third derivative of -n**8/840 + 23*n**7/2100 - 7*n**6/200 + n**5/30 + n**4/30 - 4*n**2 + 2. Factor y(m).
-m*(m - 2)**3*(4*m + 1)/10
Let c(o) be the second derivative of 0*o**2 - 1/4*o**3 + 6*o + 0*o**4 + 3/40*o**5 + 0. Factor c(v).
3*v*(v - 1)*(v + 1)/2
Let v be (-21)/(-35) - ((-28)/20 + 0). What is c in -2/7*c**v + 2/7*c + 4/7 = 0?
-1, 2
Let q(f) be the third derivative of -f**8/2520 - f**7/252 - 7*f**6/540 - f**5/60 - 2*f**3 + 11*f**2. Let i(a) be the first derivative of q(a). Factor i(m).
-2*m*(m + 1)**2*(m + 3)/3
Suppose -w**2 + 12 + 32*w + 0*w**2 + 40 - 19 = 0. Calculate w.
-1, 33
Let i(s) = -3*s**2 - 12*s - 54. Let c(l) = -4*l**2 + 1. Let o(g) = -6*c(g) + i(g). Factor o(r).
3*(r - 2)*(7*r + 10)
Let q(z) be the first derivative of 25 - 20/39*z**3 - 1/39*z**6 - 2/13*z - 5/13*z**2 - 2/13*z**5 - 5/13*z**4. Factor q(x).
-2*(x + 1)**5/13
Let p(g) be the first derivative of -8/9*g + 6 + 5/9*g**2 - 2/27*g**3. Solve p(o) = 0.
1, 4
Suppose -14*w - 9 = -15*w. Suppose -3*o + w = -3. Let -21*p**5 + 0*p**3 - 4*p - 6*p**3 - 27*p**4 + o*p = 0. Calculate p.
-1, -2/7, 0
Let q(f) = f**2 - 6*f + 5*f**3 - 4*f**2 - 6 + 0*f**2 + 12. Let h(l) = -9*l**3 + 6*l**2 + 11*l - 11. Let o(c) = -6*h(c) - 11*q(c). Factor o(y).
-y**2*(y + 3)
Suppose -3*z = z + 208. Let b be -1 + 2 + z/(-26). Suppose 1/3*q**2 - 1/3*q**4 + q**b - 2/3*q**5 + 0 - 1/3*q = 0. What is q?
-1, 0, 1/2, 1
Suppose 0 = 22*h - 1 - 41 - 46. Factor 88/5*f**2 - 8/5*f - 162/5*f**5 - 314/5*f**3 + 396/5*f**h + 0.
-2*f*(f - 1)**2*(9*f - 2)**2/5
Suppose -675/4*s + 0 + 315*s**2 - 249/2*s**3 - 21*s**4 - 3/4*s**5 = 0. What is s?
-15, 0, 1
Let x(t) be the first derivative of -t**3/15 - 2*t**2/5 - 4*t/5 + 314. Factor x(k).
-(k + 2)**2/5
Suppose -100 + 2 = -49*p. Solve 6/5*q**p + 0 + 3/5*q**4 + 0*q + 21/5*q**3 - 6*q**5 = 0.
-1/2, -2/5, 0, 1
Suppose 244 = 36*p + 25*p. Let z(b) be the first derivative of 1/2*b + 1/2*b**3 + 7 + 3/4*b**2 + 1/8*b**p. Suppose z(t) = 0. What is t?
-1
Factor -47/4*m - 45/4*m**3 + 91/4*m**2 + 1/4.
-(m - 1)**2*(45*m - 1)/4
Let -336*q - 60*q**4 + 32 - 760*q**2 - 60*q**4 + 20*q**4 - 492*q**3 = 0. What is q?
-2, -1, 2/25
Factor 52/7 + 8/7*o**2 + 30*o.
2*(o + 26)*(4*o + 1)/7
Determine q so that -48 + 13*q**2 - 9*q**2 - 10*q**2 + 3*q**2 - 30*q = 0.
-8, -2
Let u be (-13 - -17) + -2 + 1. Factor -5 + 2*x**4 - 6*x**2 + 108*x - u - 92*x - 4*x**3.
2*(x - 2)*(x - 1)**2*(x + 2)
Let x be (3/15)/((-6)/60*-3). Let o(f) be the first derivative of x*f**4 - 6 - 128/3*f - 1/30*f**5 - 16/3*f**3 + 64/3*f**2. Find c such that o(c) = 0.
4
Let x be (-2)/12 - (1639/(-264) + 6). Let j(a) be the third derivative of 1/60*a**5 - 3*a**2 + 0*a**3 + 0*a + x*a**4 + 0 - 1/120*a**6 - 1/210*a**7. Factor j(r).
-r*(r - 1)*(r + 1)**2
Let b(d) be the third derivative of -d**5/20 + d**4/4 + 3*d**3/2 - 30*d**2. Factor b(z).
