2
Let z(d) be the third derivative of -1/1344*d**8 + 0 + 0*d**4 - 34*d**2 + 0*d**3 - 1/168*d**7 - 1/80*d**5 + 0*d - 7/480*d**6. Let z(t) = 0. Calculate t.
-3, -1, 0
Let p(l) be the second derivative of -11*l**4/42 - 2*l**3/7 - 22*l. Factor p(h).
-2*h*(11*h + 6)/7
Suppose 4*d + y = -2*y + 223, -3*d = -4*y - 136. Let m be (-7)/(-4) - (-13)/d. Factor 0 - 1/4*n**m - 1/2*n.
-n*(n + 2)/4
Let c = -1651 - -1651. Suppose 0 + 0*h**4 + 2/5*h**3 + c*h**2 - 2/5*h**5 + 0*h = 0. What is h?
-1, 0, 1
Factor 2/11*k**3 + 18/11*k**2 - 42/11*k + 2.
2*(k - 1)**2*(k + 11)/11
Factor -260*k + 6*k**2 - 3*k**5 + 128*k + 135*k - 6*k**4.
-3*k*(k - 1)*(k + 1)**3
Let z(v) be the second derivative of -v**7/42 + 19*v**6/30 - 11*v**5/4 - 121*v**4/4 + 225*v - 1. Solve z(c) = 0 for c.
-3, 0, 11
Let a be -1 + 0/1 + 1. Suppose 12 = -4*y + 2*g, 154 = -4*y - 2*g + 166. Factor 2/5*q**3 + y + a*q - 2/5*q**2.
2*q**2*(q - 1)/5
Factor 0 - 768*n - 1/3*n**3 - 32*n**2.
-n*(n + 48)**2/3
Let p be 4*14 - (-12 - -13). Factor -3*k + k**2 - 13*k**2 + 3*k**4 + 9*k - 6*k**3 - 46 + p.
3*(k - 3)*(k - 1)*(k + 1)**2
Let t = 73/9 + -347/45. Find o such that -2/5*o**3 + 1/5 - 1/5*o**4 + 0*o**2 + t*o = 0.
-1, 1
Suppose 42*f - 3035 = -2783. Let -16*g + f*g**2 - 2/3*g**3 + 32/3 = 0. Calculate g.
1, 4
Solve 2258*h**4 - 2276*h**4 - 4*h**5 + h**5 - 6 - 42*h**3 - 48*h**2 - 27*h = 0 for h.
-2, -1
Let t(o) = -o + 7. Let a be t(-5). Let f = a + -9. Factor v**f + 1 - v - 1/4*v**4 - 3/4*v**2.
-(v - 2)**2*(v - 1)*(v + 1)/4
Let a be ((-5)/(140/(-8)))/(-31 - -32). Let -a*c**2 + 16/7*c - 32/7 = 0. What is c?
4
Let x(r) = 20*r**4 - 56*r**3 - 4*r**2 + 40*r. Let w(j) = 7*j**4 - 19*j**3 - j**2 + 13*j. Let c(s) = 8*w(s) - 3*x(s). Determine p so that c(p) = 0.
-1, 0, 1, 4
Let z(i) be the third derivative of i**7/630 + i**6/90 + i**5/60 - 52*i**2 + 2. Solve z(o) = 0 for o.
-3, -1, 0
Let t(j) = j + 1. Let y(w) = -9*w**2 + 12*w - 17. Let k(u) = 21*t(u) + 3*y(u). Factor k(z).
-3*(z - 1)*(9*z - 10)
Factor -2/3*k**2 - 2/3*k**3 - 2/9*k**4 + 0 - 2/9*k.
-2*k*(k + 1)**3/9
Solve -9*p - 6*p**2 + p + 11*p**3 - 15*p**3 + 32 - 14*p**2 = 0.
-4, -2, 1
Let l(d) = -7*d**3 - 8*d**2 + 295*d - 754. Let q(n) = n**3 + n**2 - 42*n + 108. Let y(g) = 4*l(g) + 30*q(g). What is s in y(s) = 0?
-7, 4
What is k in k**2 - k**4 - 1/2*k**5 + 0 + 1/2*k**3 + 0*k = 0?
-2, -1, 0, 1
Let 4 + 11*r**2 + 21 + 5 + 25*r - 6*r**2 = 0. Calculate r.
-3, -2
Determine a, given that -14/9*a**4 + 62/9*a**2 + 32/9*a**3 + 8/3 - 104/9*a = 0.
-2, 2/7, 1, 3
Let g(q) be the second derivative of -q**9/75600 - q**8/6720 - q**7/1575 - q**6/900 - q**4 - 3*q. Let p(f) be the third derivative of g(f). Factor p(m).
