).
2*k**3*(k - 3)/15
Let z be (-1566)/(-8) - 48/64. Factor 15*m**3 + 39*m**2 - 12 - 94*m + z*m - 89*m.
3*(m + 1)*(m + 2)*(5*m - 2)
Let z(j) be the first derivative of j**4/22 - 80*j**3/33 + 400*j**2/11 - 284. Factor z(m).
2*m*(m - 20)**2/11
Suppose p + 7 = -3*w, -5*p - 3*w + 10 = 9. Let i be ((-4)/3 + p)*153/68. Factor 0 + 0*n - i*n**2.
-3*n**2/2
Let n(h) be the second derivative of 5*h**5/12 + 55*h**4/36 - 5*h**3/9 - 20*h**2/3 - 481*h - 3. Factor n(d).
5*(d + 1)*(d + 2)*(5*d - 4)/3
Let f(m) be the first derivative of m**6/2880 - m**5/960 - m**4/96 + 55*m**3/3 + 24. Let i(k) be the third derivative of f(k). Factor i(n).
(n - 2)*(n + 1)/8
Find b such that -184/7*b**3 - 1072/7*b**2 - 288*b + 4/7*b**5 - 1280/7 + 12/7*b**4 = 0.
-5, -2, 8
What is w in -104*w**3 + 2*w**4 + 14*w - 18*w**2 + 227*w**3 - 125*w**3 + 4*w = 0?
-3, 0, 1, 3
Suppose 216 = 150*x - 96*x. Let v(w) be the second derivative of -1/4*w**5 + 0*w**x + 0 + 5/2*w**3 + 3*w + 5*w**2. Suppose v(b) = 0. What is b?
-1, 2
Let b(p) be the second derivative of -p**4/66 + 89*p**3/33 - 340*p**2/11 - 2*p + 255. Factor b(y).
-2*(y - 85)*(y - 4)/11
Let r(p) be the second derivative of -p**5/70 - 2*p**4 + 57*p**3/7 - 86*p**2/7 - 2056*p. Factor r(x).
-2*(x - 1)**2*(x + 86)/7
Let f(w) be the third derivative of -w**8/10080 - w**7/3780 + w**4/12 - 80*w**3/3 - 3*w**2 + 20. Let y(l) be the second derivative of f(l). Factor y(h).
-2*h**2*(h + 1)/3
Let h(r) be the third derivative of 4/9*r**3 + 7/60*r**5 + 2*r - 34*r**2 + 17/36*r**4 + 0. Find f such that h(f) = 0.
-4/3, -2/7
Let p(h) = 59*h - 70. Let q be p(1). Let a be 330/60 - q/(-2). Suppose -10/7*y**3 - 3/7*y**4 - 9/7*y**2 - 2/7*y + a = 0. What is y?
-2, -1, -1/3, 0
Suppose 2*v = -10, -o - v - 34 = 34. Let m be (-121)/o - (9 + (-830)/90). Let m*f**2 + 0 - 3/7*f**4 + 3/7*f**5 - 9/7*f**3 - 6/7*f = 0. What is f?
-2, 0, 1
Let c be 3/(6/10) - (-93 + (-16694)/(-238)). Suppose 108/7*x + 12/7 + c*x**2 = 0. Calculate x.
-2/5, -2/13
Let a = -11212/5 + 2243. Let z(d) be the first derivative of -24*d - 30*d**2 + 18 - a*d**5 - 18*d**3 - 21/4*d**4. What is o in z(o) = 0?
-2, -1
Let r(l) = l**3 - l**2 + 1. Let p = -155 + 160. Let q(n) = -5*n**4 - 7*n**3 + 16*n**2 - 4*n - 4. Let g(x) = p*q(x) + 20*r(x). What is a in g(a) = 0?
-2, 0, 2/5, 1
Suppose -279*a + 453*a = 348. Let -368/7*i - 80/7 + 404/7*i**a + 44/7*i**3 = 0. What is i?
-10, -2/11, 1
Let k(m) be the second derivative of 5*m**7/42 + 43*m**6/6 - 625*m**5/4 + 9685*m**4/12 + 520*m**3 - 4950*m**2 + 10276*m. Suppose k(a) = 0. What is a?
-55, -1, 1, 6
Let g(o) be the second derivative of -o**7/1575 + o**6/150 - o**5/90 - 98*o**2 + 36*o - 3. Let v(z) be the first derivative of g(z). Factor v(l).
-2*l**2*(l - 5)*(l - 1)/15
Factor 17/5*w - 2*w**2 + 6/5.
