 second derivative of -3*o**2 - 61/6*o**4 + 22/3*o**3 + 8/21*o**7 + 39/5*o**5 - q*o**6 + 0 - 48*o. Factor d(i).
2*(i - 3)*(i - 1)*(2*i - 1)**3
Let s(r) be the third derivative of 153*r**2 + 0*r + 1/10*r**5 - 61/8*r**4 + 61/40*r**6 + 0 - r**3. Factor s(z).
3*(z - 1)*(z + 1)*(61*z + 2)
Let m(d) be the third derivative of -156*d**2 + 0*d + 0 + 1/8*d**4 - 1/140*d**7 + 7/120*d**5 + 0*d**3 - 1/80*d**6 + 1/672*d**8. Let m(a) = 0. Calculate a.
-1, 0, 2, 3
Let u(k) be the first derivative of 5/6*k**6 + 10*k**4 + 0*k - 5*k**5 - 8 + 0*k**2 - 20/3*k**3. Determine x, given that u(x) = 0.
0, 1, 2
Factor -138/7*r - 178/7*r**2 - 38/7*r**3 + 2/7*r**4 + 0.
2*r*(r - 23)*(r + 1)*(r + 3)/7
Let d = -57862 - -173590/3. Suppose -2/9*k**2 - 16/9 + d*k = 0. What is k?
2, 4
Let w(p) be the first derivative of 7/3*p**3 - 27/2*p**2 + 22 + 15*p. Let y(v) = -v + 1. Let c(s) = 4*w(s) - 44*y(s). Let c(x) = 0. What is x?
2/7, 2
Suppose 6*o = 10*o - 72. Let g(r) = r**2 - 17*r - 3. Let p be g(o). Factor 4*c**4 + 9*c**3 + 13*c**2 + 5*c**2 + p*c**3 + 2*c**2.
4*c**2*(c + 1)*(c + 5)
Suppose -5*b + 35 = 3*a, 13 = 2*b - 2*a + 3*a. Solve 32*m**2 + 12*m**4 + 4*m + 4 + 2*m**5 + b*m + 28*m**3 + 10*m = 0.
-2, -1
Let w = -408 - -409. Suppose -6*a = -13 + w. Factor -1/6*l**a + 1/3*l - 1/6*l**3 + 0.
-l*(l - 1)*(l + 2)/6
Let x(r) be the first derivative of -2*r**5/5 - 21*r**4/2 - 90*r**3 - 243*r**2 + 721. Let x(d) = 0. What is d?
-9, -3, 0
Let a(d) be the second derivative of d**5/4 - 15*d**4/2 + 205*d**3/6 + 150*d**2 + 2139*d + 1. Determine s so that a(s) = 0.
-1, 4, 15
Let s be (0 - -11) + -12 + 1*3. Find n such that -10*n**s + 2*n**3 - 56*n**2 + 16*n + 80*n**2 - 32 = 0.
-4, 1
Factor 2 - 82/5*f - 32/5*f**3 + 176/5*f**2.
-2*(f - 5)*(4*f - 1)**2/5
Let u(x) = 3*x - 19. Suppose -36 = -5*q - 1. Let s be u(q). Find r, given that -4*r + r**5 - 10*r**4 + 10*r**s - r**5 + 5*r**5 - r = 0.
-1, 0, 1
Let n = 42/31 + 286/155. Let x = -2185 + 10941/5. Suppose n*i - x - 4/5*i**2 = 0. Calculate i.
2
Let x = 187373/281046 + -3/93682. Factor -8/21 - x*k**2 + 32/21*k.
-2*(k - 2)*(7*k - 2)/21
Let n be ((-37)/(-35))/(17/119) + -7. Determine u, given that 16/5*u**2 - 6/5*u - n - 32/5*u**4 + 24/5*u**3 = 0.
-1/2, -1/4, 1/2, 1
Factor -410/3*s**2 - 1/3 - 137*s.
-(s + 1)*(410*s + 1)/3
Suppose -3*j = -d - 3*d - 65581, -2*d + 43744 = 2*j. Factor -j*l**4 + 21*l + 21871*l**4 - 12*l**3 - 9*l - 4*l**2.
4*l*(l - 3)*(l - 1)*(l + 1)
Factor -32*q**2 - 232*q**2 + 8*q**3 + 496*q + 24 - 248 + 26*q**3 + 2*q**3.
4*(q - 2)*(3*q - 14)*(3*q - 2)
Let o(i) be the second derivative of -i**4/84 - 199*i**3/3 - 277207*i**2/2 + 4209*i. Solve o(h) = 0.
-1393
Factor 100 + 335*r - 6*r**3 - 10*r**3 + 175*r**2 + 21*r**3 + 131 - 66.
