40. Factor -b*x + 108 + 7*x + 3*x**2 - 18*x.
3*(x - 6)**2
Let q(d) be the first derivative of -50*d**2 + 5/4*d**4 - 40*d + 4*d**5 - 70/3*d**3 + 5/6*d**6 + 156. Solve q(l) = 0.
-2, -1, 2
Let k be (6/4)/(30/1820). Factor -24 - 173 - i**2 - 1 - 34*i - k.
-(i + 17)**2
Suppose 9*u**2 + 41*u**2 - 2*u**4 + 9*u**3 + u**4 - 28*u**3 - 8*u**2 = 0. What is u?
-21, 0, 2
Let q(i) be the first derivative of -1/2*i**3 + 3/20*i**5 + 3*i**2 + 15 + 16*i - 1/2*i**4. Let s(x) be the first derivative of q(x). Factor s(v).
3*(v - 2)*(v - 1)*(v + 1)
Solve -121120 + 121152 + 367*x**2 + 253*x**2 - 328*x = 0.
4/31, 2/5
Determine q, given that 2/3*q**2 - 214/3*q - 220 = 0.
-3, 110
Suppose r - 20 = -4*w, -46*r = -48*r + 2*w. Factor 159*h**3 + 4*h**4 + 1 + 0*h**5 + 3 - h**5 + 28*h**2 - 181*h**3 + r*h**4 - 17*h.
-(h - 4)*(h - 1)**4
Factor -50*j + 425*j + 32 + 85*j**2 - 60*j - 5*j**4 + 148 + 4*j**3 - 59*j**3.
-5*(j - 3)*(j + 1)**2*(j + 12)
Find k, given that -21/5*k**2 + 28/5 - 4/5*k + 2*k**3 - 1/5*k**4 = 0.
-1, 2, 7
Let i(o) be the first derivative of -o**3/4 + 185*o**2/8 - 132*o - 122. Determine t so that i(t) = 0.
3, 176/3
Let o(r) be the first derivative of 0*r + 13*r**2 - 13/8*r**4 + 169/80*r**5 + 1/2*r**3 + 21. Let y(s) be the second derivative of o(s). Factor y(l).
3*(13*l - 2)**2/4
Factor -2350 + 52*p**2 - 131*p**2 + 1740*p - 575*p + 84*p**2.
5*(p - 2)*(p + 235)
Let f(p) be the first derivative of -20*p - 3/2*p**2 - 3 - 3/2*p**3 + 5/2*p**4. Let c(x) be the first derivative of f(x). Find v, given that c(v) = 0.
-1/5, 1/2
Factor 24/5 - 26/5*c + 2/5*c**3 + 0*c**2.
2*(c - 3)*(c - 1)*(c + 4)/5
Let s(a) = 0*a + 3*a + a - 18 + 9*a - 3*a. Let k be s(2). Factor -5/6 - 1/6*h**k - h.
-(h + 1)*(h + 5)/6
Let c(l) = -72*l + 174. Let g be c(2). Suppose -216*f - g = -231*f. Factor 0 + 8/3*a - 2/3*a**3 + 0*a**f.
-2*a*(a - 2)*(a + 2)/3
Let m(a) = -11*a**3 + 8*a**2 - 38*a + 45. Let t(g) = -26*g**3 + 16*g**2 - 74*g + 89. Let d(y) = -7*m(y) + 3*t(y). Suppose d(k) = 0. Calculate k.
-12, 2
Factor 590076/7*w**2 + 1/7*w**4 - 87527054/7*w + 86938307/7 - 190*w**3.
(w - 443)**3*(w - 1)/7
Let p = 2384017/13 + -183383. Determine v, given that 6/13*v**5 + p*v**3 + 34/13*v**4 - 42/13*v**2 - 36/13*v + 0 = 0.
-3, -2/3, 0, 1
Let o(l) be the second derivative of 6/5*l**4 - 11/50*l**5 - 16/15*l**3 - 64/5*l**2 + 1/75*l**6 + 2 - 64*l. Factor o(n).
2*(n - 4)**3*(n + 1)/5
Let s(v) be the second derivative of -v**5/4 - 115*v**4/12 - 305*v**3/3 - 400*v**2 - v - 204. Factor s(l).
-5*(l + 2)*(l + 5)*(l + 16)
Suppose 0 = -9*a - 2*a + 132. Let u be (3/a)/(7/140). Determine v, given that -10 + u*v**3 + 5*v**4 + 15*v**2 - 45*v**2 - 25*v + 15*v**2 = 0.
-1, 2
Let y = 595036/17 + -35000. Solve 8/17*a**3 - y*a + 0 + 6/17*a**2 - 2/17*a**4 = 0.
