Let u(p) be the third derivative of p**8/6720 + p**7/1680 - p**6/288 - p**5/80 + 5*p**3 + 6*p**2 + 2. Let a(s) be the first derivative of u(s). Factor a(h).
h*(h - 2)*(h + 1)*(h + 3)/4
Factor -2*f**3 + 0 + 2/9*f**5 - 8/9*f + 2/9*f**4 + 22/9*f**2.
2*f*(f - 1)**3*(f + 4)/9
Let n(k) be the second derivative of 3*k**5/20 - k**3/2 - 11*k. Solve n(h) = 0.
-1, 0, 1
Let j(w) = 2*w - w - 1 + 3 + w. Let o be j(3). Factor q + 7*q - q**2 - o*q.
-q**2
Let f(u) = -u**2 - 121*u - 10 - 27 + 107*u. Let p be f(-10). Factor 0 + 2/5*j**4 - 2/5*j**2 - 4/5*j**p + 4/5*j.
2*j*(j - 2)*(j - 1)*(j + 1)/5
Let s(y) be the second derivative of 13*y + 1/30*y**3 + 0 + 1/5*y**2 - 1/60*y**4. Factor s(c).
-(c - 2)*(c + 1)/5
Let a(r) be the third derivative of -r**7/525 + r**6/150 - r**4/30 + r**3/15 - 17*r**2. Solve a(j) = 0.
-1, 1
Let d(t) be the second derivative of -1/14*t**4 - 18*t + 0*t**2 + 0*t**3 + 9/140*t**5 - 1/70*t**6 + 0. Find l, given that d(l) = 0.
0, 1, 2
Let s(b) = b + 8. Let l be s(0). Suppose l*r - 27 = 133. Factor -6 + 120*j**2 - 22*j**3 - 26 + 114*j**3 + r*j**4 + 16*j.
4*(j + 1)*(j + 2)**2*(5*j - 2)
Let o(r) be the second derivative of 5*r**7/6 + 2*r**6 - 11*r**5/4 - 5*r**4 + 10*r**3/3 - 4*r + 62. Determine n, given that o(n) = 0.
-2, -1, 0, 2/7, 1
Solve 2/9*o**2 - 124/9*o + 1922/9 = 0.
31
Let f(t) = -8*t**3 + 49*t**2 + 75*t. Let c(v) = -v**3 + 2*v**2 - 3*v. Let d(n) = -5*c(n) + f(n). Factor d(b).
-3*b*(b - 15)*(b + 2)
Let f(o) be the third derivative of -7*o**6/180 + o**5/60 - o**3/3 - 4*o**2. Let r(z) be the first derivative of f(z). Factor r(j).
-2*j*(7*j - 1)
Let k = -2/633 + 6269/2954. Let m = k - 11/6. Solve m*n**3 + 24/7*n - 16/7 - 12/7*n**2 = 0.
2
Let l = 30/7 + -99/28. Let v(t) be the second derivative of -27/10*t**5 + 10/3*t**3 + 0 + 2*t + 2*t**2 - 9/10*t**6 + l*t**4. Solve v(w) = 0.
-2, -1/3, 2/3
Determine m so that 3*m**2 + 5*m - m**4 - 5*m**2 - 11*m + 5*m**2 + 4*m**2 = 0.
-3, 0, 1, 2
Let o(q) be the third derivative of -1/3*q**3 + 0 + 1/72*q**4 + 0*q + 1/180*q**5 + 3*q**2. Find c, given that o(c) = 0.
-3, 2
Let l(v) be the second derivative of 5/2*v**2 + 0 - 6*v - 1/54*v**4 - 1/270*v**5 + 1/540*v**6 + 0*v**3. Let f(s) be the first derivative of l(s). Factor f(a).
2*a*(a - 2)*(a + 1)/9
Factor 0 + 2/3*a**4 + 22/3*a**2 + 4*a**3 + 4*a.
2*a*(a + 1)*(a + 2)*(a + 3)/3
Factor -56/11*y**2 + 106/11*y - 52/11 + 2/11*y**3.
2*(y - 26)*(y - 1)**2/11
Let t = -948 - -951. Let s(j) be the third derivative of -1/4*j**4 + 2/3*j**t + 1/60*j**6 - 6*j**2 + 0 + 0*j**5 + 0*j. Solve s(z) = 0 for z.
-2, 1
Factor 0 + 18/11*y**3 - 10/11*y**4 - 2/11*y - 6/11*y**2.
-2*y*(y - 1)**2*(5*y + 1)/11
Let r = 18 + -40. Let j = 89/4 + r. Factor -j*k**2 + 3/2*k - 9/4.
