ctor d(k).
3*(k + 2)*(k + 4)/2
Find x, given that -57/2*x**3 + 12*x**2 + 15*x**4 + 0 + 3/2*x = 0.
-1/10, 0, 1
Let y(u) be the third derivative of -u**8/191520 - u**7/47880 + u**6/3420 - 3*u**5/20 - 8*u**2. Let p(o) be the third derivative of y(o). Factor p(s).
-2*(s - 1)*(s + 2)/19
Let y(s) be the first derivative of s**3 - 111*s**2/2 + 108*s + 403. Suppose y(m) = 0. Calculate m.
1, 36
Suppose -5*t - 2*p = p - 2, 3*p = 2*t - 5. Let m(n) be the first derivative of -5 + t + 3*n + 1 - n**3 + 5. Factor m(i).
-3*(i - 1)*(i + 1)
Suppose -248*i = 232*i - 504*i. Factor 10/11*d + 2/11*d**2 + i.
2*d*(d + 5)/11
Let v(n) be the third derivative of 10*n**2 + 1/48*n**4 + 0*n + 0 - 1/120*n**5 + 0*n**3. Let v(m) = 0. What is m?
0, 1
Let l(w) be the first derivative of -12/65*w**5 - 11 - 1/39*w**6 - 20/39*w**3 - 3/13*w**2 - 6/13*w**4 + 0*w. Factor l(d).
-2*d*(d + 1)**3*(d + 3)/13
Suppose 2*b - 3*t = 21, 0*t - 3 = -3*b - 5*t. Factor -57*r - 16*r**2 + 75*r - 5*r**2 + 3*r**3 + b*r**2.
3*r*(r - 3)*(r - 2)
Let z = -724 - -332. Let r be ((-16)/z)/((-2)/(-14)). Factor 0 - r*n - 10/7*n**2 - 6/7*n**4 - 2*n**3.
-2*n*(n + 1)**2*(3*n + 1)/7
Determine d, given that -31*d**2 - 16 - 34*d**2 + 113*d**2 - 2*d**3 + 2*d - 42*d**2 + 10*d = 0.
-2, 1, 4
Let x(d) be the third derivative of -d**9/332640 - d**8/22176 - d**7/6930 - d**5/4 + 3*d**2. Let t(y) be the third derivative of x(y). Factor t(j).
-2*j*(j + 1)*(j + 4)/11
Let g = -1518 + 1520. Determine h so that 2/9*h**g - 4/9 + 2/9*h = 0.
-2, 1
Let u(n) = -214*n**3 - 30308*n**2 - 24167*n - 4824. Let x(f) = -71*f**3 - 10102*f**2 - 8056*f - 1608. Let s(m) = 4*u(m) - 11*x(m). Factor s(j).
-3*(j + 134)*(5*j + 2)**2
Let a(d) be the first derivative of 0*d - 1/2*d**4 + 2*d**2 - 20 - 2/3*d**3. Factor a(y).
-2*y*(y - 1)*(y + 2)
Factor 0*m + 0 + 0*m**2 - 75*m**3 - 3/4*m**5 + 15*m**4.
-3*m**3*(m - 10)**2/4
Let g(a) = 2*a**2 + 9*a**3 - 2*a - 13*a**3 + 2 + 2. Let z(m) = 3*m**3 - m**2 + 2*m - 4. Let j(c) = 5*g(c) + 6*z(c). Factor j(k).
-2*(k - 2)*(k - 1)*(k + 1)
Suppose 60*t - 62*t = 0. What is r in 6/5*r**3 + 0 + 0*r + t*r**2 + 9/5*r**4 = 0?
-2/3, 0
Let t be (-3 - -2)/((-4)/12). Solve -3*v**2 + 16*v**2 + 6*v**t - 12*v**3 - 12*v + 4 + 4*v**4 - 3*v**4 = 0.
1, 2
Let c(x) be the third derivative of -25*x**2 + 1/12*x**4 + 0*x**3 - 1/20*x**5 + 0 + 0*x. Factor c(a).
-a*(3*a - 2)
Let f(m) be the second derivative of 8*m**6/15 + 4*m**5 - 223*m**4/3 - 472*m**3/3 - 120*m**2 + 11*m - 15. Suppose f(l) = 0. Calculate l.
-10, -1/2, 6
Let j(g) be the first derivative of g**4/36 - 8*g**3/27 + 7*g**2/6 - 2*g + 50. Factor j(w).
(w - 3)**2*(w - 2)/9
Let n(h) = 1 - 6*h + 6 - 2 - h**2. Let x(o) = 3*o - 3. Let y = 20 + -17. Let w(g) = y*n(g) + 5*x(g). Factor w(q).
