et w(z) be the first derivative of -1/3*z**3 + 3/2*z**2 + 0*z + 3/4*z**4 + 12. Let n(j) = 4*j**3 + 2*j. Let m(q) = 5*n(q) - 6*w(q). Factor m(x).
2*x*(x - 1)*(x + 4)
Let d(f) be the third derivative of -f**6/90 + f**5/6 - f**4 + 17*f**3 + 106*f**2. Let j(k) be the first derivative of d(k). Factor j(v).
-4*(v - 3)*(v - 2)
Let j(r) be the first derivative of 13/6*r**2 + 4/3*r - 43 + 1/3*r**3. Factor j(p).
(p + 4)*(3*p + 1)/3
Suppose -r = -5*g + 5, 5*g + 2*r - 15 = r. Factor 5*j**5 - 10*j**5 - 39*j**3 - 18*j**4 + g*j**5 - 10*j - 2*j - 36*j**2.
-3*j*(j + 1)**2*(j + 2)**2
Let o be 0 + 3 + 4 + 1086/(-182). Let c = -6/13 + o. Factor c*d + 0 + 2/7*d**2.
2*d*(d + 2)/7
Let i be (-7 - -10)*10/(-3). Let u(q) = q**2 + 7*q. Let k be u(i). Factor 49*a**2 + 86*a**2 - k*a**3 - 135*a + 5*a**4 - 15*a**3.
5*a*(a - 3)**3
Let j = 749/26 + -57/2. Let c = -140060 - -1820782/13. Suppose -c + 4/13*s - j*s**3 + 2/13*s**2 = 0. Calculate s.
-1, 1/2, 1
Let y = -36/11 - -213/55. Suppose 0 = -2*w - 4*x + 52, 206*w = 207*w - 5*x + 44. Solve w*a - 15 - y*a**2 = 0.
5
Suppose -91*g = -23*g - 67*g. Suppose -6/13*m**4 + 6/13*m**3 + 0 + 2/13*m**5 + g*m - 2/13*m**2 = 0. What is m?
0, 1
Suppose -197*p = -199*p + 16. Let x(i) = -i + 2. Let l be x(0). Factor p*r + 10*r - 6*r + 15*r**3 - 36*r**l.
3*r*(r - 2)*(5*r - 2)
Let h = 37426 + -37424. Let p(c) be the second derivative of 11*c + 0 - 7/8*c**4 + 15/4*c**3 + 3/40*c**5 - 27/4*c**h. What is q in p(q) = 0?
1, 3
Let l(q) = 5*q**3 + 460*q**2 - 967*q + 582. Let k(w) = -2*w**3 - 152*w**2 + 322*w - 198. Let n(m) = -8*k(m) - 3*l(m). Determine j so that n(j) = 0.
1, 162
What is w in 0 - 1/2*w**5 + 7/2*w**3 + 5*w**2 + 0*w - 2*w**4 = 0?
-5, -1, 0, 2
Let q(i) be the first derivative of -4*i**6/33 - 34*i**5/55 + 16*i**4/11 + 146*i**3/33 - 64*i**2/11 - 40*i/11 + 188. Determine b so that q(b) = 0.
-5, -2, -1/4, 1, 2
Let g be (1 + 2 + -2)*0/(-2). Factor g*m**2 + 12 + 6*m - 17*m + m**2 - 2*m**2.
-(m - 1)*(m + 12)
Let d(v) = 5*v**2 - 165*v + 172. Let p(j) = -46*j**2 + 1521*j - 1547. Let g(n) = 19*d(n) + 2*p(n). Factor g(o).
3*(o - 29)*(o - 2)
Factor 0 + 72/7*p**2 + 34/7*p**3 + 8/7*p.
2*p*(p + 2)*(17*p + 2)/7
Let z be 6*(-1 - 25/(-30)) - -1619. Factor -14147*a**2 - 2738 - 264*a - z + 14143*a**2.
-4*(a + 33)**2
Suppose -3*t - 2408 = -3092. Let k = t + -226. Suppose 15/4*n**k - 63/8*n - 9/8*n**4 - 3/8*n**5 + 9/4*n**3 + 27/8 = 0. Calculate n.
-3, 1
Let c = 21 + -53. Let h = c + 67/2. Factor -1/2*g**2 + 0*g + 0 + h*g**3.
g**2*(3*g - 1)/2
Let i(z) be the first derivative of -2*z**3/15 + 57*z**2/5 + 4802. Factor i(u).
-2*u*(u - 57)/5
Let a = -181 - -204. What is s in 103*s - 4*s**4 + 3*s**4 - 68*s**2 - 22*s + 11*s**3 + a*s**2 - 54 = 0?
2, 3
Let c be ((-4)/(-2))/(7/((-63)/(-6))). Factor 9*d**2 + 8 - 41 - 3 - c*d**3 + 12*d.
-3*(d - 3)*(d - 2)*(d + 2)
Let p(c) = -36*c**2 - 44*c + 80. Let z(f) = -f + 3. Let v be z(0). Let a(u) = -247 + 9*u + 7*u**2 + 114 + 117. Let g(w) = v*p(w) + 16*a(w). Factor g(n).
4*(n - 1)*(n + 4)
Determine i, given that -1073/2*i**2 - 32 + 248*i + 841/4*i**3 = 0.
