*3 + 12*b**2 - 12*b + 6. Let g(r) = r**3 - r**2 - r. Let j = 69 + -55. Let p be j/10 - 12/30. Let f(l) = p*c(l) + 2*g(l). Factor f(z).
-2*(z - 3)*(z - 1)**2
Let k(c) be the first derivative of -4/51*c**3 + 0*c + 18 + 0*c**2 - 8/85*c**5 - 1/51*c**6 - 5/34*c**4. Suppose k(l) = 0. Calculate l.
-2, -1, 0
Let t(d) be the third derivative of -d**7/210 + 29*d**6/60 - 14*d**5/15 - 29*d**4/12 + 19*d**3/2 - 4*d**2 + 51. Factor t(j).
-(j - 57)*(j - 1)**2*(j + 1)
Let l be 136/5 + 4 + (-21)/5. Let x = l - 17. Determine q so that 5*q**2 + 3 - 3*q - 18*q**2 + 3 + x*q**2 = 0.
-2, 1
Let m be (4/14)/(((-24453)/462)/(-247)). Factor -w - 1/3*w**2 + m.
-(w - 1)*(w + 4)/3
Let i = 247763/8 + -30970. Let l(k) be the second derivative of -1/16*k**4 + 1/4*k**3 - i*k**2 + 0 - 36*k. Factor l(m).
-3*(m - 1)**2/4
Let a = 181488/10835 + 108/2167. Let -24 + a*r - 3/5*r**5 - 93/5*r**3 + 6*r**4 + 78/5*r**2 = 0. What is r?
-1, 2, 5
Let r = -4527/2392 - -603/184. Factor r*v - 8/13 - 4/13*v**2.
-2*(v - 4)*(2*v - 1)/13
Let d = -236885/3 + 78962. Factor 0 + 0*l + 256/3*l**2 + 32/3*l**3 + d*l**4.
l**2*(l + 16)**2/3
Let j = 710 + -995. Let o = -854/3 - j. Factor o*b**3 + 0*b**2 - 2/3 - b.
(b - 2)*(b + 1)**2/3
Let b be (6/(-8) - -1)*28. Suppose -31 = -b*h - 3. Factor -12*l**3 - 2*l**3 - 6*l**4 - 6*l**4 - h*l**2 + 0*l**4.
-2*l**2*(2*l + 1)*(3*l + 2)
Let d = -247/15994 - 27725759/7757090. Let c = 1/97 - d. Let -12/5*w**3 - 27/5*w**2 - 3/5 - c*w = 0. What is w?
-1, -1/4
Let l(a) = -8*a + 52. Let q be l(7). Let n be q + -1 + 5 - -3. Factor -71*w - 50*w**2 - 11 - 5*w**n - 29 - 14*w.
-5*(w + 1)**2*(w + 8)
Let t(m) = 19*m**3 + 667*m**2 - 2428*m + 850. Let a(b) = 59*b**3 + 2000*b**2 - 7283*b + 2543. Let d(z) = -2*a(z) + 7*t(z). What is k in d(k) = 0?
-48, 2/5, 3
Suppose -21 = -2*q + 5*g, 2*g - 6*g - 9 = q. Suppose 3*z**4 - 250*z**3 - 186*z**3 - 15912*z + 124*z**q + 7803 + 8418*z**2 = 0. Calculate z.
1, 51
Factor 719 - 1122*w**3 + 406 + 3*w**4 - 1128*w**2 + 1707*w - 585*w.
3*(w - 375)*(w - 1)*(w + 1)**2
Let p be -15 + -1 - 4/8*-4. Let x = p + 23. Determine u, given that -19*u**2 - 15*u**5 - 64*u**4 - x*u**5 + 9*u**2 - 54*u**3 + 2 + 6*u = 0.
-1, -1/2, 1/3
Let r(x) = 2*x**3 + 72*x**2 - 77*x - 109. Let i be r(-37). Solve 8/3 - 2/3*c**i - 2*c = 0 for c.
-4, 1
Let p be (-153 - -152)*(-528)/110. Factor 2/5*f**3 - 6/5*f**2 + p - 8/5*f.
2*(f - 3)*(f - 2)*(f + 2)/5
Let f(i) be the first derivative of 1600*i**6/21 + 6976*i**5/7 - 998*i**4/7 - 5168*i**3/21 + 141*i**2/7 + 198*i/7 + 229. Determine x, given that f(x) = 0.
-11, -1/4, 3/10
Let f(o) = 5*o - 4. Let v be f(2). Suppose -v*g - 5 = -7*g. Find p such that 5*p**3 - 3*p**3 + 0*p**3 - g*p**3 + 6*p**2 = 0.