-(k - 3)**2/4
Let i(l) = -2*l**4 - 16*l**3 - 32*l**2 - 12*l - 2. Let n(a) = 2*a**4 + 15*a**3 + 33*a**2 + 11*a + 3. Let v(q) = 3*i(q) + 2*n(q). Factor v(h).
-2*h*(h + 1)**2*(h + 7)
Let p(i) be the third derivative of i**9/151200 + i**8/8400 + i**7/1050 + i**6/225 + i**5/20 - 2*i**2. Let d(o) be the third derivative of p(o). Factor d(t).
2*(t + 2)**3/5
Suppose 2*x + 6*x - 40 = 0. Factor -4 + 6 - 7*s**2 + x*s + 0*s**2.
-(s - 1)*(7*s + 2)
Let o(k) = -k**3 + 11*k**2 - 9*k - 8. Let v be o(10). Factor 39*w**v - 42*w**2 + 9*w**3 - 9*w**4 + 5*w**5 - 2*w**5.
3*w**2*(w - 1)**3
Let p be 0/((120/6)/10). Let o(k) be the third derivative of -1/100*k**5 + 0 + 3*k**2 + p*k + 0*k**3 - 1/40*k**4. Factor o(c).
-3*c*(c + 1)/5
Let v(z) = -z + 26. Let c be v(8). Find y such that 7*y**3 + 16*y**3 + c*y**2 + 2*y**4 - 11*y**3 = 0.
-3, 0
Let l(p) be the third derivative of p**7/945 - 11*p**6/540 - p**5/270 + 11*p**4/108 + 41*p**2 - p. Factor l(a).
2*a*(a - 11)*(a - 1)*(a + 1)/9
Let c(n) be the first derivative of n**6/20 + n**5/10 + n**4/24 + 8*n + 7. Let t(a) be the first derivative of c(a). Factor t(v).
v**2*(v + 1)*(3*v + 1)/2
Let c(u) = -2*u**5 + u**4 - u**3 + u**2 - u + 1. Let v(l) = 19*l**5 - 16*l**4 + 23*l**3 - 11*l**2 - 6*l. Let d(j) = 18*c(j) + 2*v(j). Solve d(t) = 0 for t.
-1, 1, 3
Let h = 56689/506 + -2415/22. Factor 338/23 + h*k + 2/23*k**2.
2*(k + 13)**2/23
Let r(n) = 11*n**3 + 22*n**2 + 10*n - 52. Let l(c) = 20*c**3 + 45*c**2 + 20*c - 100. Let m(f) = -3*l(f) + 5*r(f). Factor m(v).
-5*(v - 1)*(v + 2)*(v + 4)
Let z(o) be the second derivative of 2/3*o**3 + 0*o**2 + 0 + 7*o - 1/5*o**5 + 0*o**4. What is v in z(v) = 0?
-1, 0, 1
Let k = 43714/15 - 2916. Let q = k + 7/3. Factor -q*l**2 + 9/5*l**3 + 0*l + 0 - 9/5*l**4 + 3/5*l**5.
3*l**2*(l - 1)**3/5
Let i = -20 - -21. Let b(n) = n**3 - n - 1. Let x(q) = -9*q**3 - 3*q**2 + 9*q + 15. Let y(m) = i*x(m) + 12*b(m). Let y(v) = 0. What is v?
-1, 1
Let m(y) = -4*y**2 + 340*y + 24. Let b(n) = -n**2 + 68*n + 5. Let c(v) = 24*b(v) - 5*m(v). Determine l, given that c(l) = 0.
-17, 0
Let i(x) be the first derivative of 2*x**5/25 - x**4/5 - 2*x**3/5 + 8*x**2/5 - 8*x/5 - 36. Factor i(q).
2*(q - 2)*(q - 1)**2*(q + 2)/5
Suppose 5*p - p = 0. Suppose -2 + p = -2*m. Factor 3*i + 2 - m + i**2 - 1.
i*(i + 3)
Suppose 5*b - 16 = -p, -2*b - 2*b - 5*p + 17 = 0. Factor -403 - b*z**2 - 6*z - 60*z + 40.
-3*(z + 11)**2
Let -3/2*s**3 - 441/2 - 1281/2*s + 125/2*s**2 = 0. Calculate s.
-1/3, 21
Let c be 5*(0 - (-4)/10). Suppose c + 1 = d. Factor 169*q**d - 166*q**3 + 6*q**2 - 3*q + 1 - 7.
3*(q - 1)*(q + 1)*(q + 2)
Let t(i) be the second derivative of 5*i**4/48 + i**3/12 + 17*i - 2. Factor t(c).
c*(5*c + 2)/4
Let g(p) be the second derivative of p**4/54 - p**3/9 - 2*p**2 - 54*p. Factor g(o).
2*(o - 6)*(o + 3)/9
Let g(j) = 17*j - 50. Let u be g(8). Suppose 4*l = u - 78. Factor 9/2 + 3*q + 1/2*q**l.
