. Factor 12/7 + p*z**2 - 36/7*z.
3*(z - 2)*(5*z - 2)/7
Let b(p) be the third derivative of p**6/120 - 49*p**5/40 - 25*p**4/4 - 49*p**3/6 + p**2 + 205*p. Let m(d) be the first derivative of b(d). Factor m(u).
3*(u - 50)*(u + 1)
Let z(x) be the second derivative of x**5/200 + 731*x**4/120 + 5*x + 953. Factor z(h).
h**2*(h + 731)/10
Let q = 8916/9977 - -14/907. Solve -q - 12/11*a - 2/11*a**2 = 0 for a.
-5, -1
Let u = -776 - -778. Factor 108*r**2 + 73*r + 58*r + 17*r**u - 10*r**3 + 86*r - 140 + 3*r.
-5*(r - 14)*(r + 2)*(2*r - 1)
Let j(r) be the third derivative of r**7/42 - 5*r**6/6 + 65*r**5/6 - 125*r**4/2 + 315*r**3/2 - 3440*r**2. Find g, given that j(g) = 0.
1, 3, 7, 9
Let i(z) be the first derivative of z**5/5 - 25*z**4/4 - 37*z**3 - 143*z**2/2 - 58*z - 1861. Factor i(g).
(g - 29)*(g + 1)**2*(g + 2)
Factor 101/2*f - 329 - 1/2*f**2.
-(f - 94)*(f - 7)/2
Let g(p) be the third derivative of 1/48*p**4 - 1/240*p**5 - 1/192*p**8 - p**2 - 1/32*p**6 + 0*p**3 - 8 - 19/840*p**7 + 0*p. Factor g(z).
-z*(z + 1)**3*(7*z - 2)/4
Let g(y) be the third derivative of -y**8/336 - 11*y**7/210 + 13*y**6/120 + 11*y**5/60 - y**4/2 + 3*y**2 + 38. Solve g(x) = 0 for x.
-12, -1, 0, 1
Let k(m) = 980*m**2 + 343*m + 23. Suppose -2*n = -96 + 84. Let u(z) = -490*z**2 - 171*z - 11. Let p(t) = n*k(t) + 14*u(t). Determine s so that p(s) = 0.
-2/7, -2/35
Let d(a) be the third derivative of 2*a**7/735 - a**6/210 - 2*a**5/15 + 4*a**4/7 + 2*a**2 - 611*a. Solve d(b) = 0.
-4, 0, 2, 3
Let z(c) be the first derivative of -45*c**6/2 + 135*c**5 + 6795*c**4/4 - 235*c**3/3 - 1100*c**2 + 500*c - 466. Determine j, given that z(j) = 0.
-5, -2/3, 1/3, 10
Let c(y) be the second derivative of y**5/4 + 1835*y**4/4 + 673445*y**3/2 + 247154315*y**2/2 + y + 364. Factor c(j).
5*(j + 367)**3
Let j(p) be the third derivative of -1/20*p**5 + 3*p**2 + 7/480*p**6 - 1/24*p**4 + 0*p**3 + 0*p + 1. Factor j(v).
v*(v - 2)*(7*v + 2)/4
Let m(x) be the first derivative of x**4/32 - 17*x**3/8 + 157*x**2/8 - 33*x + 7351. Factor m(q).
(q - 44)*(q - 6)*(q - 1)/8
Let j(m) = 6*m**4 - 301*m**3 + 3443*m**2 - 39*m - 13. Let n(k) = -3*k**4 + 150*k**3 - 1722*k**2 + 18*k + 6. Let l(b) = -6*j(b) - 13*n(b). Solve l(o) = 0.
0, 24
Let v(j) = -j**3 - 6*j**2 - 9*j + 2. Let x be v(-2). Factor -x*l**2 + 3*l - 14*l + l**3 + 14*l.
l*(l - 3)*(l - 1)
Suppose -22*g + 13*g + 396 = 0. Factor 10*x**5 + 10*x - 22*x**5 - 20*x**5 - 10*x**2 + 80*x**4 - g*x**3 + 2 - 6*x**3.
-2*(x - 1)**3*(4*x + 1)**2
Let r = -1003 + 1009. Let x(g) be the first derivative of 12/5*g**4 - 49/15*g**r - 42/25*g**5 + 0*g**2 + 0*g - 15 - 8/15*g**3. Determine b, given that x(b) = 0.
-1, 0, 2/7
Let c = -4 + 6. Let a be 16/(-14) - -1 - (-3216)/168. Factor 26*w**c - 7 + a*w + 27 - 21*w**2 + w.