-3*(z - 3)*(z + 1)
Let g(y) = -2*y**2 + 12*y + 14. Let v be g(5). Suppose 9*l + 6 = v. Factor -2/3*a**4 - 4/9 + 22/9*a**3 + 2*a - 10/3*a**l.
-2*(a - 1)**3*(3*a - 2)/9
Suppose 0 = -5*v - 49 + 4. Let x be (12/(-8))/(v/12). Factor -b**2 + x - b**2 + 0*b**2.
-2*(b - 1)*(b + 1)
Let h be 6 + -2 + -3 - 29. Let b = h + 33. Find r, given that -3*r**5 + 18*r**b - 2*r + 27*r**3 - 39*r**4 - 4*r + 3*r**2 = 0.
-2/5, 0, 1
Let n(b) = 3*b**4 - 46*b**3 + 292*b**2 - 724*b + 643. Let f(k) = 3*k**4 - 45*k**3 + 291*k**2 - 723*k + 642. Let r(a) = -5*f(a) + 6*n(a). Solve r(l) = 0.
3, 8
Let d(a) be the first derivative of -1/10*a**5 - 1/3*a**3 + 3/8*a**4 + 19 + 0*a**2 + 0*a. Factor d(u).
-u**2*(u - 2)*(u - 1)/2
Suppose -5*h - 3*u = -20 - 12, 4*h = 5*u - 4. Let g(j) = -j**3 + 5*j**2 - 3*j - 2. Let t be g(h). Factor -2/7*s**t + 0 + 2/7*s.
-2*s*(s - 1)/7
Let t(n) be the second derivative of -n**7/112 + 3*n**6/80 + 3*n**5/10 - 5*n**4/8 - 6*n**3 - 12*n**2 - 248*n. Solve t(r) = 0 for r.
-2, -1, 4
What is u in 0*u - 1/4*u**5 + 0 + 0*u**2 + 1/2*u**4 + 3/4*u**3 = 0?
-1, 0, 3
Let q(t) be the third derivative of 4*t**2 + 0 - 4/3*t**3 + 1/1620*t**6 - 1/180*t**5 - 1/27*t**4 + 0*t. Let l(j) be the first derivative of q(j). Factor l(w).
2*(w - 4)*(w + 1)/9
Suppose -12/7 + 22/7*j - 2/7*j**5 - 20/7*j**3 + 12/7*j**4 + 0*j**2 = 0. Calculate j.
-1, 1, 2, 3
What is r in 0*r**3 + 5*r**3 + 24*r - 8*r**3 + 3*r = 0?
-3, 0, 3
What is k in 142*k**3 + 146*k**3 + 148*k**3 - 60*k**2 - 587*k**3 + 180 + 143*k**3 + 128*k = 0?
-9, -1, 5/2
Let x = 21204 - 21200. Solve -15/2*m**3 + 10/3*m**x + 145/6*m - 15*m**2 - 5 = 0 for m.
-2, 1/4, 1, 3
Let b = 897 - 17937/20. Let t(i) be the third derivative of 0 - 1/40*i**6 + 0*i - 1/4*i**4 - 5*i**2 + 0*i**3 - b*i**5. Factor t(z).
-3*z*(z + 1)*(z + 2)
Let k(u) be the third derivative of -4/3*u**4 + 0 + 0*u + 7*u**2 + 14/3*u**3 + 1/15*u**5. Factor k(w).
4*(w - 7)*(w - 1)
Determine z, given that 3481/5*z**2 + 4/5 - 236/5*z = 0.
2/59
Let k(p) = p**3 - 8*p**2 - 2*p + 7. Let d(l) = -l**2 + 1. Let r(m) = -35*d(m) + 5*k(m). Solve r(q) = 0.
-1, 0, 2
Let x(v) be the third derivative of 3*v**6/10 - 2*v**5/15 - 6*v**2 - 12. Let x(z) = 0. What is z?
0, 2/9
Suppose -5*t + 17 - 17 = 0. Let r(g) be the second derivative of 0*g**3 + 4*g + t*g**2 + 0 - 1/56*g**7 + 0*g**5 + 1/40*g**6 + 0*g**4. Factor r(o).
-3*o**4*(o - 1)/4
Suppose -2*o = -3*y - 6, -4*y + 10 = -5*o + 25. Suppose n = 4*j - j, 0 = o*n + 3*j. Solve 0*l + 20/3*l**4 + 0 + n*l**2 + 25/3*l**5 + 4/3*l**3 = 0.
-2/5, 0
Let r(q) = -2*q**3 + 132*q**2 - 2584*q + 4624. Let t(d) = 2*d**2. Let x(p) = -r(p) - 4*t(p). Factor x(n).
2*(n - 34)**2*(n - 2)
Suppose -n = 2*n - 15. Factor -n + 6*s**2 + 10*s - 10*s**2 + 2*s**2 - 3.
