k) be the first derivative of k**4/4 + 25*k**3/3 + 69*k**2 + 216*k + 6858. Factor f(z).
(z + 3)*(z + 4)*(z + 18)
Factor 1/7*t**2 - 367/7 - 366/7*t.
(t - 367)*(t + 1)/7
Determine w so that -12425 + w**3 - 45*w**2 + 300*w + 12425 - 4*w**3 = 0.
-20, 0, 5
Let h(x) be the third derivative of -x**11/997920 + x**10/151200 - x**9/90720 - 13*x**5/20 - 6*x**2 + 2. Let o(u) be the third derivative of h(u). Factor o(i).
-i**3*(i - 2)*(i - 1)/3
Let i(w) be the first derivative of 2*w**5/25 + 4*w**4 + 154*w**3/15 + 38*w**2/5 - 6873. Suppose i(t) = 0. What is t?
-38, -1, 0
Suppose 8*z + 52 = 68. Factor q + q**2 - q**3 + z*q**3 + 3 - 7*q + q.
(q - 1)**2*(q + 3)
Let d(m) be the third derivative of -m**5/150 - 7*m**4/3 - 139*m**3/15 - 137*m**2 - 1. Factor d(t).
-2*(t + 1)*(t + 139)/5
Let t be ((-29464)/(-290))/(2/60). Let t*p**3 - 2742*p**5 - 947*p**2 + 251*p**2 + 48 - 3722*p**5 - 240*p + 3915*p**4 + 1133*p**5 - 744*p**5 = 0. What is p?
-2/5, 2/9, 1
Let n(t) = -10*t - 154. Let k be n(17). Let g = 324 + k. Determine c, given that 7/3*c**3 + 0*c + 2/3*c**2 + g = 0.
-2/7, 0
Let l(d) be the second derivative of -d**5/90 - 71*d**4/54 + 146*d**3/27 - 928*d. Factor l(z).
-2*z*(z - 2)*(z + 73)/9
Let o(g) be the first derivative of -g**7/14 - 6*g**6/5 - 36*g**5/5 - 20*g**4 - 24*g**3 - 136*g + 137. Let m(n) be the first derivative of o(n). Factor m(b).
-3*b*(b + 2)**3*(b + 6)
Factor 3*u**4 - 72*u**2 - 108*u**3 + 3382 + 129*u**2 - 806*u - 1195 + 753*u**2 - 1462*u.
3*(u - 27)*(u - 3)**3
Let g(s) be the third derivative of s**5/180 - 11*s**4/12 + 989*s**3/18 + 756*s**2. Find y, given that g(y) = 0.
23, 43
Let -152*q + 15*q - 160*q - 300 + 3*q**2 = 0. Calculate q.
-1, 100
Let -571162*b - 28*b**4 + 2*b**5 - 102*b**3 + 571162*b = 0. What is b?
-3, 0, 17
Let y be 7*483/196 - (-3 - -19). Determine d so that y*d**2 - 15 - 5/4*d**3 + 10*d = 0.
-3, 2
Let h(x) be the first derivative of 21*x**5/25 - 114*x**4/5 + 873*x**3/5 - 1518*x**2/5 - 1092*x/5 - 4323. Find k such that h(k) = 0.
-2/7, 2, 7, 13
Suppose -4*z + 113 = 3*r, -2*r + 64 = -4*z + 2. Let k(n) = n - 7. Let s be k(9). Factor -20*u + r*u - u**s - 13*u.
-u*(u - 2)
Suppose 5776*l**2 + 4*l**4 - 16 - 3154*l**3 + 16 + 2850*l**3 = 0. Calculate l.
0, 38
Let u(b) be the second derivative of 0*b**3 + 0 + 1/240*b**5 - 1/96*b**4 - 31/2*b**2 + 24*b. Let i(l) be the first derivative of u(l). Factor i(r).
r*(r - 1)/4
Let p(x) = x**2 - 103*x + 762. Let z be p(95). Solve -1/7*n**4 - 24/7*n**3 - 20/7*n**z + 0*n + 3/7*n**5 + 0 = 0 for n.
-2, -1, 0, 10/3
Factor 16/7 + 102/7*b**3 + 514/7*b**2 + 428/7*b.
2*(b + 1)*(b + 4)*(51*b + 2)/7
Suppose 31*i = -4*f + 48*i - 120, 0 = -3*f - 3*i + 36. Let 0 + 2*b**2 + 4/5*b**3 - 12/5*b - 2/5*b**f = 0. What is b?
-2, 0, 1, 3
Find o, given that -1089/2*o - 21*o**4 + 0 + 915/2*o**3 - 2442*o**2 = 0.