-3*q*(q + 1)
Find n such that 678/7*n + 22/7*n**2 - 124/7 = 0.
-31, 2/11
Let m(j) be the second derivative of j**6/90 + j**5/6 + 23*j**4/36 + 7*j**3/9 + j - 44. Factor m(z).
z*(z + 1)*(z + 2)*(z + 7)/3
Factor -470*o - 26016 - 25768 + 135*o**2 + 51184 + 5*o**3.
5*(o - 4)*(o + 1)*(o + 30)
Let i(o) be the second derivative of 0 + 6*o**2 + 13/3*o**4 + 7*o - 22/3*o**3 - o**5. Factor i(c).
-4*(c - 1)**2*(5*c - 3)
Let q(d) be the second derivative of 5*d**4/12 + 5*d**3/3 - 75*d**2/2 + 20*d. Factor q(l).
5*(l - 3)*(l + 5)
Suppose 4*r + 6 - 18 = 0. Let h(u) be the second derivative of 3/2*u**3 + 1/4*u**4 + 0 + 3*u + r*u**2. Factor h(a).
3*(a + 1)*(a + 2)
Let j(t) be the first derivative of t**6/12 - 3*t**4/4 + 4*t**3/3 - 3*t**2/4 + 47. What is r in j(r) = 0?
-3, 0, 1
Let s(l) be the second derivative of 5/36*l**3 + 1/6*l**2 - 1/18*l**4 - 1/40*l**5 + 10*l + 0. Solve s(p) = 0.
-2, -1/3, 1
Let g(k) = 6*k**3 - 16*k**2. Let n(b) = -3*b**2 + 0*b + b**3 + b + 2*b**2. Let w be -3 + 3 + 6 + -5. Let v(c) = w*g(c) - 8*n(c). Solve v(m) = 0 for m.
-2, 0
Let i(n) be the second derivative of n**5/90 - 19*n**4/18 - 58*n**3/27 - 11*n - 1. Factor i(q).
2*q*(q - 58)*(q + 1)/9
Let t be (-24)/66 - 260/(-110). What is w in 3/5 - 4/5*w + 1/5*w**t = 0?
1, 3
Find t, given that -3/8*t**5 - 33*t**2 + 675/4 - 333/4*t**3 + 1845/8*t + 45/4*t**4 = 0.
-1, 2, 15
Determine t, given that 3*t**2 + 4 - 5*t**2 - 2 + 6*t**2 - 6*t**2 = 0.
-1, 1
Let p(s) = -s**2 - 19*s + 4. Let h be p(-19). Let n(x) be the third derivative of 0 + 1/4*x**6 + 4*x**2 + 1/6*x**h + 0*x + 0*x**3 - 11/30*x**5. Factor n(o).
2*o*(3*o - 1)*(5*o - 2)
Let l(h) be the first derivative of -h**6/30 + 184*h**5/25 + 373*h**4/10 + 1124*h**3/15 + 751*h**2/10 + 188*h/5 + 612. Find z, given that l(z) = 0.
-1, 188
Factor -4*v**3 - 4 - 21/2*v**2 - 1/2*v**4 - 11*v.
-(v + 1)**2*(v + 2)*(v + 4)/2
Let d(r) be the third derivative of -1/20*r**5 + 0 + 20*r**2 + 23/1080*r**6 + 0*r + 13/216*r**4 - 1/270*r**7 - 1/27*r**3. Factor d(w).
-(w - 1)**3*(7*w - 2)/9
Suppose -7 = 5*o + 38. Let s(x) = 20*x**2 + 49*x - 51. Let f(y) = 5*y**2 + 12*y - 13. Let k(m) = o*f(m) + 2*s(m). Factor k(t).
-5*(t - 1)*(t + 3)
Let v(k) be the third derivative of -k**8/4032 + 5*k**7/504 + 11*k**6/144 - 7*k**5/30 - 5*k**2. Let d(i) be the third derivative of v(i). Factor d(t).
-5*(t - 11)*(t + 1)
Let u(q) be the first derivative of -q**5/20 + q**4/2 + 5*q**3/2 + 25*q**2/2 - 3. Let v(c) be the second derivative of u(c). Find b such that v(b) = 0.
-1, 5
Suppose d + 2*v = 4, -2*v - 29 - 3 = -2*d. Factor d*b**2 + 3*b**3 + 12*b - 566 + 566.
3*b*(b + 2)**2
Let v(f) be the first derivative of -19*f**4/10 + 16*f**3/3 - 23*f**2/5 + 4*f/5 - 81. Suppose v(g) = 0. Calculate g.
2/19, 1
Let j(g) be the second derivative of -3/5*g**5 + 7/9*g**4 - 4/9*g**3 + 2/9*g**6 + 0 - 4*g + 0*g**2 - 2/63*g**7. Factor j(i).
