(u + 1)/9
Factor 1/4*k**4 + 0 + 1/4*k**3 - k - k**2.
k*(k - 2)*(k + 1)*(k + 2)/4
Factor -5/2 - 1/6*g**3 + 1/2*g**2 + 13/6*g.
-(g - 5)*(g - 1)*(g + 3)/6
Let i(l) be the second derivative of -4*l + 1/4*l**4 + 2 - 12*l**3 + 216*l**2. Suppose i(k) = 0. Calculate k.
12
Let x(l) be the second derivative of -1/60*l**6 + 1/8*l**4 + 0*l**2 + 0*l**5 + 0 + 40*l - 1/6*l**3. Determine c so that x(c) = 0.
-2, 0, 1
Let h(m) = -m**2 + m. Let a(w) = 3*w**2 + 7*w. Let j(i) = -a(i) + 2*h(i). Factor j(v).
-5*v*(v + 1)
Let q(j) be the third derivative of 7 - 13/315*j**7 - j**2 + 16/9*j**4 + 1/504*j**8 + 1/3*j**6 + 0*j + 0*j**3 - 56/45*j**5. Determine m so that q(m) = 0.
0, 1, 4
Let p(i) be the third derivative of -i**5/240 + i**4/12 - 5*i**3/8 - 59*i**2. Find s such that p(s) = 0.
3, 5
Let d(u) = -u**3 - 40*u**2 - 11*u - 440. Let f be d(-40). Suppose -2/5*i**4 - 1/5*i**3 + 1/5*i**5 + 2/5*i**2 + f + 0*i = 0. Calculate i.
-1, 0, 1, 2
Let v(o) be the second derivative of 39*o + 1/4*o**4 - 1/5*o**5 + 1/84*o**7 + 0*o**6 + 7/12*o**3 + 0 - 3/2*o**2. Determine k so that v(k) = 0.
-3, -1, 1, 2
Suppose -8 = 2*z - 12. Let d be (-105)/(-75) + 2*z/(-4). Factor 0*l - 2/5*l**2 + d.
-2*(l - 1)*(l + 1)/5
Let z be (-18)/99 + (-48)/(-22). Factor 21 + 12 - 4*j**z - 13 - j**2.
-5*(j - 2)*(j + 2)
Suppose 5*p + 4*k = 7, 9*p - 11*p = -4*k - 14. Let c(y) be the first derivative of 8/21*y**p - 7 + 0*y + 4/7*y**4 + 0*y**2 - 22/35*y**5 + 1/7*y**6. Factor c(z).
2*z**2*(z - 2)**2*(3*z + 1)/7
Suppose -7*w = -w. Suppose 15 = 5*v - w*v. Factor 14/5*i**4 + 0 + 2*i**2 + 4/5*i**5 + 18/5*i**v + 2/5*i.
2*i*(i + 1)**3*(2*i + 1)/5
Let m(z) = -6*z**4 - 3 + 12*z**3 - 3 - 5. Let w(x) = -2*x**4 + 4*x**3 - 4. Let n(q) = -4*m(q) + 11*w(q). Suppose n(d) = 0. Calculate d.
0, 2
Let m = 260/931 + 6/931. Solve 2/7*z**3 - 2/7*z**2 - 2/7*z + m = 0.
-1, 1
Let c(a) be the first derivative of -a**6/1440 + 7*a**5/480 - a**4/8 + a**3/3 - 26*a - 5. Let p(o) be the third derivative of c(o). Factor p(l).
-(l - 4)*(l - 3)/4
Let w(j) = -15*j - 54. Let i be w(-4). Let b(d) be the first derivative of 1/11*d**2 + 0*d - i - 2/33*d**3. Factor b(z).
-2*z*(z - 1)/11
Let r(n) = 5*n**4 + n**3 - n**2 - n - 1. Let y(d) = 16*d**4 + 404*d**3 - 10000*d**2 - 404*d + 9996. Let b(i) = -4*r(i) + y(i). Factor b(c).
-4*(c - 50)**2*(c - 1)*(c + 1)
Factor 3/2*o**2 + 294 + 42*o.
3*(o + 14)**2/2
Let n(y) be the third derivative of -1/12*y**3 - 3/80*y**5 + 0*y + 4*y**2 - 1/96*y**6 + 0 - 1/840*y**7 - 7/96*y**4. Factor n(i).
-(i + 1)**3*(i + 2)/4
Let m be -2 + -1 + 1 - ((-720)/81)/4. Factor 2/9*v**3 - 2/9*v**2 + 2/9*v**4 - m*v + 0.
2*v*(v - 1)*(v + 1)**2/9
Let b(h) = -h**2 + 12*h - 21. Let p be b(9). Suppose p*o = 11 + 13. Suppose -2*x + 1/2*x**3 + x**2 - o = 0. What is x?
