*2 - 11*c + 0 - 3/40*c**5 + 1/4*c**3 - 1/8*c**4. Factor r(g).
-3*(g - 1)*(g + 1)**2/2
Let u be 20/(33/((-99)/(-6))) + 5/((-120)/207). Find c, given that 1/8*c**5 + 8 - 4*c - 11/2*c**2 + 5*c**3 - u*c**4 = 0.
-1, 2, 4
Suppose 0 = -2*u - 56 + 32. Let o = u - -20. Suppose -20*s + 70*s**3 - o*s**2 - 50*s**3 + 0 + 8 = 0. What is s?
-1, 2/5, 1
Suppose -4*k = 23 - 47. Suppose 9*i**5 - 3*i**4 + 51 + 36*i**2 - k*i**2 + 36*i - 45*i**3 - 75 - 3*i**4 = 0. Calculate i.
-2, -1, 2/3, 1, 2
Let i(x) = -24*x + 26. Let g be i(1). Factor -54*m**2 + 77*m - m**3 - 23*m**g + 39 + 114*m**2.
-(m - 39)*(m + 1)**2
Let c(y) = -y**4 - 425*y**3 + 47958*y**2 - 47524*y. Let j(d) = -9*d**4 - 3394*d**3 + 383663*d**2 - 380192*d. Let u(l) = -51*c(l) + 6*j(l). Solve u(o) = 0 for o.
0, 1, 218
Let d(u) be the third derivative of 0*u + 8/27*u**3 + 0 - 1/135*u**6 + 5/54*u**5 - 19/54*u**4 + 5*u**2. Factor d(q).
-2*(q - 4)*(q - 2)*(4*q - 1)/9
Let r(j) = -8*j**2 - 680*j - 3372. Let c(k) = 7*k**2 + 679*k + 3349. Let w(x) = 4*c(x) + 3*r(x). Factor w(u).
4*(u + 5)*(u + 164)
Let h(a) = -a**2 - 10*a - 18. Let x be h(-3). Let -x*t**5 - 6*t**5 + 51*t - 93*t - 12*t**4 + 48*t**2 + 54*t + 33*t**3 = 0. Calculate t.
-2, -1, -1/3, 0, 2
Let m = -775697/9 - -86191. Factor -4 - m*w - 2/9*w**2.
-2*(w + 2)*(w + 9)/9
Let r(v) be the first derivative of -v**6/48 - v**5/20 + v**4/4 + 2*v**3/3 - v**2 - 4*v + 2385. What is d in r(d) = 0?
-2, 2
Let u(i) be the second derivative of i**5/5 - 23*i**4/3 + 254*i**3/3 - 210*i**2 - 28*i + 30. What is f in u(f) = 0?
1, 7, 15
Let v(k) be the second derivative of 32/3*k**2 + k**4 - 16/3*k**3 - 1/15*k**5 + 0 + 229*k. Find n, given that v(n) = 0.
1, 4
Let r(i) = 2*i**2 + 6*i + 13. Let y be r(-3). Suppose 0 = 3*v + y - 13. Factor u**3 + 1 - 267*u - u**2 + 266*u + v.
(u - 1)**2*(u + 1)
Let g = -933323 - -2799974/3. Let g*c**5 - 10/3*c**3 - 1/3 + 5/3*c + 2/3*c**2 - 1/3*c**4 = 0. Calculate c.
-1, 1/5, 1
Let v = 3620 - 3616. Let z(y) be the second derivative of 0 + y + 0*y**2 + 5/3*y**v - 1/4*y**5 - 10/3*y**3. Factor z(i).
-5*i*(i - 2)**2
Let r(z) = 3*z**3 - 4*z**2 + 14. Let u be r(-6). Let p = 780 + u. Factor -5/2*s**p - 1/2*s**3 + 9/2 - 3/2*s.
-(s - 1)*(s + 3)**2/2
Let i(q) = q**4 - 124*q**3 + 366*q**2 - 361*q + 121. Let g(n) = -n. Let y(v) = 15*g(v) + 5*i(v). What is f in y(f) = 0?
1, 121
Find g, given that 1/4*g**2 + 5/4 - 3/2*g = 0.
1, 5
Let h(u) = -u**2 - 25*u - 75. Let l be h(-21). Factor -16 + 55 + l*d - 27 + 3*d**2 + 6*d.
3*(d + 1)*(d + 4)
Let r be 27/1512*903 + -16. Factor 0*p - r*p**4 - 1/4*p**3 + 0*p**2 + 0.
-p**3*(p + 2)/8
Let d(c) = c**2 - c - 2. Let j(p) = p**3 + 3*p**2 + 10*p + 8. Let u be (-2)/((-7)/(-2) - 4). Let r(f) = u*d(f) + 2*j(f). Factor r(o).