-m*(m + 1)*(m + 2)**2/5
Let u(o) be the first derivative of -o**7/525 + o**6/30 - 13*o**5/150 - o**4 - 12*o**3/5 + 10*o**2 - 21. Let l(x) be the second derivative of u(x). Factor l(q).
-2*(q - 6)**2*(q + 1)**2/5
Let d(l) be the first derivative of -5/6*l**6 + 7/4*l**4 + l**3 - 3/5*l**5 - l**2 + 0*l - 19. Suppose d(w) = 0. Calculate w.
-1, 0, 2/5, 1
Let g(d) be the third derivative of d**8/4032 - d**5/60 + 3*d**2. Let z(c) be the third derivative of g(c). Solve z(h) = 0 for h.
0
Factor -1/3*p**4 - 8/3*p**3 - 5/3 - 16/3*p - 6*p**2.
-(p + 1)**3*(p + 5)/3
Let y be 233/(-2 + 4 + -1). Let i = -231 + y. Determine m, given that -1/4*m**5 + 5/4*m**3 - 1/4*m**2 + 1/4*m**4 - 1 - i*m = 0.
-1, 2
Let s be ((-824)/(-1133))/(((-60)/33)/(-2)). Factor 2/5 - z - 1/5*z**3 + s*z**2.
-(z - 2)*(z - 1)**2/5
Let o be 70/104 - (8/(-13))/8. Factor -3/4*p**4 + o*p**5 + 0*p**3 + 0 + 0*p + 0*p**2.
3*p**4*(p - 1)/4
Determine h, given that 260*h**2 - 36*h + 50*h**3 - 9*h**4 + 64*h + 169*h + 4*h**4 + 83*h = 0.
-2, 0, 14
Let m be 1/8*53/((-159)/(-36)). Factor 1/2 + 2*w + m*w**2.
(w + 1)*(3*w + 1)/2
Let p(u) = -u**3 - 21*u**2 - 22*u - 35. Let q be p(-20). Solve -f + q*f**2 - f**2 + 9*f = 0.
-2, 0
Let u(c) be the third derivative of -c**9/453600 + c**8/10800 - 7*c**7/5400 + 7*c**5/30 - 32*c**2. Let y(q) be the third derivative of u(q). Factor y(j).
-2*j*(j - 7)**2/15
Let v(d) be the second derivative of -1/24*d**6 - 1/168*d**7 - 1/12*d**3 - 9/80*d**5 + 25*d + 0*d**2 + 0 - 7/48*d**4. Let v(z) = 0. What is z?
-2, -1, 0
Let 182*r - 825*r**2 - 817*r**2 + 1643*r**2 + 8281 = 0. Calculate r.
-91
Let m be (-4)/20 - (-244)/20 - -1. Suppose -m*p = -18 - 8. Factor 0*x**3 + 0*x + 0*x**p - 4/7*x**4 + 2/7*x**5 + 0.
2*x**4*(x - 2)/7
Let h(a) be the third derivative of a**8/13440 - a**7/1120 - a**6/120 - 9*a**5/10 - a**2 + 33. Let f(k) be the third derivative of h(k). Factor f(b).
3*(b - 4)*(b + 1)/2
Let a(m) be the first derivative of 11*m**4/8 - 35*m**3/4 + 9*m**2/2 - 38*m - 8. Let n(b) be the first derivative of a(b). What is c in n(c) = 0?
2/11, 3
Let 12/5*o**2 + 0 + 4*o**3 + 0*o - 4/5*o**5 + 4/5*o**4 = 0. Calculate o.
-1, 0, 3
Let j(f) be the third derivative of f**8/7560 + f**7/1890 + f**6/1620 + 7*f**3/3 - f**2. Let g(c) be the first derivative of j(c). Factor g(b).
2*b**2*(b + 1)**2/9
Let m = -321 + 332. Let u(s) be the second derivative of -1/70*s**5 + 0*s**2 + 1/21*s**3 + 0 - m*s - 1/105*s**6 + 1/42*s**4. Determine n so that u(n) = 0.
-1, 0, 1
Find g such that -92/5*g**3 - 4/5*g**5 - 12/5*g**2 - 36/5*g**4 + 144/5*g + 0 = 0.
-4, -3, 0, 1
Suppose 135/2*i**2 - 40 + 0*i + 15/4*i**4 - 125/4*i**3 = 0. What is i?
-2/3, 1, 4
Let t = -39 - -159/4. Let k = 95/4 - 47/2. Factor 1 - t*r**2 + 0*r + k*r**3.
(r - 2)**2*(r + 1)/4
Let m(r) be the third derivative of 1/12*r**3 + 0 - 1/240*r**5 + 8*r**2 + 0*r + 1/96*r**4. Suppose m(k) = 0. What is k?