-(w - 2)*(10*w + 3)/5
Let r(s) be the first derivative of s**6/8 + 3*s**5/20 - 21*s**4/16 - s**3/4 + 9*s**2/4 + 2379. Find p, given that r(p) = 0.
-3, -1, 0, 1, 2
Let t be 9/648*12*30. Let a = 158 + -2368/15. Factor 2/5*n - 2/15*n**t - 4/15*n**3 - 4/15*n**2 - a + 2/5*n**4.
-2*(n - 1)**4*(n + 1)/15
Let r = -191 + 299. Factor -78 - 75*t + r - 48 - 12*t**2.
-3*(t + 6)*(4*t + 1)
Let a(g) be the first derivative of 2*g**5/25 + 15*g**4/2 + 962*g**3/5 + 1369*g**2/5 + 6399. Factor a(x).
2*x*(x + 1)*(x + 37)**2/5
Factor 14*w**3 - 9*w**3 - 1095*w**2 + 27856*w - 44103 + 32639*w - 15302.
5*(w - 109)**2*(w - 1)
Let g(y) be the second derivative of 1/10*y**4 + 1/5*y**2 + 0 + 1/50*y**5 + 1/5*y**3 + 55*y. What is w in g(w) = 0?
-1
Let o(l) be the first derivative of -l**6/1080 + l**5/360 - 55*l**3/3 + 48. Let s(r) be the third derivative of o(r). Factor s(q).
-q*(q - 1)/3
Let k(l) = -21 - 27*l + 7*l + 13. Let t be k(-2). What is h in -6*h**2 - 18*h**3 - 12*h**3 + 8 + t*h**3 = 0?
-1, 2
Let j(g) be the first derivative of 1/15*g**3 - 27/5*g - 13/5*g**2 - 13. What is a in j(a) = 0?
-1, 27
Let x(j) be the first derivative of 88 - 1922/13*j - 2/39*j**3 + 62/13*j**2. Determine d so that x(d) = 0.
31
Let r(q) be the second derivative of -q**7/560 + 7*q**6/240 + 2*q**3/3 + q**2/2 - q + 3. Let u(k) be the second derivative of r(k). Factor u(i).
-3*i**2*(i - 7)/2
Let o(k) be the second derivative of 3*k - 25 - 3/7*k**2 + 17/42*k**3 - 5/84*k**4. Suppose o(n) = 0. Calculate n.
2/5, 3
Suppose 902 = -5*f - 76*f + 4231 + 6634. Suppose -f*k**2 + 798*k + 588 + 9/2*k**3 = 0. Calculate k.
-2/3, 14
Let r = 153792/60151 - -126/8593. Factor r + 24/7*v**2 - 39/7*v - 3/7*v**3.
-3*(v - 6)*(v - 1)**2/7
Determine a so that 5*a**2 + 25349 - 15*a**3 - 54*a**2 - 25333 - 30*a = 0.
-2, -8/5, 1/3
Suppose -3*p + 4 = -p. Let r = p + 2. Determine v so that -64 - r*v - 22*v + 10*v - v**2 = 0.
-8
Let q(j) be the first derivative of j**6/8 - 2*j**5/5 + 2*j**4/5 + 31*j**2/2 - 94. Let t(b) be the second derivative of q(b). Factor t(m).
3*m*(5*m - 4)**2/5
Let o(w) be the third derivative of w**6/80 + 131*w**5/40 + 125*w**4/2 + 492*w**3 - 36*w**2 - 5. Factor o(n).
3*(n + 4)**2*(n + 123)/2
Let a = -8513935/17 + 500823. Determine r, given that -22/17*r**2 + 0 - a*r - 2/17*r**3 = 0.
-7, -4, 0
Suppose 6*b + 0 + 3/2*b**2 - 3/2*b**4 - 6*b**3 = 0. Calculate b.
-4, -1, 0, 1
Let x(d) be the first derivative of -4*d**5/5 - 4*d**4 - 16*d**3/3 - 2957. Factor x(c).
-4*c**2*(c + 2)**2
Suppose 32 = 4*u + 8*h - 3*h, -16 = -4*h. Suppose -2*a - 25*a**2 + u*a**5 - 9*a**3 + 2*a**5 - 2*a**5 - 4*a + 10*a**2 + 3*a**4 = 0. What is a?
-1, 0, 2
Let 6/11*q**2 - 5184/11*q + 1119744/11 = 0. What is q?
432
Let q(k) = 2*k**3 - 2*k**2 + 4*k - 213. Let n be q(0). Let z = 215 + n. Factor 1/4*u**z + 1/2 - 3/4*u.