0, 2
Let v be -1 - ((-115)/30 + (6 - (-111)/(-18))). Let s(g) be the first derivative of -25 - 24/5*g - 26/5*g**2 - 1/5*g**4 - 32/15*g**v. Solve s(x) = 0.
-6, -1
Let n(k) = k - 17. Let d be n(19). Factor 2*l**4 + 12*l**3 + 20*l + 137*l**2 - 113*l**d + 1 + 5.
2*(l + 1)**3*(l + 3)
Let l(o) be the third derivative of 1/30*o**5 + 1/6*o**4 - 5*o**3 - 35*o**2 + 0*o + 0. Factor l(c).
2*(c - 3)*(c + 5)
Suppose -18522 + 252*l**2 + 2/7*l**4 - 16*l**3 + 0*l = 0. What is l?
-7, 21
Let t(r) be the third derivative of -r**7/840 - r**6/60 - 19*r**5/240 - r**4/8 + 8216*r**2. Solve t(q) = 0.
-4, -3, -1, 0
Factor -130810*b - 18 + 130795*b - b**4 + 15*b**3 + 21*b**2 - 2*b**4.
-3*(b - 6)*(b - 1)*(b + 1)**2
Let t be 2*(-63)/(6993/(-1258)). Find a, given that -t*a + 16 - 2*a**2 = 0.
-12, 2/3
Suppose 5*o - a - 2 = 0, -7*a = -4*o - 6*a. Determine u so that -6*u**o + 0 - 9*u - 3/4*u**3 = 0.
-6, -2, 0
Let h be 12*((-6625)/400)/(-53). Let i(y) be the first derivative of -5*y**3 - h*y**4 + 43 - y**5 + 0*y - 5/2*y**2. Solve i(q) = 0 for q.
-1, 0
Let x(t) be the second derivative of 4*t + 0 + 19/2*t**2 + 1/15*t**5 - 10/3*t**3 - 2/3*t**4. Let h(a) be the first derivative of x(a). Let h(g) = 0. What is g?
-1, 5
Let u(w) be the second derivative of -w**4/4 + 39*w**3/2 - 297*w**2 + 481*w. Determine j, given that u(j) = 0.
6, 33
Let a(i) be the third derivative of -4/9*i**4 + 2/315*i**7 - 144*i**2 + 0 - 2/15*i**5 + i + 0*i**6 - 2/3*i**3. Determine f so that a(f) = 0.
-1, 3
Let u(x) be the first derivative of -x**6/300 - x**5/150 + x**4/30 - 9*x**2/2 + 30. Let c(f) be the second derivative of u(f). Factor c(r).
-2*r*(r - 1)*(r + 2)/5
Suppose 2*d + 3*j = -d + 42, 4*j = d - 34. Suppose -s = 5*s - d. Factor -s*g**2 + 5*g**2 + 3*g**2 + 16*g - 6*g.
5*g*(g + 2)
Suppose -139*t + 70 = -274*t + 170*t. Find h, given that -4*h + 2/9*h**t + 0 = 0.
0, 18
Let z(s) = -s**3 - 6*s**2 - 2*s + 17. Suppose 5*i = 4*i - k, -2*k + 10 = 0. Let d be z(i). Factor 0 - x - 13/4*x**3 - 1/4*x**5 - 3/2*x**4 - 3*x**d.
-x*(x + 1)**2*(x + 2)**2/4
Solve 0 - 197/4*y**3 - y**5 + 509/2*y**2 + 66*y - 181/4*y**4 = 0 for y.
-44, -3, -1/4, 0, 2
Let z(b) be the third derivative of 35 + b**2 - 29/210*b**7 + 0*b**3 + 0*b + 0*b**4 + 1/30*b**5 - 1/120*b**6 + 1/12*b**8. Find l, given that z(l) = 0.
-1/4, 0, 2/7, 1
Let i(b) be the first derivative of 4*b**3/3 - 6*b**2 + 8*b - 589. Find m, given that i(m) = 0.
1, 2
Let z(b) be the second derivative of -2 + 1/4*b**4 + 50/3*b**2 + 32*b - 10/3*b**3. Factor z(l).
(3*l - 10)**2/3
Let t(j) be the second derivative of 7*j**5/10 - 16*j**4 + 203*j**3/3 + 66*j**2 - 1595*j. Solve t(v) = 0.
-2/7, 3, 11
Let j(c) = -19*c**5 + 87*c**4 + 222*c**3 + 132*c**2 + 6*c - 5. Let q(m) = m**5 - m**4 + 2*m**2 + 2*m + 1. Let u(i) = -j(i) - 5*q(i). Let u(v) = 0. What is v?