-2, 0, 3
Factor 0 + 0*b - 1/5*b**3 + 462/5*b**2.
-b**2*(b - 462)/5
Let a(m) be the third derivative of -7/9*m**4 - 1/360*m**5 - 784/9*m**3 + 2*m**2 + 0 + 78*m. Determine q so that a(q) = 0.
-56
Let s(u) = -20*u**2 + 56*u + 336. Let o(i) = -i**3 + 19*i**2 - 55*i - 320. Let k(m) = 4*o(m) + 5*s(m). Factor k(l).
-4*(l - 4)*(l + 5)**2
Let s(x) be the second derivative of -2*x + 0*x**2 - 57/20*x**5 - 9/2*x**4 - 18 - 1/10*x**6 + 0*x**3. Factor s(i).
-3*i**2*(i + 1)*(i + 18)
Let o(z) be the first derivative of -2/21*z**3 - 34 - 2*z**2 + 64/7*z. Determine i, given that o(i) = 0.
-16, 2
Let b(t) be the second derivative of t**6/240 + 9*t**5/160 - 15*t**4/32 - 113*t**3/48 - 15*t**2/4 + 1473*t. Factor b(d).
(d - 5)*(d + 1)**2*(d + 12)/8
Suppose -279*p + 191*p + 1083 = 273*p. Find j, given that -42/11 + 50/11*j - 6/11*j**2 - 2/11*j**p = 0.
-7, 1, 3
Let w(d) be the second derivative of -d**4/42 - 1375*d**3/42 + 344*d**2/7 - 12029*d. Solve w(b) = 0 for b.
-688, 1/2
Factor 1255/3*g + 418/3 + g**2.
(g + 418)*(3*g + 1)/3
Let s be 1/(-2) + 49/14 + 5. Let -48 - 40*g + 42*g**3 + 81*g**2 + 3572*g**4 - 3586*g**4 - s*g**5 - 13*g**2 = 0. Calculate g.
-2, -3/4, 1, 2
Let q = -34 - -35. Let n be (-2)/(-2) + (6 - (q + 1)). Suppose 17*j**5 - j**2 + 20*j**n + j**4 - 38*j**5 + j**3 = 0. Calculate j.
-1, 0, 1
Let u(b) = -94*b**2 + 14*b + 6. Let z(y) = -143*y**2 + 15*y + 9. Let i(n) = 3*u(n) - 2*z(n). Factor i(o).
4*o*(o + 3)
Find z, given that -58*z**3 - 716*z**2 - 37*z**3 - 299*z + 205*z**3 - 9*z + 4*z = 0.
-2/5, 0, 76/11
Let u(c) be the first derivative of 27 + 44*c + 20*c**2 - 4/3*c**3. Factor u(q).
-4*(q - 11)*(q + 1)
Suppose 0 - 4/11*i**5 + 42/11*i**4 + 0*i + 124/11*i**3 + 78/11*i**2 = 0. What is i?
-3/2, -1, 0, 13
Let t(s) be the first derivative of 2556801*s**3/5 - 19188*s**2/5 + 48*s/5 + 10629. Determine g so that t(g) = 0.
4/1599
Let s(b) be the first derivative of b**5/35 + 1053*b**4/28 - 1408*b**3/7 + 302*b**2 + 12898. Factor s(z).
z*(z - 2)**2*(z + 1057)/7
Find j such that -48*j**2 + 81*j**2 - 175*j**4 + 155*j**5 - 5*j**3 - 150*j**5 + 142*j**2 = 0.
-1, 0, 1, 35
Let r(u) be the second derivative of 2/15*u**6 - 1/3*u**4 + 22/3*u**3 + 3 + u - 11/5*u**5 + 0*u**2. Solve r(a) = 0 for a.
-1, 0, 1, 11
Suppose 2*p = 95 + 43. Factor -57*h - 17 + 32 - p - h**2 - 2*h**2.
-3*(h + 1)*(h + 18)
Let y = 419701/7 + -59955. Suppose 32/7*r + 2/7*r**5 - 24/7*r**2 + 6/7*r**4 - y*r**3 + 0 = 0. What is r?
-4, -2, 0, 1, 2
Let q(u) be the first derivative of -u**3/3 + 54*u**2 - 107*u - 2372. Factor q(y).
-(y - 107)*(y - 1)
Suppose -3 = -f + 2, -4*t = -4*f + 8. Suppose t*n + x = 11, 2*n + 0*n - 4*x = 26. What is o in 6*o**3 + 178*o**2 + 32*o**4 - 186*o**2 - 18*o**3 - 12*o**n = 0?
-1/3, 0, 1, 2
Suppose 0 = h - 2*f - 144, h - 132 = -0*h - 4*f. Factor 903*x - 2686*x + h + 1078*x + 25*x**2.
