 5
Suppose 0 = -w - 4*t + 6, 3*t + 5 = 4*w - 0*t. Let y(u) be the second derivative of -w*u - 3*u**2 + 0 + 4/3*u**3 - 1/6*u**4. Factor y(r).
-2*(r - 3)*(r - 1)
Suppose 67 = 3*v - 5*p, 0*v + v - 4 = -2*p. Find i such that -35 - v*i**3 + 6*i**4 - 32 + 4*i**2 + 67 = 0.
0, 1/3, 2
Solve 12/7*x**4 + 30*x + 2/7*x**5 - 100/7 - 20/7*x**3 - 104/7*x**2 = 0 for x.
-5, 1, 2
Factor 22*d - 2*d**3 - 13 - 18*d**2 + 1 + 10*d**2.
-2*(d - 1)**2*(d + 6)
Suppose -10*v - 5*a = -12*v - 19, -3*v = 2*a - 19. Let n(x) be the first derivative of -x**v - 1/4*x**4 + 4*x + 0*x**2 + 2. Factor n(r).
-(r - 1)*(r + 2)**2
Solve 270*w**4 - 395*w**3 + 5596*w**2 + 125*w**5 - 5566*w**2 - 30*w**4 = 0 for w.
-3, 0, 2/25, 1
Let f(s) be the first derivative of 5 - 27/10*s**2 - 2*s**3 - 9/20*s**4 - 6/5*s. Determine n so that f(n) = 0.
-2, -1, -1/3
Let h(f) be the first derivative of -f**4/9 + 10*f**3/9 + 20*f - 11. Let q(j) be the first derivative of h(j). Factor q(m).
-4*m*(m - 5)/3
Let a(s) be the second derivative of -s**6/105 - 3*s**5/35 + 18*s**3/7 + 81*s**2/7 + 3*s + 1. Factor a(k).
-2*(k - 3)*(k + 3)**3/7
Let x(b) = 5*b - 22. Let g be x(6). Suppose -11*u = g*u - 2*u. Solve u - 1/5*h**2 - 3/5*h**4 - h**3 + 1/5*h = 0 for h.
-1, 0, 1/3
Let q(k) be the third derivative of -k**6/24 + k**5/12 + 25*k**4/12 + 20*k**3/3 + 50*k**2. Factor q(i).
-5*(i - 4)*(i + 1)*(i + 2)
Let d(y) = -4*y**2 + 19*y + 20. Let i(s) = 7*s**2 - 37*s - 39. Let q(a) = -5*d(a) - 3*i(a). Factor q(z).
-(z - 17)*(z + 1)
Let p(v) be the third derivative of 0 + 3*v**2 - 1/20*v**5 + 0*v + 1/2*v**4 - 3/2*v**3. What is r in p(r) = 0?
1, 3
Let n(y) be the second derivative of -2/25*y**5 + 0*y**2 + 8/15*y**4 - 64/45*y**3 + 1/225*y**6 - 4*y + 0. What is d in n(d) = 0?
0, 4
Let w be ((-15)/20)/(42/(-32)). Let f = w + -54/119. Let 6/17*u**4 + 0 + 0*u**2 - 4/17*u**5 - f*u**3 + 0*u = 0. Calculate u.
0, 1/2, 1
Let x(o) be the third derivative of -o**7/3960 - o**6/3960 + 3*o**4/8 + 8*o**2. Let a(s) be the second derivative of x(s). What is z in a(z) = 0?
-2/7, 0
Factor 2/7*o**4 - 18/7 + 12/7*o**3 - 48/7*o**2 + 52/7*o.
2*(o - 1)**3*(o + 9)/7
Let x(g) = 0*g + 5*g**2 - 4 + 4*g + 0*g**3 - 3*g**2 + g**3. Let s(r) = -r**3 + r**2 - r + 1. Let w(t) = -4*s(t) - x(t). Factor w(d).
3*d**2*(d - 2)
Let n be (0 - 3) + 15 + -10. Let f(g) be the second derivative of 0 + 0*g**n - 1/28*g**5 + 2/21*g**4 + 2/21*g**3 - 2*g. Find m such that f(m) = 0.
-2/5, 0, 2
Let q(u) = u**2 - 10*u - 115. Let a be q(-7). What is h in -3/2*h**2 + 3/2*h**a + 0 - 3/2*h + 3/2*h**3 = 0?
-1, 0, 1
Let j(s) = -2*s - 13. Let d be j(-11). Let n = d - 7. Factor -12/7*p + 2/7*p**n + 18/7.
2*(p - 3)**2/7
Let n(r) = 194*r**2 + 1552*r + 3. Let t be n(-8). Factor 0*x + 0 - 39/2*x**3 - t*x**2.