5*(r + 1)**2*(r + 33)
Suppose -a + 3*s - 48 = -35, 0 = 2*a + 5*s - 29. Let z(j) = -j**3 + 4*j**2 + 3*j - 2. Let o be z(3). Factor 30 + o*h + 2*h**a + 0*h - 16.
2*(h + 1)*(h + 7)
Let q(b) be the third derivative of -2 - 2/11*b**3 + 0*b + 11*b**2 + 1/330*b**5 + 1/132*b**4. Factor q(h).
2*(h - 2)*(h + 3)/11
Let i(x) be the second derivative of -13/45*x**5 - 20/9*x**2 + 0 - 75*x - 1/45*x**6 + 8/27*x**3 + 41/54*x**4. Find c, given that i(c) = 0.
-10, -2/3, 1
Let 0 + 64/3*m + 124/3*m**2 + 14/3*m**4 + 74/3*m**3 = 0. What is m?
-16/7, -2, -1, 0
Let g(q) be the third derivative of q**7/2940 - q**6/630 - q**5/140 - 53*q**3/6 - 39*q**2. Let u(n) be the first derivative of g(n). Factor u(m).
2*m*(m - 3)*(m + 1)/7
Let i = -34728 + 34733. Let r(f) be the third derivative of 0*f + 0 - 35/24*f**4 - 23*f**2 - i*f**3 + 1/4*f**5. Factor r(u).
5*(u - 3)*(3*u + 2)
Suppose 0 = 78*g - 81*g + 3. Factor g + 6*c**3 + 28 + 2*c**3 + 63*c + 33*c**2 + 2 - 7*c**3.
(c + 1)**2*(c + 31)
Let n(x) = -3*x**5 + x**3 - x - 6. Let b(f) = -23*f**5 + 19*f**4 - 81*f**3 + 73*f**2 + 80*f - 140. Let u(w) = -3*b(w) + 24*n(w). Suppose u(p) = 0. Calculate p.
-23, -1, 1, 2
Let t(c) = 4*c**3 - 80*c**2 + 160*c - 84. Let o(d) = d**2 - d. Let p be (7 - 8)*(-1)/(-3 - -2). Let v(z) = p*t(z) + 12*o(z). Solve v(a) = 0.
1, 21
Determine u so that -720*u**2 - 50*u**3 + 191*u**2 + u**4 + 206*u**2 + 218*u**2 + 50*u - 41 + 145 = 0.
-2, -1, 1, 52
Let c(d) be the second derivative of -d**6/105 + 3*d**5/10 - 45*d**4/14 + 81*d**3/7 - 52*d. Find l such that c(l) = 0.
0, 3, 9
Let w(m) be the third derivative of m**8/336 - m**7/210 - m**6/40 + m**5/12 - m**4/12 - 7953*m**2. Factor w(x).
x*(x - 1)**3*(x + 2)
Let d(a) be the third derivative of a**8/784 + 163*a**7/245 + 1293*a**6/280 + 403*a**5/35 + 23*a**4/2 + a**2 - 140*a - 10. Find m, given that d(m) = 0.
-322, -2, -1, 0
Suppose -3*l + 2*u + 943 = -2*u, 0 = 3*u + 12. Let g be 17/24 + l/(-824). Solve 27 + g*i**2 - 6*i = 0.
9
Let k = -26430 - -185014/7. Find p such that -44/7*p**3 + 0 + 144/7*p + 96/7*p**2 + k*p**4 = 0.
-1, 0, 6
Let h = 12/27211 - -435292/190477. Determine c so that 2/7*c**2 - h*c + 32/7 = 0.
4
Let j(b) be the first derivative of -7*b**6/20 + 167*b**5/25 - 107*b**4/5 + 141*b**3/5 - 71*b**2/4 + 26*b/5 + 4748. Suppose j(o) = 0. Calculate o.
1/3, 4/7, 1, 13
Let q(l) be the second derivative of -l**5/300 - l**4/12 + 64*l**2 + 74*l. Let o(r) be the first derivative of q(r). Find j, given that o(j) = 0.
-10, 0
Let r(q) be the second derivative of q**7/56 + 457*q**6/40 + 210657*q**5/80 + 3718375*q**4/16 + 1755677*q**3 + 10328853*q**2/2 - 744*q. Factor r(m).
3*(m + 2)**2*(m + 151)**3/4
Let s(a) be the first derivative of 2*a**3/3 - 58*a**2 + 224*a + 1187. Factor s(j).
2*(j - 56)*(j - 2)
Let t(z) be the third derivative of 121*z**6/120 - 1727*z**5/60 + 217*z**4 + 1176*z**3 + 914*z**2. Solve t(w) = 0 for w.
