(c) = r(c) - 2*v(c). Factor h(a).
-a*(a - 1)**2*(a + 1)*(a + 2)
Factor -8/13*s + 64/13 - 2/13*s**2.
-2*(s - 4)*(s + 8)/13
Let u(q) be the second derivative of 21*q + 0 + 2*q**2 + 0*q**3 - 2/5*q**5 - q**4. Factor u(x).
-4*(x + 1)**2*(2*x - 1)
Let q(u) = -11*u - 64. Let h be q(-6). Let k(i) be the first derivative of 4 + i**4 - 2*i + 2/5*i**5 - h*i**2 + 0*i**3. Factor k(p).
2*(p - 1)*(p + 1)**3
Let t = -12 - 3. Let g be -2 + 4/(-12)*t. Solve -2*z + 7*z**2 - 7*z**4 + 5*z**5 - 3*z**3 - 2*z**3 + z**g + z**3 = 0 for z.
-1, 0, 2/5, 1
Let x be 12/10*65/26. Suppose x*n - 25 = -3*j - n, -n + 4 = 0. Find i, given that 126/5*i**j + 8/5*i + 49/5*i**4 + 12*i**2 + 0 = 0.
-2, -2/7, 0
Let c(w) be the third derivative of 1/56*w**7 + 9/160*w**6 + 0*w + 0 + 0*w**3 + 28*w**2 + 1/448*w**8 + 1/16*w**4 + 7/80*w**5. Factor c(i).
3*i*(i + 1)**3*(i + 2)/4
Let n = -285 + 6841/24. Let h(j) be the second derivative of n*j**3 - 1/16*j**4 + 0*j**2 + 0 + 5*j. Factor h(b).
-b*(3*b - 1)/4
Let h(v) be the first derivative of -v**4/4 - v**3 - 3. Factor h(m).
-m**2*(m + 3)
Suppose -6*t + 143 = 35. Let g be 25/(75/(-18))*(-4)/t. Let g*o + 0 - 10/3*o**2 + 2*o**3 = 0. What is o?
0, 2/3, 1
Suppose -34*l + 35*l = 2. Let f(x) be the second derivative of 1/18*x**4 + 2*x + 0*x**l + 0 + 1/30*x**5 + 0*x**3. Factor f(b).
2*b**2*(b + 1)/3
Factor -480*y + 828/7*y**2 - 12*y**3 + 3/7*y**4 + 4800/7.
3*(y - 10)**2*(y - 4)**2/7
Suppose -13*b + 43 = -9. Let k(f) be the second derivative of 1/54*f**4 + b*f + 2/27*f**3 + 0 + 1/9*f**2. Factor k(j).
2*(j + 1)**2/9
Suppose 19*d - 9*d = 5*d. Let q be (1 - 2) + 4 - (d - 0). What is g in 1/2*g**2 + 0*g**q + 0 - 1/2*g**4 + 0*g = 0?
-1, 0, 1
Factor -104/3*r**2 - 16/3 + 22*r + 2/3*r**5 - 8*r**4 + 76/3