-2, 2
Suppose -5 = -2*l + 3. Factor -25*i**l - 9 - 6 + 20*i**2 + 15 + 40*i**3.
-5*i**2*(i - 2)*(5*i + 2)
Let b be ((-14)/10 + -1)*-10*(-33)/(-330). Factor b*s**2 + 9/5 - 39/5*s.
3*(s - 3)*(4*s - 1)/5
Let j be 124/44 - (-7 + 75/11). Let c(o) be the second derivative of 9/2*o**j - 7*o + 0*o**2 - 3/2*o**4 + 0 + 3/20*o**5. Suppose c(t) = 0. What is t?
0, 3
Let u(z) be the second derivative of -z**4/72 - 65*z**3/36 + 899*z. Factor u(w).
-w*(w + 65)/6
Let m = 28861/43305 - -3/14435. Determine d so that -16/3*d + m*d**2 + 8 = 0.
2, 6
Let p(g) be the second derivative of 0 + 8*g + 1/114*g**4 + 2/19*g**2 + 1/19*g**3. Determine l so that p(l) = 0.
-2, -1
Let g(k) be the second derivative of k**8/6720 - k**7/630 + k**6/144 - k**5/60 + 41*k**4/12 - 24*k. Let r(u) be the third derivative of g(u). Factor r(z).
(z - 2)*(z - 1)**2
Let h(k) be the third derivative of -k**8/84 - k**2 - 41. What is d in h(d) = 0?
0
What is o in -10*o**3 + 8/5*o**5 + 102/5*o**4 - 52/5 + 282/5*o - 58*o**2 = 0?
-13, -2, 1/4, 1
Factor -18*n - 108 - 3/4*n**2.
-3*(n + 12)**2/4
Factor 24*u**2 + 6517*u - 13033*u + 2*u**3 + 6516*u.
2*u**2*(u + 12)
Let p(t) be the second derivative of 5*t**7/42 - 4*t**6/3 - 4*t**5 + 155*t**4/6 + 25*t**3/2 - 135*t**2 - 3*t + 23. Suppose p(w) = 0. Calculate w.
-3, -1, 1, 2, 9
Factor j**2 - 72 + 72 + 2*j**2.
3*j**2
Let u(j) be the third derivative of -j**7/105 - 17*j**6/360 + j**5/60 + j**4/3 - 2*j**3/9 + 359*j**2. What is r in u(r) = 0?
-2, 1/6, 1
Find k such that 5*k**3 + 14 - 21/2*k**2 - 2*k - 1/2*k**4 = 0.
-1, 2, 7
Let o be (-454)/(-3859) + 3524/102. Find t such that 140/3*t**3 + 0 - o*t**2 + 16/3*t + 98/3*t**4 = 0.
-2, 0, 2/7
Let m = 110/51 + -14/17. Factor m*j**2 + 1/3*j**3 + 0 + j.
j*(j + 1)*(j + 3)/3
What is q in 0 + 8/3*q - 1/3*q**2 = 0?
0, 8
Let d(g) be the third derivative of g**7/210 - g**6/8 + 6*g**5/5 - 9*g**4/2 - 208*g**2. Let d(y) = 0. What is y?
0, 3, 6
Let g(u) be the first derivative of -1 + 1/5*u**2 + 3/20*u**4 + 0*u - 1/30*u**6 - 1/25*u**5 + 1/3*u**3. Let g(y) = 0. Calculate y.
-1, 0, 2
Let a(d) be the first derivative of -1/10*d**5 + 2/3*d**3 + 1/6*d**4 - 7*d + 0*d**2 + 11. Let z(s) be the first derivative of a(s). Factor z(r).
-2*r*(r - 2)*(r + 1)
Suppose -14 = 2*u - 56. Suppose -3 + f**2 + f + u*f**3 + 16*f**3 + 2 - 38*f**3 = 0. What is f?
-1, 1
Factor 14/9*g**2 - 2/9*g**3 - 32/9*g + 8/3.
-2*(g - 3)*(g - 2)**2/9
Let m = -18/505 + 1172/4545. Factor 2/9*w**4 + 0*w - m*w**3 + 0 + 0*w**2.
2*w**3*(w - 1)/9
Let h = 1/12521 + -42177/12521. Let l = h + 780/209. Let l*x + 2/11*x**2 + 0 = 0. Calculate x.
-2, 0
Factor -165/2*l**2 - 1/4 - 1575/8*l**3 - 67/8*l.
-(7*l + 2)*(15*l + 1)**2/8
Let z(g) be the second derivative of 1/16*g**3 + 0 - 14*g + 1/32*g**4 + 1/16*g**2 + 1/160*g**5. Factor z(s).