2*(o + 1)*(o + 2)**2
Let r(m) be the third derivative of -3/100*m**5 + 0*m**3 + 0*m + 1/100*m**6 + m**2 + 0*m**4 + 1/350*m**7 + 58. Suppose r(t) = 0. What is t?
-3, 0, 1
Suppose -i + 11 + 5 = 0. Suppose 2*v + 4*h = 16, -v + 1 + i = 5*h. Let 4*n - v*n**2 + n**2 + 2*n**2 + 4 + 0*n**2 = 0. What is n?
-2
Let f = 525125/4 - 131279. Suppose -45/4*q - 21/4*q**2 + 3/4*q**4 + f*q**3 + 27/2 = 0. Calculate q.
-3, 1, 2
Let h(m) be the second derivative of -88/3*m**3 + 28*m**2 + 7/10*m**5 + 0 - 37/6*m**4 + 171*m. Determine f, given that h(f) = 0.
-2, 2/7, 7
Factor -24*p**2 + 2/5*p**3 + 156 - 662/5*p.
2*(p - 65)*(p - 1)*(p + 6)/5
Let i(z) = z**3 + 24*z**2 - z. Let l(u) = u**3 + 3615*u**2 - 1375933*u + 179329413. Let o(k) = -4*i(k) + l(k). Factor o(x).
-3*(x - 391)**3
Let r = 54/5 + -7187/665. Let j = r - -135/266. What is z in -1/2*z**3 - 1/8*z**5 + j*z**4 + 0*z + 0 + 0*z**2 = 0?
0, 2
Suppose -45*w + 348 = 42*w. Let d(f) be the second derivative of -1/3*f**w + 6*f**2 - 8*f - 4/3*f**3 + 0. Factor d(m).
-4*(m - 1)*(m + 3)
Let r(h) be the third derivative of -h**6/960 - h**5/10 - 3*h**4 - 632*h**2. Find t, given that r(t) = 0.
-24, 0
What is l in 88869*l**2 + 36 + 740702*l + 11584*l**2 - 96721*l**3 - 744470*l = 0?
6/311, 1
Factor 48*y + 1150*y**3 - 100 + 168*y**4 - 1791*y**3 + 451*y**2 + 5*y**5 + 69*y**4.
(y - 1)**3*(y + 50)*(5*y + 2)
Let d be 36/15*((-320)/(-15) - 8). Factor -d*l**4 + 54*l**5 - 50*l**5 - 28*l**3 + 76*l**3.
4*l**3*(l - 6)*(l - 2)
Let d(n) = -n**3 - n**2 + 2*n - 3. Let y be d(0). Let g = y - -5. Factor -5*k**2 - 2904 + 3*k**g + 2906.
-2*(k - 1)*(k + 1)
Let w = -260 - -319. Let -23*u - 16*u + w*u + 43 + 17 - 5*u**2 = 0. Calculate u.
-2, 6
Suppose -19*f = -509 - 99. Suppose -15*d = d - f. Factor 19*v**2 + 3/2 - 12*v**3 - 10*v - 1/2*v**4 + d*v**5.
(v - 1)**3*(v + 3)*(4*v - 1)/2
Suppose -g = -4*r - 2, 0 = -g - 3*r + 5*r. Let z be (-1)/((-19)/g - 10). Determine y so that 0*y + 9/2*y**z + 3/4*y**3 - 24 = 0.
-4, 2
Let r(y) be the first derivative of -y**3/15 - 657*y**2/10 + 1318*y/5 + 4036. Factor r(b).
-(b - 2)*(b + 659)/5
What is y in 10*y**2 - 538 + 414*y - 5*y**2 - 2*y**2 + 121 = 0?
-139, 1
Suppose -315*b - 8 = -307*b. Let k(v) = v**3 + v**2 - v + 2. Let s(n) = -3*n**4 - 7*n**3 - 7*n**2 - 5*n + 4. Let j(w) = b*s(w) + 2*k(w). Factor j(a).
3*a*(a + 1)**3
Let l = 3780 + -3776. Factor -5/3*h**5 + 0 + 0*h + 5*h**l - 10/3*h**3 + 0*h**2.
-5*h**3*(h - 2)*(h - 1)/3
Let q be 3/15 + (-288)/90. Let z(a) = 13*a**4 - 8*a**3 - 13*a**2 + a - 7. Let j(y) = -6*y**4 + 3*y**3 + 6*y**2 + 3. Let r(c) = q*z(c) - 7*j(c). Factor r(x).
3*x*(x - 1)*(x + 1)**2
Let p be (2/(-12)*6)/((-10)/8 - -1). Let o(u) be the second derivative of 1/120*u**p + 0*u**2 + 0 + 19*u + 1/200*u**5 + 0*u**3. Solve o(k) = 0.