(q + 3)**2/2
Let d(l) be the second derivative of -l**6/10 + 27*l**5/20 + l**4/4 - 9*l**3/2 + 654*l. Factor d(f).
-3*f*(f - 9)*(f - 1)*(f + 1)
Let k be (-8)/((-24)/9) - (-15)/(-9). Let 1/6*n**3 + k*n - 7/6*n**2 + 8/3 = 0. What is n?
-1, 4
Let y(j) = -j**3 + 42*j**2 + 34*j + 390. Let i be y(43). Let 1/5*o**i - 1/5*o**2 - 4/5*o + 4/5 = 0. What is o?
-2, 1, 2
Let b(p) = 7*p**2 - 6*p + 4. Let x(f) = 2*f + 1. Suppose 0*z = -z - 3. Let u be x(z). Let v(c) = 8*c**2 - 6*c + 4. Let s(j) = u*v(j) + 6*b(j). Factor s(m).
2*(m - 2)*(m - 1)
Let o(n) be the second derivative of -n**5/40 - n**4/12 + n**3/4 + 117*n. Factor o(h).
-h*(h - 1)*(h + 3)/2
Factor -5/3*w**3 - 35/3*w**2 - 50/3*w + 0.
-5*w*(w + 2)*(w + 5)/3
Factor -10 - 8*t**2 - 4*t + 2 + 4*t**3 + 26 - 10.
4*(t - 2)*(t - 1)*(t + 1)
Let g(q) be the first derivative of q**8/10080 - q**7/1680 + q**6/720 - q**5/720 + 10*q**3/3 + 1. Let i(u) be the third derivative of g(u). Factor i(n).
n*(n - 1)**3/6
Suppose -6/5 - 1/5*a**2 - a = 0. What is a?
-3, -2
Suppose u - 4*h - 4 = -3*h, -5*h = 2*u - 22. Let p(y) be the third derivative of 0*y + 0 + 0*y**3 - 1/135*y**5 + 1/108*y**4 + 1/540*y**u - y**2. Factor p(d).
2*d*(d - 1)**2/9
Factor -24/11*m**2 + 0 + 2/11*m**3 + 72/11*m.
2*m*(m - 6)**2/11
Let c(r) = -5*r**4 + r**3 - 2*r**2 + 4. Let s = 46 + -42. Let t(o) = 4*o**4 + 2*o**2 - 3. Let d(i) = s*t(i) + 3*c(i). Factor d(j).
j**2*(j + 1)*(j + 2)
Solve 61*u**4 - 95*u**3 + 5 - 4*u**5 - 69*u**3 - 5 - 13*u**4 + 120*u**2 = 0.
0, 1, 5, 6
Let d(a) be the second derivative of -a**7/2520 - a**6/240 - a**5/60 + a**4/2 + 9*a. Let j(l) be the third derivative of d(l). Factor j(t).
-(t + 1)*(t + 2)
Suppose x - 18 = -4*v, 4*v = v - x + 14. Factor 512*o - 192 - 192*o**2 + 101 + 32*o**3 - 2*o**v - 237 - 184.
-2*(o - 4)**4
Let f = -96 - -106. Factor 1098*g**3 + 2*g**5 + f*g**4 - 1084*g**3 + 0*g**5 + 6*g**2.
2*g**2*(g + 1)**2*(g + 3)
Let t(b) be the first derivative of 2/5*b**5 - 1/2*b**4 + 4*b + b**2 + 15 - 2*b**3. Let t(h) = 0. Calculate h.
-1, 1, 2
Factor 3/2*h**3 - 27/2 - 21/2*h**2 - 51/2*h.
3*(h - 9)*(h + 1)**2/2
Let c(m) be the third derivative of -m**6/165 - 23*m**5/330 - 5*m**4/44 - 576*m**2. Factor c(r).
-2*r*(r + 5)*(4*r + 3)/11
Let g(t) = 5*t**2 - 159*t + 154. Let o(u) = 15*u**2 - 476*u + 461. Let s(l) = -11*g(l) + 4*o(l). Factor s(n).
5*(n - 30)*(n - 1)
Let p(i) be the second derivative of -i**5/60 - i**4/8 - i**3/3 - 6*i**2 - 21*i. Let r(h) be the first derivative of p(h). Solve r(q) = 0.
-2, -1
Let r = 6 - -6. Factor -27*s**2 + 4*s + 12*s + 8*s**3 - 5*s**2 + r*s**2 - 4.
4*(s - 1)**2*(2*s - 1)
Find d, given that 6706 - 460*d + 29*d**2 - 200*d**3 - 32*d**4 + 154*d - 6760 - 437*d**2 = 0.
-3, -3/2, -1/4
Let o be 