-3*x**2*(13*x + 2)/2
Factor -280*g**3 + 4900*g**2 + 618*g**4 - 309*g**4 - 305*g**4.
4*g**2*(g - 35)**2
Let s(w) be the third derivative of 0*w + 0*w**3 - 1/120*w**5 - 4*w**2 - 1/16*w**4 + 0. Factor s(l).
-l*(l + 3)/2
Let n(c) be the second derivative of -29*c + 0 + c**2 - 1/6*c**4 + 1/6*c**3 - 1/20*c**5. Let n(b) = 0. Calculate b.
-2, -1, 1
Let x = -18966/7 + 2710. Find p such that -4/7*p**3 + 0*p + 4/7*p**5 - x*p**4 + 4/7*p**2 + 0 = 0.
-1, 0, 1
Let d = -277/2 - -140. Let g(o) be the first derivative of 3/4*o**4 - 4 - o**3 - d*o**2 + 3*o. Factor g(l).
3*(l - 1)**2*(l + 1)
Let m be (-4)/((-1968)/(-21)) - (-3)/(-12). Let r = 101/205 + m. Factor -2/5 + 0*y**2 + r*y**3 - 3/5*y.
(y - 2)*(y + 1)**2/5
Let k(t) be the third derivative of -t**5/15 - t**4/3 + t**2 + 8*t. Factor k(w).
-4*w*(w + 2)
Let g(a) be the third derivative of a**6/40 + 9*a**5/20 + a**4 + 123*a**2 - 3. What is d in g(d) = 0?
-8, -1, 0
Let t(a) be the first derivative of -2/5*a**5 + 54*a - 4*a**4 + 7 - 12*a**3 + 0*a**2. Let t(p) = 0. What is p?
-3, 1
Let q(d) be the second derivative of d**6/60 + 3*d**5/20 - 11*d**3/6 + 15*d**2/4 + 725*d. Factor q(j).
(j - 1)**2*(j + 3)*(j + 5)/2
Let r = 1051 + -1048. Factor 0*y**4 + 0 + 1/7*y**5 + 1/7*y - 2/7*y**r + 0*y**2.
y*(y - 1)**2*(y + 1)**2/7
Let p(h) be the second derivative of 2*h**6/15 + 9*h**5/5 + 8*h**4/3 - h + 11. Let p(z) = 0. What is z?
-8, -1, 0
Let 29/2*c**2 - 1/2*c**3 + 0 + 0*c = 0. Calculate c.
0, 29
Let c(g) be the first derivative of -3*g**5/25 + g**3/5 - 72. Factor c(x).
-3*x**2*(x - 1)*(x + 1)/5
Let l be 13/4 + 3*(-3)/(-12). Factor -l*r**3 + 20*r - 5*r**4 - 7*r**3 - 12*r**3 + 8*r**3.
-5*r*(r - 1)*(r + 2)**2
Let g = 326 - 322. Let k = -2/157 + 650/1727. Factor 2/11*a**3 + 0*a + 0*a**2 + 2/11*a**5 + 0 - k*a**g.
2*a**3*(a - 1)**2/11
Let u(f) be the third derivative of f**6/105 + 239*f**5/210 + 295*f**4/7 - 300*f**3/7 - 234*f**2. Factor u(v).
2*(v + 30)**2*(4*v - 1)/7
Suppose -47/5*h - 13*h**3 - 18/5 - 9/5*h**4 + 139/5*h**2 = 0. Calculate h.
-9, -2/9, 1
Suppose -89*v - 4 = -18*v - 4. What is p in 1/3*p**3 + v - 2/3*p**2 + 0*p = 0?
0, 2
Suppose 16*a - 50 + 2 = 0. Let n(u) be the second derivative of -12*u + 1/4*u**4 + 0 - 6*u**2 + 3/2*u**a. Let n(z) = 0. Calculate z.
-4, 1
Let i(v) be the third derivative of 1/42*v**7 - 3*v**2 + 5/4*v**4 - 5/12*v**5 + 0*v**3 - 1/12*v**6 + 0 + 0*v. Solve i(l) = 0.
-2, 0, 1, 3
Let h(u) be the third derivative of 2*u**7/525 - 34*u**6/75 + 1156*u**5/75 - 31*u**2. Factor h(i).
4*i**2*(i - 34)**2/5
Suppose 1349*d - 90 + 71*d**2 + 5*d**4 - 1334*d - 6*d**2 - 35*d**3 = 0. What is d?
-1, 2, 3
Let d(a) = -3*a**4 - 6*a**2 - 9*a - 9. Let n = 117 + -108. Let f(z) = z**3 + z**2 + 1. Let p(y) = n*f(y) + d(y). Factor p(c).