-3/14, 0, 11
Let w(f) be the second derivative of 6/5*f**5 - 26/3*f**3 - 26*f - 4/3*f**4 - 2 - 2/21*f**7 - 12*f**2 + 4/15*f**6. Factor w(z).
-4*(z - 3)*(z - 2)*(z + 1)**3
Let b(j) be the third derivative of 0 + 0*j**3 + 1/4*j**4 + 10*j + 1/160*j**6 - 9/80*j**5 + j**2. Factor b(k).
3*k*(k - 8)*(k - 1)/4
Let j be -30 + (-30 - (-21 - 42)). Factor 0 + 6/7*g + 8/7*g**2 + 2/7*g**j.
2*g*(g + 1)*(g + 3)/7
Let m = 4799/7023 + -39/2341. Determine u, given that m*u**2 - 5*u + 7/3 = 0.
1/2, 7
Let m(s) = 16*s - 3*s**2 + 538 + 0*s**2 + 2*s**2 - 518. Let l be m(17). Factor -5/4*c + 5/2 + 5/4*c**l - 5/2*c**2.
5*(c - 2)*(c - 1)*(c + 1)/4
Let m(p) = -16*p**3 + 22*p**2 - 46*p - 180. Let n(q) = 13*q**3 - 19*q**2 + 49*q + 182. Let i(y) = -5*m(y) - 6*n(y). Find s such that i(s) = 0.
-4, 6
Let p be (-222)/5400*-5 + (9 - 4433/495). Find n such that p*n**3 + n + n**2 + 0 = 0.
-2, 0
Let o = -48/107 - -2319/5885. Let r = 71/715 - o. Factor 0*h + 0*h**3 - r*h**2 + 0 + 2/13*h**4.
2*h**2*(h - 1)*(h + 1)/13
Let h be (-3236)/10*(-115)/(-92) + -1. Let u = h + 406. Factor 0 - u*m**2 + 2*m.
-m*(m - 4)/2
Let x(p) be the second derivative of p**4/42 - 51*p**3/7 - 10*p + 14. Find m such that x(m) = 0.
0, 153
Suppose -2945*u - 2946*u = -5901*u + 160. Let o(f) be the first derivative of 0*f + u*f**2 + 42 + 4/5*f**5 + 6*f**4 + 16*f**3. Factor o(r).
4*r*(r + 2)**3
Determine m, given that -100/3*m**3 - 30*m - 2/3*m**5 + 8*m**4 + 0 + 56*m**2 = 0.
0, 1, 3, 5
Let p(a) be the third derivative of -1/90*a**5 + 17*a**2 + 1/4*a**4 - 8/9*a**3 + 0 - 4*a. Suppose p(y) = 0. What is y?
1, 8
Suppose -4*r + f = 6*f + 32, 40 = -5*r + 2*f. Let p be ((-5 - -9)/(-4))/(2/r). Let -8*z**2 - 6*z**3 + 4*z**3 + 0*z**2 + 8*z**p - 2*z + 4*z**3 = 0. What is z?
-1, -1/4, 0, 1
Let n = 16 + -6. Suppose -2*s - n = -7*s, s = 5*m - 13. Let -3*d + 6 - 2*d + 0*d**2 - m*d**2 + 2*d**2 = 0. Calculate d.
-6, 1
Let f = -71 - -59. Let u be 9 - ((-6)/f + 4). Factor 0 - 15/2*c**4 + 21/2*c**3 - u*c**2 + 0*c + 3/2*c**5.
3*c**2*(c - 3)*(c - 1)**2/2
Let r(o) = 5*o + 12. Let g(t) = -4*t - 11. Let k(i) = -4*g(i) - 3*r(i). Let u be k(0). Find f, given that f**2 - u*f - 8 + 22 - 14 = 0.
0, 8
Suppose -4*o = -3*k - 49, -443*o = -444*o - 4*k - 40. Suppose -11/3 - o*v - 1/3*v**2 = 0. What is v?
-11, -1
Let k(h) be the first derivative of 2*h**5/35 - 7*h**4/2 - 880*h**3/21 - 912*h**2/7 - 2726. Factor k(w).
2*w*(w - 57)*(w + 4)**2/7
Let v be (-1)/15 + 159*(-18)/5670 - (-16 - -15). Let 3/7*i - 6/7 + v*i**2 = 0. Calculate i.
-2, 1
Let m(c) = -c**3 - 61*c**2 + 64*c + 128. Let v be m(-62). Suppose -y = i, -27*i + v*y = -29*i - 10. Factor 1/4*r**i + r**2 - r**4 + 1/2*r**3 - 3/4*r + 0.
r*(r - 3)*(r - 1)**2*(r + 1)/4
Let h = -175390 + 175394. Factor 0 + 8/7*q**3 + 4/7*q**5 + 0*q**2 + 12/7*q**h + 0*q.