-1, 84/11
Suppose 6166 = -9*r + 6202. Factor 1/2*y**3 - 1/2*y**5 - 1/2*y**2 + 0 + 1/2*y**r + 0*y.
-y**2*(y - 1)**2*(y + 1)/2
Suppose -90*g - 44*g + g - 43*g = 0. Let r(j) be the third derivative of -2*j**2 + 0 + 1/60*j**5 + g*j - 5/96*j**4 + 0*j**3 + 1/480*j**6. Factor r(c).
c*(c - 1)*(c + 5)/4
Let c(z) = z**3 + z**2. Let u(q) be the first derivative of q**4/2 - 16*q**3/3 - 17*q**2 - 16*q - 12. Let h(x) = -4*c(x) + u(x). Solve h(j) = 0.
-8, -1
Let w(l) be the second derivative of l**7/280 - 3*l**5/80 - l**4/16 - 59*l**2 + 100*l. Let r(o) be the first derivative of w(o). Let r(j) = 0. Calculate j.
-1, 0, 2
Let s(x) = 5*x**5 - 47*x**4 + 67*x**3 + 79*x**2 - 72*x - 28. Let f(q) = -q**4 + 2. Let a(v) = 12*f(v) - 3*s(v). Find t, given that a(t) = 0.
-1, -2/5, 1, 3, 6
Let o be -28 + 7384/234 + 0/(-4). Let o - 2*l**5 - 296/9*l**3 - 32*l**2 - 64/9*l - 122/9*l**4 = 0. What is l?
-2, -1, 2/9
Let u = 24586/597 + -7930/199. Factor -2/3*r**2 - u*r + 2.
-2*(r - 1)*(r + 3)/3
Let i be (152/(-57))/(-23 + 19). Factor 2/3*o**2 + 0*o + 0 + i*o**3.
2*o**2*(o + 1)/3
Let g be (1512/10332)/(10/205). Find z such that 87/4*z**2 + 165/4*z + g*z**3 + 9 = 0.
-4, -3, -1/4
Factor 165 + 2*l**4 - 168*l**2 + 5*l**3 - l**3 + 104 + 316*l - 423.
2*(l - 7)*(l - 1)**2*(l + 11)
Suppose 0 = 10*d - 6*d - 16. Suppose 0 = -2*i - d, -327 = -p + 2*i + 177. Solve -8*f + p + 5*f**2 - 34*f - 2*f - 56*f = 0 for f.
10
Let m(q) be the third derivative of -47/10*q**5 + 1/4*q**4 + 7/15*q**6 + 7*q + 10/3*q**3 + 3*q**2 + 0. Factor m(r).
2*(r - 5)*(4*r + 1)*(7*r - 2)
Determine m, given that 6*m**2 - 4*m**5 + 32*m - 14*m**3 - 8*m**2 - 22*m**2 - 11*m**4 - 14*m**3 + 35*m**4 = 0.
-1, 0, 1, 2, 4
Let p be 44 + (-9 - 26) - 2/(22/97). What is n in -8/11*n**3 - 32/11 - 54/11*n**2 - 76/11*n + p*n**4 = 0?
-2, -1, 8
Factor 3/5*l**3 - 834/5*l**2 + 0 + 57963/5*l.
3*l*(l - 139)**2/5
Let a = 26633 + -26633. Let l(y) be the second derivative of a - 1/36*y**4 - 6*y**2 + 2/3*y**3 - 41*y. Factor l(j).
-(j - 6)**2/3
Factor -2/9*y**2 + 88/3 + 2/9*y.
-2*(y - 12)*(y + 11)/9
Let i(n) = -n**4 + n**3 - n**2 + 35*n + 1. Let m(a) = 4*a**4 - 404*a**3 - 774*a**2 + 1382*a + 3146. Let b(y) = -6*i(y) - m(y). Find x such that b(x) = 0.
-197, -2, 2
Let m(z) be the third derivative of z**5/300 + 371*z**4/20 + 412923*z**3/10 - 60*z**2 - 3. What is x in m(x) = 0?
-1113
Factor 435 + 47881*g + 47849*g - 95570*g + 5*g**2.
5*(g + 3)*(g + 29)
Let h be (182 + -182)/(4 - 10). Suppose 2*d + 4*x = -0*x - 6, 5*x + 30 = 5*d. Solve -j + h*j**2 + 1/3*j**d + 2/3 = 0 for j.
-2, 1
Let n = -253 - -255. Suppose -4*z = 2*q + 10, 0 = -5*q - 7*z + n*z - 5. Let 27/7*m**5 + 24/7*m + 12/7 - 51/7*m**3 - q*m**2 + 9/7*m**4 = 0. What is m?
-1, -2/3,