-4*i*(i - 2)*(i - 1)**3/3
Let o(u) be the third derivative of 0*u**4 + 1/30*u**6 + 1/105*u**7 + 0*u - 7*u**2 + 0*u**3 + 1/30*u**5 + 0. Find r such that o(r) = 0.
-1, 0
Suppose 4*s = 3*l - 19, -l + 27 = 4*l - 2*s. Factor -l*t**3 - 52*t + 5*t**2 - 5*t**4 + 5*t**5 + 52*t.
5*t**2*(t - 1)**2*(t + 1)
Find a such that 60/11*a**2 + 336/11 - 6/11*a**3 + 312/11*a = 0.
-2, 14
Let s = -7025 - -28103/4. Find n such that -1/2*n + s*n**2 + 0 - 1/4*n**3 = 0.
0, 1, 2
Let m(o) = -8*o**4 + 8*o**3 + 10*o**2 - 5*o + 2. Let i(c) = -808*c + c**3 - c**4 + c**2 + 808*c. Let b(a) = 21*i(a) - 3*m(a). Factor b(k).
3*(k - 1)**3*(k + 2)
Let l = 1356/427 + -2/61. Factor l*a + 50/7*a**3 + 2/7 + 10*a**2.
2*(a + 1)*(5*a + 1)**2/7
Let o(f) be the first derivative of 2*f**3/15 + 24*f**2/5 + 46*f/5 - 94. Factor o(q).
2*(q + 1)*(q + 23)/5
Let z(o) be the second derivative of o**5/4 + 25*o**4/4 - 15*o**3 - 80*o**2 + 3*o. Solve z(u) = 0.
-16, -1, 2
Factor -2/5*v**2 - 14/5 + 29/5*v.
-(v - 14)*(2*v - 1)/5
Factor 24 + 21*n + 0*n**2 - 7*n - n**2 - 2*n + 11*n.
-(n - 24)*(n + 1)
Let s(c) be the third derivative of 0*c + 3/32*c**5 + 0 - 75/64*c**4 - 1/320*c**6 + 5*c**2 + 125/16*c**3. Solve s(l) = 0.
5
Let v(w) be the first derivative of 250/9*w + 53/9*w**4 + 580/27*w**3 + 325/9*w**2 + 1/27*w**6 - 7 + 34/45*w**5. Factor v(d).
2*(d + 1)**2*(d + 5)**3/9
Let u = 136 + -139. Let a be 3/u*(-4 + 25/7). Find b, given that 0 + 9/7*b**2 - a*b**5 + 6/7*b - 9/7*b**4 - 3/7*b**3 = 0.
-2, -1, 0, 1
Suppose -18 = -2*a + 4*h, 21 = 2*a + a - 4*h. Let s(w) be the first derivative of 0*w + 2/27*w**a - 2/9*w**2 - 1. Solve s(r) = 0 for r.
0, 2
Let j(h) = h**3 - 29*h**2 + 28*h. Let b be j(28). Suppose -2*p + a = b, -6*p = -p + a. Factor p - 2/9*x**3 - 4/9*x - 2/3*x**2.
-2*x*(x + 1)*(x + 2)/9
Let f(i) be the second derivative of -i**4/66 + 2*i**3/33 + 3*i**2/11 + 2*i. Factor f(b).
-2*(b - 3)*(b + 1)/11
Let l(h) = 21 - 8*h**2 + 5*h**3 - 22*h - 4*h - 3*h**2. Let y(c) = c**3 - 2*c**2 - 5*c + 4. Let v(m) = -2*l(m) + 11*y(m). Determine z, given that v(z) = 0.
-2, 1
Let m(w) = 6*w**5 + 5*w**4 + w**3 - 2*w**2 + 8*w + 7. Let i(c) = c**5 + c**4 + c**3 + c + 1. Let b be 8 + 3/(3 + -4). Let q(k) = b*i(k) - m(k). Factor q(u).
-(u - 2)*(u - 1)*(u + 1)**3
Let l = 17 - -118. Factor 5*m**4 + 291*m**2 - 72*m**2 + 40*m**3 - 129*m**2 - l.
5*(m - 1)*(m + 3)**3
Let k(h) be the second derivative of h**7/3360 + h**6/480 - h**4/24 - 2*h**3/3 + 11*h. Let r(v) be the second derivative of k(v). Factor r(m).
(m - 1)*(m + 2)**2/4
Let g(z) be the first derivative of z**4 + 2*z**3 - 39/20*z**5 + 8*z - 5 + 1/2*z**6 + 0*z**2. Let f(y) be the first derivative of g(y). Solve f(t) = 0 for t.
-2/5, 0, 1, 2
Let g(c) be the third derivative 