-3*c*(c - 3)*(c - 1)*(c + 1)
Let u be ((-2)/(-60))/(-8*8/(-64)). Let f(y) be the second derivative of 2/5*y**2 + u*y**4 - 1/5*y**3 + y + 0. Factor f(b).
2*(b - 2)*(b - 1)/5
Let m = -49 + 51. Let 9*v + 8*v**3 + 20*v**m - 1 - 11*v - 16*v**2 = 0. Calculate v.
-1/2, 1/2
Let g(m) be the third derivative of -m**8/9450 - m**7/4725 - m**6/5400 - 7*m**5/30 + 8*m**2. Let u(i) be the third derivative of g(i). Factor u(b).
-2*(4*b + 1)**2/15
Let v = -1714 + 1714. Suppose -4/9*j + 2/9*j**2 + v = 0. Calculate j.
0, 2
What is x in -54/5*x**4 - 132/5*x**3 - 8/5*x**5 + 0 - 136/5*x**2 - 48/5*x = 0?
-2, -3/4, 0
Let t = 5608/5 + -1118. Let v = 81/10 - t. Suppose -7/2*d - v*d**2 + 1 = 0. Calculate d.
-1, 2/9
Let d = -7 + 8. Let f be 3 - ((0 - d) + 1). Factor -k**3 - 8*k - 5*k**2 + 2*k**f - 2*k**3 - 4 + 0.
-(k + 1)*(k + 2)**2
Let k(h) be the third derivative of h**6/2160 + h**5/240 + 2*h**3/3 - 10*h**2. Let a(m) be the first derivative of k(m). Let a(g) = 0. Calculate g.
-3, 0
Let m = -90 + 41. Let a be m/21*(0 - 3). Factor -9*d**4 + 6*d**4 + a*d**4 - 16*d**2.
4*d**2*(d - 2)*(d + 2)
Let q(s) be the first derivative of -s**6/9 + 4*s**5/3 - 7*s**4/2 - 341. Let q(y) = 0. Calculate y.
0, 3, 7
Let g be ((-450)/(-250))/((-12)/(-15) + 0). Factor -6*k + g*k**2 - 9/4.
3*(k - 3)*(3*k + 1)/4
Suppose 17*t**3 + 23*t**3 - 46 - 8*t + 45 - 6*t**2 - 25*t**4 = 0. Calculate t.
-1/5, 1
Let g(h) = -h**3 + 7*h**2 - 6*h + 4. Let v be g(6). Factor -14*s**4 - 19*s**v + 43*s**4 + 5*s**5.
5*s**4*(s + 2)
Factor 14/3*x + 2/3*x**3 - 10/3*x**2 - 2.
2*(x - 3)*(x - 1)**2/3
Let r(m) be the third derivative of m**7/420 - m**6/60 + m**5/60 + m**4/12 - m**3/4 + 195*m**2. Factor r(b).
(b - 3)*(b - 1)**2*(b + 1)/2
Suppose 6*r - 3*r = 17*r + 7*r. Find y, given that r*y + 0 + 3/5*y**2 = 0.
0
Let r be 40/(-100) - 66/10. Let b be (-27)/42*14/r. Let 0*o**2 - b*o + 6/7 + 3/7*o**3 = 0. What is o?
-2, 1
Let h(j) be the first derivative of -j**4 + 72*j**2 + 16. Solve h(k) = 0 for k.
-6, 0, 6
Let o(i) be the second derivative of -i**10/68040 - i**9/34020 + 4*i**4/3 + 18*i. Let u(k) be the third derivative of o(k). Solve u(z) = 0.
-1, 0
Let l(x) be the third derivative of x**8/112 + x**7/21 + x**6/30 - 2*x**5/15 - 433*x**2. Factor l(d).
d**2*(d + 2)**2*(3*d - 2)
Let s be ((-2)/(((-48)/(-44))/6))/(-5). Factor -2/5*x**2 - 6/5*x**4 + 8/5 - 12/5*x + s*x**3 + 1/5*x**5.
(x - 2)**3*(x - 1)*(x + 1)/5
Let h(s) be the first derivative of 1/6*s**2 - 1/3*s**3 + 13 + 1/4*s**4 + 0*s - 1/15*s**5. Factor h(c).
-c*(c - 1)**3/3
Let a(r) be the third derivative of r**7/1260 - 13*r**6/2160 + r**5/240 + 4*r**3 - 11*r**2. Let t(y) be the first derivative of a(y). Factor t(v).
v*(v - 3)*(4*v - 1)/6
Suppose 0 - 6/5*a**2 - 2/5*a = 0. Calculate a.
-1/3, 0
Let f(a) be the first derivative of 22 + 4/9*a**3 - 16/3*a - 2*a**2. Solve f(k) = 0 