(u - 2)*(u - 1)/4
Let l(g) = g**3 + 2*g - 2. Let a(m) = -375*m**3 - 2205*m**2 - 860*m - 160. Let n(c) = -a(c) + 30*l(c). What is u in n(u) = 0?
-5, -2/9
Let q(c) = -c**2 - 12*c + 29. Let o be q(-13). Suppose -2*r + 2 + o = 0. Factor -2 - 15*k**2 + 0*k**2 - 19*k**4 - 12*k**4 + 11*k**3 + r*k + 28*k**4.
-(k - 1)**3*(3*k - 2)
Let p(t) be the first derivative of -2*t**7/21 + 2*t**6/15 + 3*t**5/5 - 5*t**4/3 + 4*t**3/3 + 18*t - 48. Let c(n) be the first derivative of p(n). Factor c(q).
-4*q*(q - 1)**3*(q + 2)
Let r be ((-16)/24)/((-1382)/(-6552) - 444/1924). Factor 10976/5 + 4/5*s**3 + r*s**2 + 2352/5*s.
4*(s + 14)**3/5
Let i = -8777889/5 - -1755585. What is s in -2/5*s**2 - i - 38/5*s = 0?
-18, -1
Let x(d) be the second derivative of 0 + 160*d - 1/120*d**6 - 1/80*d**5 + 5/48*d**4 - 1/8*d**3 + 0*d**2. Factor x(z).
-z*(z - 1)**2*(z + 3)/4
Factor -13745*h + 5821*h + 6349*h - 3625 - 195*h**2 - 5*h**3.
-5*(h + 5)**2*(h + 29)
Suppose 225/4*w**2 + 3/4*w**3 + 0 - 237*w = 0. Calculate w.
-79, 0, 4
Let k(u) = u**2 + 14*u + 1. Let r be (-4)/(-3)*(-21)/2. Let i be k(r). Factor -i + 3*s - 5/4*s**2.
-(s - 2)*(5*s - 2)/4
Let x(c) be the first derivative of c**7/2240 - 17*c**6/160 + 2601*c**5/320 - 76*c**3/3 + 184. Let h(w) be the third derivative of x(w). Factor h(q).
3*q*(q - 51)**2/8
Let l be 36/(-18) + 49/21. Let m(a) be the first derivative of 10 - 5/9*a**3 + 1/3*a**2 + l*a**4 + 0*a - 1/15*a**5. Factor m(o).
-o*(o - 2)*(o - 1)**2/3
Let y(l) = 34*l + 20. Let k be y(0). Let w be 5/(k/(-12)) + (46 - 41). Solve -8/7*u**w + 0*u**3 + 2/7*u**4 + 0*u + 0 = 0 for u.
-2, 0, 2
Let g(m) be the first derivative of -m**4/18 + 16*m**3/27 + 61*m**2/9 + 104*m/9 + 3268. Find k such that g(k) = 0.
-4, -1, 13
Factor 1198854/5 - 3/5*r**3 + 2688/5*r**2 - 604791/5*r.
-3*(r - 447)**2*(r - 2)/5
Suppose 281 + 309 = 5*b. Suppose -5*c - 28 + b = 0. Factor 18 - 2*r**2 - 4*r - 30 + c.
-2*(r - 1)*(r + 3)
Factor 0 + 5/4*u**4 - 2*u**3 + 1/4*u**2 + 1/2*u.
u*(u - 1)**2*(5*u + 2)/4
Let -664 - 668*x**2 + 132141*x + 2*x**3 - 2*x**3 - 133471*x - 2*x**3 = 0. Calculate x.
-332, -1
Let k be 15/420 + 20576/896. Let i(f) be the first derivative of -f**4 + 0*f + 0*f**2 - k + 4/5*f**5 + 2/3*f**6 - 4/3*f**3. Factor i(b).
4*b**2*(b - 1)*(b + 1)**2
Let 64/3*b**4 + 207*b + 80*b**3 - 252*b**2 - 54 = 0. Calculate b.
-6, 3/4
Let t(k) be the first derivative of -28 + 1/24*k**4 + 0*k + 1/4*k**2 + 2/9*k**3. Determine x, given that t(x) = 0.
-3, -1, 0
Suppose 3*s + 3*v - 1116 = 0, 0 = 3*s - 4*v - 1264 + 134. Let z = s - 370. Determine t, given that -3/2*t**2 + 1/2*t**z - 2*t + t**3 + 2 = 0.
-2, 1
Suppose -2*z = -0*z + 3*r - 13, z - 5*r = 0. Suppose -z*w - 12 + 22 = 0. Factor 6*t + 2*t**3 - w*t - 2*t - 6*t**2 + 2*t.
2*t*(t 