 = 0. Suppose -z + 135 = v*z. Factor -2*s**2 - 43 - 3*s + 2*s**2 + z + s**3.
(s - 1)**2*(s + 2)
Suppose -16*t = -15*t. Suppose t*p = p. Factor -6*g**2 + 3*g + 0*g + 3*g**3 + p*g**3.
3*g*(g - 1)**2
Let z(v) = -1224*v - 2446. Let m be z(-2). Solve -1/5*c**4 - 2*c**3 - 22/5*c - 24/5*c**m - 7/5 = 0 for c.
-7, -1
Let v(j) be the third derivative of j**7/525 + j**6/100 + j**5/75 - 100*j**2. Factor v(t).
2*t**2*(t + 1)*(t + 2)/5
Let w be 30/5 - -1*(-4 + 1). Factor -g**3 - 5*g**3 + 5*g**w - 3*g**4 + g**4 - g**5.
-g**3*(g + 1)**2
Let w(g) be the second derivative of -g**6/210 + 3*g**5/10 - 262*g. Let w(y) = 0. What is y?
0, 42
Let c(t) be the first derivative of 75*t**3 - 295*t**2 + 120*t - 640. Factor c(o).
5*(5*o - 12)*(9*o - 2)
Let h(x) be the third derivative of -x**10/75600 + x**8/10080 + x**5/10 + 5*x**2. Let o(p) be the third derivative of h(p). Find c, given that o(c) = 0.
-1, 0, 1
Find b such that 0 + 2*b + 5/3*b**2 - b**4 - 8/3*b**3 = 0.
-3, -2/3, 0, 1
Let z(o) be the first derivative of o**8/1848 - o**7/1155 - o**6/330 - 23*o**2/2 + 27. Let m(k) be the second derivative of z(k). Factor m(b).
2*b**3*(b - 2)*(b + 1)/11
Let o(c) be the second derivative of -3*c**5/100 + 13*c**4/20 - 6*c**3/5 + 88*c. Factor o(h).
-3*h*(h - 12)*(h - 1)/5
Let i(y) be the second derivative of 7*y**6/60 - 19*y**5/40 - y**4/4 + 7*y**3/3 + 2*y**2 - 114*y. Factor i(r).
(r - 2)**2*(r + 1)*(7*r + 2)/2
Suppose -6*t + 16 = -2. Factor -6*j**3 - 5*j**4 + 9*j**t - 3*j**3 - 5*j**3.
-5*j**3*(j + 1)
Factor 0 - 10/7*a**2 + 1/7*a**3 + 25/7*a.
a*(a - 5)**2/7
Let k = 4 - -12. Suppose 4 - k = -4*f. Find h, given that 0*h**f - 2/5 - 2/5*h**4 + 0*h + 4/5*h**2 = 0.
-1, 1
Factor -2/3*u**2 - 24*u - 70/3.
-2*(u + 1)*(u + 35)/3
Suppose 8*p = -4*p - 12. Let t be ((-4)/(-8))/(p + (-25)/(-10)). Determine i so that i**4 + 0 + 5/3*i**3 - 1/3*i + t*i**2 = 0.
-1, 0, 1/3
Suppose -5*c + 1 = -9. Let a = 369 + -364. Solve y**c + a - y - 11 + y**3 + 5 = 0.
-1, 1
Let b(j) = 4*j - 38. Let o be b(10). Determine q, given that -8*q**4 + 12*q**3 + 17*q**2 - 8 + 0*q - 12*q - q**o = 0.
-1, -1/2, 1, 2
Let a be (6*(-2)/8)/((-9)/(-4))*-3. Factor -1/2*c**a + 0*c - 1/2*c**3 + 0.
-c**2*(c + 1)/2
Let c = -26461/32 - -827. Let v(t) be the third derivative of -4*t**2 - 1/80*t**5 + 0 + 0*t - 1/4*t**3 - c*t**4. Find n, given that v(n) = 0.
-2, -1
Suppose 0 = -11*m - 28*m + 156. Let f(k) be the third derivative of -1/270*k**5 - 3*k**2 - 4/27*k**3 + 0 + 0*k - 1/27*k**m. Let f(j) = 0. What is j?
-2
Let r(o) be the second derivative of 9*o**7/280 - o**6/10 + 2*o**5/15 - 3*o**4/4 - 6*o. Let d(a) be the third derivative of r(a). Find t such that d(t) = 0.
4/9
Factor -24*u + 13*u - 10*u + 3*u**2.
3*u*(u - 7)
Let d(z) be the first derivative of z**3 - 7 + 11*z**2 - 2 - 2*z**2 + 27*z. Factor d(g).