4*q**3*(q + 1)*(q + 2)/7
Suppose 12 = 3*l, 13*x - 14*x + 5*l - 16 = 0. Suppose -3*z + 6 = x*o - 17, -4*z + 26 = 3*o. Factor -33/2*f - 3/2*f**4 + 9/2 + 3/2*f**z + 21*f**2 - 9*f**3.
3*(f - 1)**4*(f + 3)/2
Let v(o) = -2*o**2 + 155*o + 187. Let f(q) = q**2 - 78*q - 91. Let n(u) = 5*f(u) + 2*v(u). Factor n(a).
(a - 81)*(a + 1)
Let k(o) be the third derivative of o**7/1470 - 17*o**6/280 - o**5/420 + 17*o**4/56 + 3*o**2 - 7*o. Factor k(v).
v*(v - 51)*(v - 1)*(v + 1)/7
Let z(p) be the third derivative of p**6/280 + 27*p**5/14 + 801*p**4/56 + 7595*p**2 - p. Let z(y) = 0. Calculate y.
-267, -3, 0
Let t be (-1)/((-9)/27 + 0). Let x = 1698 - 1693. Find u such that 2/11*u**t - 2/11*u**x + 0 - 4/11*u**2 + 4/11*u**4 + 0*u = 0.
-1, 0, 1, 2
Suppose 0 = -5*n + 3*m - 26, -m - 59 = -4*n - 63. Factor -14/5*v**3 + 2/5*v**n + 0*v + 0.
-2*v**2*(7*v - 1)/5
Suppose 138*v - 137*v - 296*v = -265 - 620. Let 0*t + 0 + 2*t**2 + 1/2*t**v = 0. Calculate t.
-4, 0
Let h(f) = -960*f**3 - 4855*f**2 - 6865*f - 2950. Let r(o) = o**4 + o**3 - 2*o**2 + 4*o + 2. Let t(q) = -h(q) - 5*r(q). Find g, given that t(g) = 0.
-3, -1, 196
Let c(n) = -9*n + 65. Let y(k) = 18*k - 133. Let a(t) = -5*c(t) - 3*y(t). Let v be a(8). Factor 0*f**3 - 3/2*f + 9/4*f**v + 0 - 3/4*f**4.
-3*f*(f - 1)**2*(f + 2)/4
Let j(y) be the third derivative of 2*y**7/525 + 4*y**6/75 + 17*y**5/75 + y**4/3 - 2331*y**2. Find g such that j(g) = 0.
-5, -2, -1, 0
Let j(v) be the first derivative of -5*v**4/4 + 1340*v**3/3 - 1335*v**2/2 + 2135. Let j(c) = 0. Calculate c.
0, 1, 267
Let n(k) be the third derivative of 0*k**3 - 1/105*k**5 + k**2 + 72*k - 1/840*k**6 + 0 + 5/168*k**4. Factor n(x).
-x*(x - 1)*(x + 5)/7
Let j(t) be the third derivative of 125/6*t**3 - 3*t**2 + 7 - 25/2*t**4 + 3*t**5 + 0*t. Find k such that j(k) = 0.
5/6
Let j(g) be the first derivative of -482*g**3/3 - 2*g**2 + 3699. Factor j(p).
-2*p*(241*p + 2)
Solve -1/2 + 891/4*n**3 - 2241/4*n**2 + 3267/4*n**4 + 133/4*n = 0 for n.
-1, 1/33, 2/3
Let s(o) be the third derivative of o**8/14 + 38*o**7/105 + o**6/10 - 15*o**2 - 53*o. What is b in s(b) = 0?
-3, -1/6, 0
Let x be (-140)/(-210)*(-27)/(-2). Determine c so that -c**3 + 3 + 77*c - 69*c + 0*c**3 + 2*c**2 - 3*c**2 + x = 0.
-2, 3
Let j(a) = -60*a**2 + 2736*a + 9540. Let o(k) = -4*k**2 + 182*k + 636. Let t(g) = -3*j(g) + 44*o(g). Factor t(f).
4*(f - 53)*(f + 3)
Factor 8*d**2 + 0 - 84/5*d - 4/5*d**3.
-4*d*(d - 7)*(d - 3)/5
Let b(i) be the third derivative of -2/525*i**7 - 2/25*i**6 - 44*i**2 - 12/25*i**5 + 0*i**4 + 0 + 0*i**3 + 0*i. Factor b(l).
-4*l**2*(l + 6)**2/5
Let t = -365985 + 1463945/4. Find a such that 0 + t*a**4 - 5/4*a**2 - 3/4*a**3 - 1/4*a + a**5 = 0.
-1, -1/4, 0, 1
Let f(c) = -7*