5*(w + 2)**2
Let a = -29625 + 29628. Let i(x) be the second derivative of -1/8*x**5 + 11/12*x**a + 0 + 3/2*x**2 - 42*x - 1/2*x**4. Suppose i(b) = 0. Calculate b.
-3, -2/5, 1
Let y = 36/71 - 1801/3692. Let v(z) be the third derivative of 3*z**2 + 0*z + y*z**4 + 0 + 0*z**3 - 1/390*z**5. Find u, given that v(u) = 0.
0, 3
Let f = -9753 + 78051/8. Determine d so that 17/4*d**3 - 27/4 + 1/8*d**5 + 9/2*d**2 + 5/4*d**4 - f*d = 0.
-3, -2, 1
Suppose -19 - 10 = 2*o + 5*a, 0 = -5*o + 2*a + 29. Let b(f) be the first derivative of 4/5*f**2 + 25 + 0*f + 1/10*f**4 + 8/15*f**o. Factor b(i).
2*i*(i + 2)**2/5
Factor 141/5*j + 71/5 - 2/5*j**2.
-(j - 71)*(2*j + 1)/5
Let z(d) be the third derivative of d**7/105 - d**6/30 + d**4/6 - d**3/3 + 4033*d**2. Factor z(r).
2*(r - 1)**3*(r + 1)
Let 316969/2 + 1/8*m**2 - 563/2*m = 0. Calculate m.
1126
Let v(q) = 3*q**3 - 2*q**2 - 4*q - 3. Let j be v(3). Let 63 - 3*u**2 - 164 + 15*u + j + 71 = 0. Calculate u.
-1, 6
Let x(h) be the first derivative of h**6/3 + 11*h**5/5 + 4*h**4 - 2*h**3/3 - 9*h**2 - 9*h + 1096. Suppose x(d) = 0. Calculate d.
-3, -3/2, -1, 1
Factor -16/3*q**3 - 3136/15*q - 336/5*q**2 + 10976/15 - 2/15*q**4.
-2*(q - 2)*(q + 14)**3/15
Let u(d) be the first derivative of -d**5/50 + 81*d**4/10 - 12959*d**3/15 - 13203*d**2/5 - 26569*d/10 + 3650. What is l in u(l) = 0?
-1, 163
Let w(v) be the second derivative of v**6/60 + 31*v**5/80 + 13*v**4/48 - 31*v**3/24 - 15*v**2/8 + 1543*v. Solve w(i) = 0.
-15, -1, -1/2, 1
Let l(v) be the third derivative of v**6/72 + 8*v**5/3 + 640*v**4/3 - 67*v**3/3 - 51*v**2. Let h(j) be the first derivative of l(j). Factor h(r).
5*(r + 32)**2
Let a = -68 - -81. Determine v so that 25*v + 0 - a - 7 - 5*v**2 = 0.
1, 4
Let r(c) be the second derivative of 12 - 20*c**2 - 28/5*c**6 + 38*c**3 - 116/3*c**4 + 106/5*c**5 + 10/21*c**7 + 3*c. Factor r(w).
4*(w - 5)*(w - 1)**3*(5*w - 2)
What is f in -372*f**2 - 214 + 1055*f - 317*f + 82 - 212 - 24 + 2*f**3 = 0?
1, 184
Let w(h) be the first derivative of h**3/7 + 117*h**2/7 + 3975*h/7 - 7389. Let w(z) = 0. Calculate z.
-53, -25
Let z(p) be the third derivative of -p**5/60 + p**4/2 + 271*p**3/6 + 227*p**2. Let s be z(23). Factor s*k**3 + 3/2*k**5 + 9*k**4 + 0*k + 0 + 12*k**2.
3*k**2*(k + 2)**3/2
Let f(o) = 2*o**5 - 159*o**4 - 71*o**3 + 9*o**2 + 9*o + 27. Let v(q) = -q**3 - q**2 - q - 3. Let z(d) = 5*f(d) + 45*v(d). Determine p so that z(p) = 0.
-1/2, 0, 80
Factor 676*b - 29 - 1394*b + 666*b + 3*b**3 + b**3 - 19.
4*(b - 4)*(b + 1)*(b + 3)
Determine b so that 0*b + 2*b**2 + 16/5*b**4 + 0 + 26/5*b**3 = 0.
-1, -5/8, 0
Suppose -4*f + 0*f - 6523 = -5*a, a = f + 1305. Factor -74*b**2 - a*b + 26*b**2 - 40*b**3 + 1343*b + 4*b**4 + 44.
4*(b - 11)*(b - 1)*(b + 1)**2
Suppose 7*p - 7 = 7. Let k(m) = 3*m**2 - 2*m - 6. Let d be k(p). Determine x so that 1854 + 157*x**2 + 353*x + 2146 + 4*x**3 + 847*x - 37*x**d = 0.