-1, 2
Let s(i) be the first derivative of -4*i**5/5 + 14*i**4 - 64*i**3 + 36*i**2 + 324*i - 48. Factor s(x).
-4*(x - 9)*(x - 3)**2*(x + 1)
Factor -12*y**2 + 0*y + 650/9*y**3 + 2*y**5 + 0 - 328/3*y**4.
2*y**2*(y - 54)*(3*y - 1)**2/9
Let f(g) be the first derivative of -7*g**6/36 - 13*g**5/15 - 9*g**4/8 - 2*g**3/9 + g**2/3 - 622. Let f(d) = 0. Calculate d.
-2, -1, 0, 2/7
Let t = 138 + -133. Let i(u) be the second derivative of 0*u**2 + 1/5*u**6 + 0 - 1/2*u**4 - 5*u + 0*u**t - 1/14*u**7 + 1/2*u**3. Factor i(v).
-3*v*(v - 1)**3*(v + 1)
Suppose 3*c + 3 = 0, 4*m + 5*c - 17 + 2 = 0. Let k(x) be the first derivative of -4/27*x**3 + 2/9*x + 0*x**4 + 1 + 0*x**2 + 2/45*x**m. Factor k(o).
2*(o - 1)**2*(o + 1)**2/9
Let w be 0 - 2 - -9 - 45/18. Suppose -3*f**2 + w*f**3 + 0 + 0*f + 0*f**4 - 3/2*f**5 = 0. What is f?
-2, 0, 1
Let n(z) be the second derivative of -22*z + 0 - z**2 + 1/9*z**4 - 4/9*z**3 + 1/45*z**6 + 2/15*z**5. Factor n(b).
2*(b - 1)*(b + 1)**2*(b + 3)/3
Let u be (-12)/15*(0 + (-35)/294). Factor 4/21*s**2 + 0*s**3 + 0*s - 2/21*s**4 - u.
-2*(s - 1)**2*(s + 1)**2/21
Let y be (-12)/48*-20 + -1. Let o(l) be the first derivative of 0*l**5 + l**2 - l**y - 10 + 0*l**3 + 1/3*l**6 + 0*l. Factor o(i).
2*i*(i - 1)**2*(i + 1)**2
Let u be (-8)/(-10)*(-10 - -15). Factor -24*w**4 - 12*w**u + 11*w**4 + 10*w - 35*w**2 + 5*w**5 + 45*w**3.
5*w*(w - 2)*(w - 1)**3
Let q(w) = 99*w + 99. Let c(v) = v**2 - 99*v - 100. Let f(x) = 3*c(x) + 2*q(x). Solve f(b) = 0 for b.
-1, 34
Let u(r) be the second derivative of r**4/30 - 6*r**3 + 405*r**2 + 394*r. Factor u(j).
2*(j - 45)**2/5
Solve -34*d**2 + 41*d**2 - 57 - 10*d - 8*d**2 - 12*d = 0 for d.
-19, -3
Let p(w) be the second derivative of w**5/2 - 115*w**4/24 + 35*w**3/6 + 25*w**2/4 - 222*w. Solve p(a) = 0 for a.
-1/4, 1, 5
Let n(k) be the third derivative of k**7/210 + k**6/10 + 3*k**5/5 + 56*k**2. Factor n(o).
o**2*(o + 6)**2
Solve -205*w**3 - 53*w**4 - 179*w**4 + 111*w**4 + 105*w**5 - 4 + 45*w**2 + 20*w = 0 for w.
-1, -1/3, 1/5, 2/7, 2
Let m = 12833 - 12831. Factor 8/5*d - 1/5*d**m - 12/5.
-(d - 6)*(d - 2)/5
Let c(q) = -35*q**3 - 772*q**2 + 1013*q - 230. Let k(a) = -385*a**3 - 8490*a**2 + 11145*a - 2530. Let w(f) = -65*c(f) + 6*k(f). What is y in w(y) = 0?
-23, 2/7, 1
Let n = -2642 + 29064/11. Factor -4/11*g**3 + 0 + 0*g**2 + n*g + 2/11*g**5 + 0*g**4.
2*g*(g - 1)**2*(g + 1)**2/11
Let q(g) = 3*g**2 - 66*g - 1296. Let a(f) = -2*f**2 - 3*f. Let w(d) = 6*a(d) + 3*q(d). What is b in w(b) = 0?
-36
Suppose 5*r - 17 = 3. Factor -3*t + 2*t + 5*t**3 - 5*t**2 - 5*t - r*t.
5*t*(t - 2)*(t + 1)
Let m(t) be the first derivative of -196*t**3/3 - 56*t**2 - 16*t + 118. Factor m(y).
-4*(7*y + 2)**2
Suppose 5*v + 35 + 15 = 5*q, -5*q - 4*v = -32. Find r, given that -10 + 23 - q + 15*r + 10*