(s + 1)**3/8
Let f(z) be the second derivative of -z**6/30 + 11*z**5/20 - 5*z**4/6 + 319*z. Factor f(m).
-m**2*(m - 10)*(m - 1)
Let l(s) be the second derivative of -s**6/10 - 48*s**5/5 - 330*s**4 - 3872*s**3 + 31944*s**2 - 14*s - 5. Suppose l(t) = 0. What is t?
-22, 2
Let n = -731 - -734. Suppose 0*p - 8/3*p**n + 2*p**2 + 0 + 2/3*p**4 = 0. What is p?
0, 1, 3
Let f(v) be the third derivative of v**6/200 - v**5/50 + v**4/40 - 99*v**2. Determine p so that f(p) = 0.
0, 1
Let k = -1196 + 1196. Let q(j) be the second derivative of -1/30*j**6 + 0*j**3 + k*j**4 + 0 + 0*j**5 + 0*j**2 + 3*j. Suppose q(m) = 0. What is m?
0
Let w(h) be the first derivative of 125*h + 5/3*h**3 + 25*h**2 - 20. Factor w(n).
5*(n + 5)**2
Let q(u) be the third derivative of u**6/60 + 2*u**5/15 - 19*u**4/12 + 14*u**3/3 + 183*u**2. Factor q(d).
2*(d - 2)*(d - 1)*(d + 7)
Let l(h) be the first derivative of -h**4 + 0*h + 0*h**2 + 15 + 4/3*h**3. Factor l(b).
-4*b**2*(b - 1)
Let d be (63 + -5)/116*((-14)/(-4) - 0). Factor -d*f**3 + 1/2 - 11/4*f + 4*f**2.
-(f - 1)**2*(7*f - 2)/4
Let z(v) = -2*v**3 - 9*v**2 - 4*v + 15. Let g(p) = -p**3 - 10*p**2 - 3*p + 14. Let f(q) = -3*g(q) + 2*z(q). Factor f(o).
-(o - 12)*(o - 1)*(o + 1)
Let v(l) be the third derivative of l**5/40 + 3*l**4/16 - 15*l**2. Solve v(d) = 0 for d.
-3, 0
Let j(p) be the third derivative of -p**6/150 + 13*p**5/75 + p**4/30 - 26*p**3/15 + 82*p**2. Find k such that j(k) = 0.
-1, 1, 13
Suppose 0 = -4*g + 3*t + 8, 7*g + 10 = 12*g + 5*t. Let l be 0/(-3 + -1 + 3). Determine h so that -2/7*h**4 + l*h + 0 + 2/7*h**5 - 2/7*h**3 + 2/7*h**g = 0.
-1, 0, 1
Let s(g) = -g**3 + 2*g**2 + 7*g - 9. Let y be s(3). Solve -20*c**3 + 8*c**3 + 14*c**y - 6*c**2 - 8*c = 0.
-1, 0, 4
Let f(j) be the third derivative of j**8/672 - 2*j**7/105 + 3*j**6/40 - j**5/30 - 19*j**4/48 + j**3 - 794*j**2. What is q in f(q) = 0?
-1, 1, 3, 4
What is n in 6/5*n**4 + 276/5*n**2 - 276/5*n + 3/5*n**5 - 21*n**3 + 96/5 = 0?
-8, 1, 2
Let v(c) = 2*c - 1. Let h(i) = -2*i**3 + 12*i**2 + 12*i - 2. Let z(a) = 2*h(a) - 36*v(a). Let z(g) = 0. Calculate g.
2
Suppose -11 = -4*q + 5. Suppose -q*f + 0*f + 19 = 5*k, 2*k - 2*f - 4 = 0. Factor -4*i**k + 3*i**3 + 2*i - 1 - i + 0*i**3 + i**2.
-(i - 1)**2*(i + 1)
Let m(o) = 3*o**2 + 12*o + 12. Suppose -s - 8 = -4*x + 3, -x + 4*s = 16. Let r(q) = 6*q**2 + 24*q + 24. Let f(h) = x*r(h) - 9*m(h). Factor f(j).
-3*(j + 2)**2
Suppose 6*k + 5*c + 10 = 7*k, 5*c = -10. Suppose -d - d = -k*d. Factor 3/2*h**2 + d + 3*h.
3*h*(h + 2)/2
Let x(c) be the second derivative of 1/126*c**7 + 3 - 7/135*c**6 + 0*c**2 + 0*c**3 - 2/27*c**4 + 15*c + 1/9*c**5. Let x(v) = 0. What is v?
0, 2/3, 2
Suppose -c - 3*c + 32 = 0. Factor -16 - 25*g**4 - 114*g**2 - 99*g**3 - 52*g + 4*g**3 + c.
-(g + 1)*(g + 2)*(5*g + 2)**2