3*(g + 3)**2
Let t(s) = -s**3 + 4*s**2 - 5*s - 8. Let m be t(-4). Let i be 1*(m/147 - 4/6). Find r such that 0 - i*r - 2/7*r**2 = 0.
-1, 0
Let o(d) be the second derivative of d**5/15 - 3*d**4 + 52*d**3/9 - 12*d. Determine s so that o(s) = 0.
0, 1, 26
Factor 0 + 2/7*h**4 + 12/7*h**3 - 12/7*h - 2/7*h**2.
2*h*(h - 1)*(h + 1)*(h + 6)/7
Let 0 - 1/2*v**4 + 0*v**2 + 0*v - 13*v**5 + 0*v**3 = 0. Calculate v.
-1/26, 0
Let t be 1 + (0 - 1) - 6/(-9). Let f(j) be the second derivative of t*j**2 + 5/36*j**4 + 1/60*j**5 + 0 - 5*j + 4/9*j**3. What is r in f(r) = 0?
-2, -1
Let j(x) be the first derivative of 1/6*x**4 - 2/45*x**5 + 0*x - 5 - 2/9*x**3 + 1/9*x**2. Determine f so that j(f) = 0.
0, 1
Suppose 7*q - 15 = 10*q, 0 = 5*n + q - 40. Suppose -l + 2*t - 3 = 0, -l - n*t + 6*t = -12. Factor -1/2*w**2 + 2*w + 2 - 1/2*w**l.
-(w - 2)*(w + 1)*(w + 2)/2
Let d(l) be the third derivative of 0*l**3 + 0*l**5 - 11*l**2 + 2/525*l**7 - 1/420*l**8 + 0*l + 0*l**6 + 0 + 0*l**4. Factor d(j).
-4*j**4*(j - 1)/5
Let o(y) = 7*y**3 - 2*y**2 - 122*y + 387. Let r(a) = a**3 + 2*a**2 + 2*a + 1. Let w(q) = -o(q) + 3*r(q). Factor w(v).
-4*(v - 4)**2*(v + 6)
Suppose -29*t - 32*t + 305 = 0. Let n(r) be the third derivative of 0 + 2*r**2 + 0*r + 1/32*r**4 - 1/240*r**t + 0*r**3. Factor n(x).
-x*(x - 3)/4
Suppose 4/5*i**3 + 12/5*i**4 + 4/5*i**5 + 0 - 12/5*i**2 - 8/5*i = 0. Calculate i.
-2, -1, 0, 1
Let u(x) be the third derivative of -x**7/210 - x**6/20 + x**5/4 - x**4/3 + 96*x**2. Determine m so that u(m) = 0.
-8, 0, 1
Let g(d) be the first derivative of 3*d**4/32 + 15*d**3/8 + 225*d**2/16 + 375*d/8 - 13. Let g(s) = 0. What is s?
-5
Let n(u) be the second derivative of -4*u**2 + 0 - u - u**3 + 1/6*u**4. Factor n(f).
2*(f - 4)*(f + 1)
Let j = 87 - 67. Suppose j - 53 = -11*a. Determine q, given that -18/7*q**2 - 10/7*q**4 - 24/7*q**a + 0 - 4/7*q = 0.
-1, -2/5, 0
Let r(v) = -17*v**3 - 118*v**2 - 135*v - 39. Let x(s) = -9*s**3 - 58*s**2 - 67*s - 19. Let d(b) = 3*r(b) - 7*x(b). Let d(q) = 0. What is q?
-2, -1/3
Let j(c) be the second derivative of 20*c - 1/21*c**4 - 1/14*c**2 - 2/21*c**3 + 0. Factor j(i).
-(2*i + 1)**2/7
Let q = 22 - 19. Suppose q*y + 0 = 12. Factor 0*u**2 + 0*u**3 - 2/3*u**y + 0*u + 2/3*u**5 + 0.
2*u**4*(u - 1)/3
Find z, given that 12/11*z**2 + 14/11*z**3 - 24/11*z - 16/11 - 6/11*z**4 = 0.
-1, -2/3, 2
Let i(n) be the third derivative of -n**7/945 + 29*n**6/540 - 11*n**5/10 + 45*n**4/4 - 54*n**3 + 2*n**2 - 2*n. Solve i(h) = 0.
2, 9
Let m = -25 + 38. Factor 3*x**2 - 4 + 18*x**4 + 9*x**3 - 12*x**2 - m*x**2 + 21*x**3 - 22*x.
2*(x - 1)*(x + 2)*(3*x + 1)**2
Let y(i) be the first derivative of -17 + 0*i**4 + 0*i**2 + 0*i + 4/9*i**3 - 4/15*i**5. Factor y(j).