-1, -1/7, 0, 8
Let u = 9697 - 87272/9. Let c(l) be the first derivative of -u*l**3 - 19 - 1/3*l**2 + 0*l. Solve c(p) = 0 for p.
-2, 0
Factor -3*h**5 - 229906 - 47628*h + 229906 + 8316*h**2 - 66*h**4 + 393*h**3.
-3*h*(h - 7)**2*(h + 18)**2
Let g(k) be the second derivative of k**5/20 - 37*k**4/4 - 75*k**3/2 - 113*k**2/2 - 6366*k. Factor g(m).
(m - 113)*(m + 1)**2
Let x(a) be the first derivative of 3*a**4/16 - 131*a**3/4 + 195*a**2/4 + 223. Factor x(h).
3*h*(h - 130)*(h - 1)/4
Let f = 35 + 1. Factor 31*j**2 - f*j**3 - 24*j**3 - 12*j + 22*j**4 + 27*j**2 - 8*j**4.
2*j*(j - 3)*(j - 1)*(7*j - 2)
Let f(u) be the third derivative of -135/8*u**4 - 1/200*u**6 + 0 - 675/2*u**3 + u**2 - 2*u - 9/20*u**5. Factor f(d).
-3*(d + 15)**3/5
Factor -66/5*m - 2/5*m**3 + 72/5*m**2 - 28.
-2*(m - 35)*(m - 2)*(m + 1)/5
Let l = 753709 - 753706. Factor -2/5*h + 2/5*h**l + 0*h**2 + 0.
2*h*(h - 1)*(h + 1)/5
Let o(g) be the third derivative of g**6/990 + g**5/132 + g**4/66 - 13*g**3/2 - 71*g**2. Let q(u) be the first derivative of o(u). Factor q(f).
2*(f + 2)*(2*f + 1)/11
Let d(i) be the second derivative of -11*i**7/84 - 51*i**6/20 - 513*i**5/40 + 217*i**4/24 + 49*i**3 - 11007*i. Suppose d(j) = 0. What is j?
-7, -1, 0, 12/11
Let j(s) be the third derivative of -9*s**7/35 + 3357*s**6/20 - 3351*s**5/10 + 3349*s**4/12 - 124*s**3 - 5216*s**2. Suppose j(x) = 0. Calculate x.
1/3, 372
Factor 274*o**2 + 262*o**2 - 222*o**2 - 24649*o - o**3.
-o*(o - 157)**2
Let x be 2/(-9)*(2448/1700)/(6/(-20)). Let o(u) be the first derivative of -1/25*u**5 - 24 - x*u**3 + 0*u + 0*u**2 + 2/5*u**4. Factor o(p).
-p**2*(p - 4)**2/5
Solve 2017*k + 1956*k + 160 + 5*k**2 - 4138*k = 0 for k.
1, 32
Let w(c) = -c**3 + c**2 - 1. Let r(u) = -8*u**3 + 12*u**2 - 4*u - 4. Let h be (2/5)/(13/130). Suppose 12 = 2*t + 14. Let l(i) = h*w(i) + t*r(i). Factor l(v).
4*v*(v - 1)**2
Let s = 46952/70383 + -10/23461. Suppose 4/3*m**2 + 1/3*m**5 - s*m + 1/2*m**3 - 7/6*m**4 + 0 = 0. Calculate m.
-1, 0, 1/2, 2
Let y(n) = n**3 - n**2. Let p(q) = 8*q**2 + 16*q + 12. Let l(s) = 12*s + 21. Let c be l(-2). Let d(t) = c*y(t) - 3*p(t). Factor d(g).
-3*(g + 2)**2*(g + 3)
Let p be (16/6)/((-13)/((-819)/14)). Solve -18*x**3 + 131 - 131 - p*x - 32*x**2 - 2*x**3 = 0.
-1, -3/5, 0
Let y(v) be the second derivative of -v**5/8 + 65*v**4/24 - 235*v**3/12 + 175*v**2/4 + 519*v + 2. Find s such that y(s) = 0.
1, 5, 7
Suppose 57*p + 683 = 968. Let t(n) be the third derivative of 0*n + 0 + 1/30*n**6 - 8*n**2 + 0*n**3 - 1/3*n**4 - 1/15*n**p. Factor t(d).
4*d*(d - 2)*(d + 1)
Let l(o) be the first derivative of -14*o**3 - 10*o**2 + 0*o - 2/5*o**5 - 6*o**4 + 43. Factor l(v).
-2*v*(v + 1)**2*(v + 10)
Let i = 3449/6 + -1723/3. Let a be ((-1)/10)/(2/(-35)). Factor -a*s - i - 5/4*s**2.
-(s + 1)*(5*s + 2)/4
Let g(p) = 18*p**3 - 1857*p**2 - 90014*p - 