-2*(s - 4)*(s - 1)
Let d(a) = a + 5. Let z be d(-4). Let o be -3 - (z*-9 + 3). Factor q**o - 3*q**3 + 6*q**3 + 3*q**4 - q**3.
3*q**3*(q + 1)
What is q in 20/3*q**3 + 12 - 266/9*q + 152/9*q**2 - 2/9*q**5 - 52/9*q**4 = 0?
-27, -2, 1
Let s = -66 + 117. Factor -7*f + 41*f**3 - 15*f**2 + 22*f - s*f**3 + 10.
-5*(f - 1)*(f + 2)*(2*f + 1)
Let h(d) = -3*d**2 + 23*d + 11. Let b be h(8). Let g(v) be the first derivative of 4/3*v + 6 - 2*v**2 - 7/9*v**b. Solve g(o) = 0.
-2, 2/7
Let h(n) be the first derivative of 2*n**3/9 + 40*n**2/3 + 26*n - 177. Factor h(t).
2*(t + 1)*(t + 39)/3
Let p = -137 - -140. Let y(k) be the third derivative of 0*k + k**2 + 0 - 1/4*k**4 + 1/30*k**5 + 0*k**p. Factor y(b).
2*b*(b - 3)
Determine r so that 3*r**5 - 25*r**4 - 18*r**2 + 16*r**4 + 3*r**3 + 24*r**4 - 3*r**4 = 0.
-3, -2, 0, 1
Let x = 57 + -57. Let y be 1 - (0 + (-3)/3). Solve 4 + k**y + 6*k + k**2 + x = 0 for k.
-2, -1
Let t(z) be the second derivative of -2/3*z**4 + 2/21*z**7 + 0 - 4*z**2 + 8/15*z**6 - 10/3*z**3 + 4/5*z**5 + 9*z. Suppose t(b) = 0. Calculate b.
-2, -1, 1
Let x be 1/2*-2 + 3. Let h(g) = 30*g**2 + 34*g**2 - 67*g**2. Let j(m) = -m**2. Let p(i) = x*j(i) - h(i). Factor p(l).
l**2
Let a(i) be the third derivative of -i**8/84 + 11*i**7/21 - 151*i**6/30 - 71*i**5/2 - 75*i**4/2 - 18*i**2 - 7. What is n in a(n) = 0?
-2, -1/2, 0, 15
Let 0 + 1/10*z**4 - 32/5*z + 24/5*z**2 - 6/5*z**3 = 0. Calculate z.
0, 4
Let u(n) = 69*n - 828. Let o be u(12). Let i(d) be the first derivative of 1/5*d**5 + 1/2*d**4 + o*d + 0*d**2 - 2 - d**3. Factor i(k).
k**2*(k - 1)*(k + 3)
Factor 5 + 8*a**3 + 20*a**3 + 43 + 1361*a - 132*a**2 - 1233*a.
4*(a - 3)*(a - 2)*(7*a + 2)
Let c(k) = 2*k**5 - 27*k**4 + 114*k**3 - 125*k**2 + 41*k. Let b(f) = 2*f**5 - 27*f**4 + 113*f**3 - 124*f**2 + 40*f. Let v(s) = 5*b(s) - 4*c(s). Factor v(z).
z*(z - 6)**2*(z - 1)*(2*z - 1)
Let g(q) be the third derivative of 0*q + 29*q**2 - 1/40*q**5 + 0 - 1/2*q**3 + 3/16*q**4. Solve g(f) = 0 for f.
1, 2
Let s(c) be the first derivative of 5*c**4/4 - 5*c**3 - 70*c**2 + 229. Factor s(w).
5*w*(w - 7)*(w + 4)
Let o(x) be the second derivative of -x**6/420 + x**5/42 - x**4/21 + 10*x**2 - 9*x. Let q(b) be the first derivative of o(b). Factor q(y).
-2*y*(y - 4)*(y - 1)/7
Let r(v) be the second derivative of 7/20*v**5 - 1/30*v**6 - 1/2*v**4 + 8*v + 0*v**3 + 0 + 0*v**2. Factor r(z).
-z**2*(z - 6)*(z - 1)
Let i(o) be the third derivative of o**8/56 - o**7/15 + 2*o**5/15 + 15*o**2 + o. Find j, given that i(j) = 0.
-2/3, 0, 1, 2
Let g be (1 + 60)/(14/56). Let m = g - 485/2. Factor 0 - 3/4*q**2 - m*q**3 - 3/4*q**4 + 0*q.
-3*q**2*(q + 1)**2/4
Let r(t) be the first derivative of 0*t**2 - 3/16*t**4 + 18 + 1/8*t**3 + 0*t + 3/40*t**5. Factor r(u).
3*u**2*(u - 1)**2/8
Let a(k) = k