5*(x - 28)*(5*x - 1)
Suppose -131*x = -3*b - 129*x + 2, -4*b + 14 = 3*x. Factor 4/5*m**b - 12/5*m - 4/5*m**4 + 0 + 12/5*m**3.
-4*m*(m - 3)*(m - 1)*(m + 1)/5
Let f = 283847/81100 + 3/81100. Suppose -1/2*h**2 - 4*h - f = 0. What is h?
-7, -1
Suppose -3*c - 4*n = -90, -3*c + 5587 = -4*n + 5641. Factor -45 - 1/5*x**2 - c*x.
-(x + 15)**2/5
Let f(p) be the first derivative of 5/3*p**3 - 20*p + 78 + 0*p**2. Suppose f(d) = 0. What is d?
-2, 2
Let f = 20731 + -20729. Let 8/3*k - 28/3*k**f - 26/3*k**3 - 2*k**4 + 16/3 = 0. What is k?
-2, -1, 2/3
Factor -30 + 3/5*a**2 + 147/5*a.
3*(a - 1)*(a + 50)/5
Factor -373246/23*k**2 + 374978/23*k - 2/23*k**4 - 1730/23*k**3 + 0.
-2*k*(k - 1)*(k + 433)**2/23
Let s(a) be the third derivative of -4*a**7/1155 - a**6/132 + a**5/165 + a**4/44 - 2340*a**2. Find f, given that s(f) = 0.
-1, 0, 3/4
Let r(n) = n**3 + 16*n**2 + 26*n - 22. Let b be r(-14). Factor z - 4*z**2 - 3*z**3 + b*z**2 - z - 8*z**2.
-3*z**2*(z + 2)
Let i be 8 + 28/5 + (159 - 147). Determine r, given that -96/5*r - i - 24/5*r**2 - 2/5*r**3 = 0.
-4
Determine r so that 9*r**4 + 0*r + 0*r**2 + 0 - 3/7*r**5 - 114/7*r**3 = 0.
0, 2, 19
Let b(r) be the first derivative of r**5/360 + r**4/48 + r**3/18 - 27*r**2/2 + 12. Let f(q) be the second derivative of b(q). Factor f(s).
(s + 1)*(s + 2)/6
Suppose -4*l + 5*w + 33 = 0, -5*l - 3*w + 17 + 15 = 0. Suppose -l*t - 16*t = 0. Factor -8/9*s + 0 + t*s**2 + 2/3*s**3 + 2/9*s**4.
2*s*(s - 1)*(s + 2)**2/9
Suppose -14*u = -9*u - 15. Let f be u/1 + (15 - 13). Suppose -o**3 - 2*o**4 - o**f + 9*o - 19*o + 10*o = 0. Calculate o.
-1, 0
Let n(j) be the first derivative of -j**8/1008 + j**7/210 + j**6/40 + j**5/36 - 7*j**2/2 - 15. Let o(b) be the second derivative of n(b). Factor o(i).
-i**2*(i - 5)*(i + 1)**2/3
Let o(f) be the first derivative of -5/9*f**3 - 5/6*f**2 + 114 + 0*f. Find a, given that o(a) = 0.
-1, 0
Let m(t) be the first derivative of t**6/6 + 4*t**5/5 - 3*t**4/2 - 4*t**3/3 + 5*t**2/2 - 1579. Factor m(l).
l*(l - 1)**2*(l + 1)*(l + 5)
Let c(r) = -2*r**5 - 266*r**4 + 420*r**3 - 112*r**2 + 22*r + 22. Let j(s) = 38*s**4 - 60*s**3 + 16*s**2 - 3*s - 3. Let q(b) = -3*c(b) - 22*j(b). Solve q(d) = 0.
0, 1/3, 2, 4
Solve -77*t**2 - 19/2*t**3 - 122*t - 12 = 0 for t.
-6, -2, -2/19
Factor -153 - r**2 + 4147*r + 2*r**2 + 0*r**2 - 3995*r.
(r - 1)*(r + 153)
Factor 0*l + 88/3*l**2 + 2/3*l**4 + 0 + 16*l**3.
2*l**2*(l + 2)*(l + 22)/3
Factor -356/5*i + 0 - 4/5*i**2.
-4*i*(i + 89)/5
Let c(y) be the second derivative of 0*y**3 - 1/24*y**6 - 1/4*y**5 + 0 + 0*y**2 + 25/48*y**4 + 12*y. Suppose c(u) = 0. Calculate u.
-5, 0, 1
Let q(x) be the second derivative of -8/3*x**3 - 1/120*x**6 + 0 + 3/40*x**5 - 1/4*x**4 + 0*x**2 - 13*x. Let u(m) be the