-10
Let p(q) = 2*q**3 + 18*q**2 + 2*q + 9. Let w be p(-9). Let j(r) = -2*r**2 - 2*r + 34. Let m(b) = -8*b**2 - 9*b + 137. Let g(z) = w*j(z) + 2*m(z). Factor g(k).
2*(k - 4)*(k + 4)
Let p(s) = 8*s**2 + s. Let i be p(2). Suppose 0 = 5*h - 46 - i. Solve -17*m**4 - 225*m**3 - h*m - 3*m**4 + 48 + 73*m**3 - 196*m**2 = 0.
-6, -1, 2/5
Suppose -17*a + 6 = -23*a. Let t(m) = -6*m**3 + 9*m**2 + 27*m + 18. Let r(c) = -c**3 + 1. Let w(h) = a*t(h) + 3*r(h). Suppose w(i) = 0. Calculate i.
-1, 5
Let f(a) = a**2 + 7*a + 24. Let v(w) = w**2 - w + 22. Let k(l) = -5*f(l) + 10*v(l). Suppose k(j) = 0. Calculate j.
4, 5
Let k(p) be the second derivative of 3*p**5/20 + 139*p**4/2 + 277*p**3/2 + 156*p + 2. Let k(t) = 0. Calculate t.
-277, -1, 0
Let p be 18/(-8) + 3713/188. Let z(f) be the first derivative of p*f**2 - 17 + 0*f + 5/3*f**3. Factor z(i).
5*i*(i + 7)
Let u(k) be the third derivative of -k**8/8064 + k**7/672 + 5*k**6/144 + 74*k**5/15 + 3*k**2 - 6*k. Let t(q) be the third derivative of u(q). Factor t(l).
-5*(l - 5)*(l + 2)/2
Let o(y) = -3*y**3 - 6*y**2 - 3*y - 42. Let u(g) = 4*g**3 + 6*g**2 + 3*g + 50. Let z(v) = 7*o(v) + 6*u(v). Let z(n) = 0. What is n?
-1, 1, 2
Let g(c) be the third derivative of 5*c**9/756 + c**8/336 + 19*c**3/2 - 4*c**2 - 2*c. Let q(d) be the first derivative of g(d). Let q(p) = 0. Calculate p.
-1/4, 0
Determine p, given that 0 + 5/2*p**2 - 715/2*p = 0.
0, 143
Let p(x) be the second derivative of -1/40*x**6 + 1/80*x**5 - 37*x - 1/168*x**7 - 2 + 1/2*x**3 + 1/2*x**2 + 11/48*x**4. Factor p(q).
-(q - 2)*(q + 1)**3*(q + 2)/4
Let d(f) = -f**2 + 2*f + 2. Let v(z) = -3*z**2 + 24*z + 4. Suppose -40 = 12*g - 100. Let o(b) = g*v(b) - 10*d(b). Factor o(q).
-5*q*(q - 20)
Let r be ((-4)/6)/(50/(-1800)). Suppose 29*q**2 - r + q**2 - 6*q**4 - 19*q**5 - 15*q**3 + 22*q**5 + 12*q = 0. Calculate q.
-2, -1, 1, 2
Factor -5122/9*f + 2*f**3 + 854/9 + 2558/3*f**2.
2*(f + 427)*(3*f - 1)**2/9
Let h be (-25 + 303/12)/((-2)/(-4 + 0)). Let t(f) be the second derivative of 48*f**3 - 7/4*f**4 - 54*f**2 + 0 - 33/10*f**5 + h*f**6 + 39*f. Factor t(w).
3*(w - 3)**2*(w + 2)*(5*w - 2)
Let q(j) = 11*j**2 - 262*j - 920. Let i(a) = 6*a**2 - 138*a - 460. Let r(s) = -7*i(s) + 4*q(s). Factor r(v).
2*(v - 46)*(v + 5)
Factor 75*r**3 + 457 + 3*r**4 + 483 + 207*r**2 + 201*r - 874.
3*(r + 1)**3*(r + 22)
Determine r so that 32/5*r + 2/5*r**4 - 32/5*r**3 - 6 + 28/5*r**2 = 0.
-1, 1, 15
Let n(a) = -a**2 - 7*a - 6. Let s be n(-5). Let x be -1 + 41 + -3*(s - 3). Let 37 - x + 3*t**5 - 2*t**3 + t**4 = 0. Calculate t.
-1, 0, 2/3
Let k(w) = -13*w**3 - 93*w**2 + 656*w + 768. Let n(p) = 5*p**3 + 31*p**2 - 218*p - 256. Let o(a) = 3*k(a) + 8*n(a). Fa