-1, 0
Let z(m) be the third derivative of -2*m**7/315 + 2*m**6/15 - 6*m**5/5 + 6*m**4 - 18*m**3 - 9*m**2 - 7*m. Solve z(c) = 0.
3
Let h be 7/(-9) + (-14)/63. Let m be (-4)/(-8) + h/2. Factor 9 - 7*q + 4*q**2 + m*q**2 - q - 4*q.
(2*q - 3)**2
Let u(m) be the first derivative of 4*m**5/5 + 27*m**4 - 1576*m**3/3 + 1896*m**2 + 5472*m - 1564. Factor u(f).
4*(f - 6)**2*(f + 1)*(f + 38)
Let o(t) be the second derivative of 7/78*t**4 - 41*t + 2/13*t**2 + 0 + 3/13*t**3. Factor o(q).
2*(q + 1)*(7*q + 2)/13
Let i(m) = -88*m**3 - 28*m**2 - 637*m + 620. Let o(l) = 25*l**3 + 9*l**2 + 212*l - 208. Let d(t) = -4*i(t) - 14*o(t). Factor d(x).
2*(x - 18)*(x - 1)*(x + 12)
Let t(f) = -17*f - 289. Let o be t(-17). Let i(d) be the first derivative of 1/4*d**4 + 8 - 1/3*d**3 - 1/15*d**5 + 1/6*d**2 + o*d. Solve i(j) = 0 for j.
0, 1
Let p(l) = 48*l - 528. Let g be p(11). Let o(c) be the second derivative of g*c**2 + 5/48*c**4 + 1/12*c**3 + 3*c + 0 + 3/80*c**5. Factor o(v).
v*(v + 1)*(3*v + 2)/4
Let z(b) be the second derivative of -19/2*b**2 + 4/15*b**3 + 5/6*b**4 + 23/75*b**5 + 41*b + 0. Let n(g) be the first derivative of z(g). Factor n(v).
4*(v + 1)*(23*v + 2)/5
Suppose 3*u - 251 = 5*x, 0 = 5*x - 10*u + 12*u + 241. Let v be (1/119*4)/((-14)/x). Factor 2/17*a**2 + v*a**3 + 0 - 4/17*a.
2*a*(a - 1)*(a + 2)/17
Let a = -47253 + 47255. Solve 0 + 2/7*o - 2/7*o**a = 0 for o.
0, 1
Find a such that -2/3*a**3 + 20/3*a**2 + 0 - 14*a = 0.
0, 3, 7
Solve 1/9*v**3 + 0*v - 5/9*v**2 + 5/9*v**4 + 0 - 1/9*v**5 = 0.
-1, 0, 1, 5
Let x(a) be the first derivative of 22*a**3 - 35*a**2 + 4*a + 962. Suppose x(m) = 0. Calculate m.
2/33, 1
Find p such that -56*p**2 + 24/5*p**4 + 108/5*p**3 + 30*p - 2/5*p**5 + 0 = 0.
-5, 0, 1, 15
Suppose 21*g + 3 = 20*g - 4*x, 10 = 4*g + 5*x. Let p(n) be the second derivative of -5/6*n**4 - 13/3*n**3 + 0 - 7*n**2 + 1/10*n**g - 46*n. Factor p(a).
2*(a - 7)*(a + 1)**2
Let n be 21/((-15)/((-20)/(-4))) + 10. Let s(f) be the second derivative of 0*f**2 + 1/12*f**6 + 0 + 8*f - 35/24*f**4 - 5/2*f**n + 0*f**5. Factor s(x).
5*x*(x - 3)*(x + 1)*(x + 2)/2
Let c(j) be the second derivative of j**7/5040 + 11*j**6/1440 + j**5/24 + 11*j**4/12 + j**2 - 216*j. Let m(b) be the third derivative of c(b). Factor m(r).
(r + 1)*(r + 10)/2
Let s = 686726 + -686726. Let o = 166/5 + -398/15. Find g such that -o*g**2 + s - 8*g - 4/3*g**3 = 0.
-3, -2, 0
Solve -288/7 - 2/7*j**2 - 48/7*j = 0 for j.
-12
Let i(f) = -f**2 + 281*f - 5439. Let h(n) = -2*n**2 + 492*n - 9520. Let d(q) = 9*h(q) - 16*i(q). Factor d(v).
-2*(v - 14)*(v + 48)
Let y(m) be the third derivative of -m**5/510 - 125*m**4/51 - 62500*m**3/51 + 177*m**2 + 3. Let y(v) = 0. Calculate v.
-250
Let m(t) be the second derivative of 1/48*t**3 - 1/16*t**4 + 3 + 1/40*t**6 + 0*t**2 + 1/40*t**5 + 10*t - 5/336*t**7. Solve m(u) = 0.
-1, 0, 1/5