-4*j**2*(j - 1)*(j + 1)/3
Factor 266 - 16*j**4 + 76*j**2 + 141*j**3 + 159*j**3 - 266.
-4*j**2*(j - 19)*(4*j + 1)
Factor -2*g**3 - 124*g**4 + 5*g**3 - 2*g**2 + 0*g**2 + 123*g**4.
-g**2*(g - 2)*(g - 1)
Let v(o) be the first derivative of -o**4/36 + o**3/9 + 5*o**2/9 + 33. Factor v(q).
-q*(q - 5)*(q + 2)/9
Let i(x) be the first derivative of 7*x**4/4 + 43*x**3/12 - 55*x**2/8 - 4*x - 342. Suppose i(m) = 0. Calculate m.
-16/7, -1/4, 1
Let j(o) be the third derivative of o**5/12 + 5*o**4/6 + 10*o**3/3 + 141*o**2. Solve j(s) = 0 for s.
-2
Let x = -1484 + 1994497/1344. Let c(k) be the third derivative of 9*k**2 - 1/480*k**6 + 0 + 0*k + 0*k**7 + 0*k**3 + 0*k**4 + 0*k**5 + x*k**8. Factor c(n).
n**3*(n - 1)*(n + 1)/4
Let a(p) be the first derivative of -2*p**5/45 - 2*p**4/9 - 8*p**3/27 - 127. Suppose a(m) = 0. What is m?
-2, 0
Suppose 4*j - 2*d = -6*d + 16, 3*j + d = 4. Suppose -247*f + 12 = -249*f, 4*o + 6 = -f. Find i, given that o*i + 2/9*i**3 + j*i**2 + 0 = 0.
0
Let b(d) be the first derivative of -d**4/4 + 5*d**3/3 - 5*d**2/2 + 6*d + 3. Let n be b(4). Let j**3 - 4*j - 3*j**n - 2*j**3 - 5*j**3 + 13*j**2 = 0. What is j?
0, 2/3, 1
Suppose 0 = -35*i + 10*i + 35 + 40. Suppose 3*f - 2*f = 0. Factor 1/3*p**4 + f*p**2 + 2/3*p - 2/3*p**i - 1/3.
(p - 1)**3*(p + 1)/3
Let p(m) = -m - 16. Let b be p(-20). Let l(i) = -i + 1. Let q(s) = -s**3 + 5*s - 4. Let t = -5 + 6. Let g(h) = b*l(h) + t*q(h). Factor g(n).
-n*(n - 1)*(n + 1)
Let o = -3983/4 + 996. Let n(h) be the first derivative of 0*h + 13 + 1/15*h**5 - 1/9*h**3 - o*h**4 + 1/18*h**6 + 1/3*h**2. Factor n(q).
q*(q - 1)**2*(q + 1)*(q + 2)/3
Let w = -75545/54 + 1399. Let x(s) be the second derivative of -1/9*s**3 + 0 - w*s**4 - 10*s + 0*s**2. Let x(q) = 0. Calculate q.
-3, 0
Let s(x) be the first derivative of x**3/6 + 18*x**2 + 648*x - 67. Factor s(m).
(m + 36)**2/2
Let f = 4852/7269 + -2/2423. Factor -2*p + 0 + f*p**2.
2*p*(p - 3)/3
Suppose h + 15 = 7. Let p be (-3905)/(-120) - 1/h. Factor -p*m**2 - 56/3*m - 8/3.
-2*(7*m + 2)**2/3
Suppose n = 6*n - 10. Suppose 0 = n*a - 6*a. Factor 0*m**3 + 0*m**2 + 1/5*m**4 + 0 + 1/5*m**5 + a*m.
m**4*(m + 1)/5
Let l = 250 - 245. Let m(r) be the second derivative of -4/15*r**3 - 1/75*r**6 - 5*r - 1/5*r**4 - 1/5*r**2 - 2/25*r**l + 0. Factor m(a).
-2*(a + 1)**4/5
Let g(c) be the first derivative of 5*c**3/3 + 40*c**2 + 75*c + 47. Determine m, given that g(m) = 0.
-15, -1
Let y(m) be the third derivative of m**5/60 - 77*m**4/12 + 5929*m**3/6 + 120*m**2 + 1. Find g, given that y(g) = 0.
77
Let v(h) = -h**5 - h**4 + h**3 + h**2. Let a(s) = -s**5 - 28*s**4 + 4*s - 14*s**3 - 3*s + 24*s**4 + 28*s**2 - 10*s. Let z(n) = a(n) - 4*v(n). Factor z(i).
3*i*(i - 1)**3*(i + 3)
Let g(p) be the first derivative of 0*p**4 + 7 + 0*p**2 - 2*p**3 + 0*p + 3/10*p**5. Factor g(