8/29, 2
Let l(g) be the first derivative of 0*g - 1/2*g**2 - 11 + 0*g**3 + 1/24*g**6 + 0*g**4 + 0*g**5. Let c(m) be the second derivative of l(m). Factor c(t).
5*t**3
Suppose 3*k + 19*d - 17*d = 3, 2*k + 5*d = -9. Let f(n) be the first derivative of 15 - 1/8*n**k + 3/4*n - 3/16*n**2. Let f(p) = 0. What is p?
-2, 1
Let p(z) = -20*z + 5. Let n be p(-3). Factor -293*g**5 - n*g**4 - 305*g**5 + 110*g**3 + 603*g**5.
5*g**3*(g - 11)*(g - 2)
Let j(g) be the first derivative of 4*g**2 + 104*g + 16. Let o be j(-13). What is f in 0 + 1/3*f**5 - 2/3*f**2 - 1/3*f + 2/3*f**4 + o*f**3 = 0?
-1, 0, 1
Let r(k) be the third derivative of k**2 - 27*k**3 - 1/480*k**5 - 19*k - 3/8*k**4 + 0. Determine j, given that r(j) = 0.
-36
Let w(d) be the third derivative of -d**5/20 + 69*d**4/2 + 277*d**3/2 + 1103*d**2. Find r, given that w(r) = 0.
-1, 277
Let j(a) be the third derivative of -a**8/13440 - a**7/315 - 2*a**6/45 + 13*a**4/8 - a**3/6 - 7*a**2. Let b(y) be the second derivative of j(y). Factor b(t).
-t*(t + 8)**2/2
Let b(y) be the first derivative of 6 + 0*y**3 - 1/120*y**6 + 1/8*y**4 - 1/30*y**5 + 0*y - 6*y**2. Let f(x) be the second derivative of b(x). Factor f(o).
-o*(o - 1)*(o + 3)
Let k(b) be the first derivative of 81*b**6/65 + 189*b**5/130 + 8*b**4/13 + 4*b**3/39 - 141*b - 100. Let c(h) be the first derivative of k(h). Factor c(y).
2*y*(3*y + 1)*(9*y + 2)**2/13
Let m(s) = 92*s + 5. Let w be m(2). Suppose 183*b = w*b. Factor 8/5*c**3 - 4/5*c + b*c**2 - 4/5*c**5 + 0*c**4 + 0.
-4*c*(c - 1)**2*(c + 1)**2/5
Let m(w) be the third derivative of w**6/720 + 17*w**5/24 + 25*w**2 - 1. Factor m(a).
a**2*(a + 255)/6
Suppose 4651905*a = 4651869*a + 1620. Factor -87/2*t + 3/2 - a*t**2.
-3*(t + 1)*(30*t - 1)/2
Suppose 5*h + 4*h = 2*h. Suppose 7*u - 5 - 9 = h. Find b such that 5 + 4*b**3 - 4*b**2 - b**u - 3*b**2 + 3 - 4*b = 0.
-1, 1, 2
Let m(p) be the third derivative of -p**6/180 - 11*p**5/18 - 38*p**4/9 + 208*p**3/9 - 180*p**2 - 3*p. Suppose m(v) = 0. What is v?
-52, -4, 1
Let q(o) be the third derivative of o**7/105 - 19*o**6/30 + 119*o**5/10 + 38*o**4/3 - 1444*o**3/3 - 3*o**2 + 194*o. Factor q(m).
2*(m - 19)**2*(m - 2)*(m + 2)
Solve -174436*m - 177783*m**3 - 486*m**4 + 641601 + 1919998*m**2 - m**5 - 341076*m - 1113*m**4 - 459015*m**3 - 1407689*m = 0 for m.
-801, 1
Determine q so that 135*q + 1095 - 1907 - 5*q**2 + 1612 = 0.
-5, 32
Let t(w) be the third derivative of -w**6/24 - 87*w**5/4 - 28165*w**4/8 + 85805*w**3/6 - 64*w**2 + 4*w. Find s such that t(s) = 0.
-131, 1
Let d(x) be the first derivative of x**6/6 + 7*x**5/5 + x**4/2 - 28*x**3/3 - 12*x**2 + 3652. Suppose d(r) = 0. Calculate r.
-6, -2, -1, 0, 2
What is t in -5/6*t**4 + 35/6*t + 25/3 - 15/2*t**2 - 35/6*t**3 = 0?
-5, -2, -1, 1
Let q(r) = 985*r**2 - 49*r + 92. Let h be q(2). Suppose h*f - 3943*f + 27 = 0. Determine d, given that -12/7*d**2 - 20/7*d**f - 4/7*d**4 + 16/7 + 20/7*d = 0.
-4, -1, 1
Factor -363/4 - 3/4*s**2 + 33/2*s.
-3*(s - 11)**2/4
Let l = -14 + 168/11. Let t = 14253 + -14253. Solve l*y**3 - 4/11*y - 6/11*y**4 - 10/11*y**5 + 6/11*y**2 + t = 0 for y.
-1, 0, 2/5, 1
Let b be -8 + 12 + -16 + 14. Let n(m) be the second derivative of 1/8*m**b + 1/240*m**6 - 1/48*m**3 - 1/32*m**4 + 0 + 1/160*m**5 + m. Solve n(u) = 0.
-2, -1, 1
Let b(v) = v. Suppose 5*g + 1 = -k, 16*g = 19*g. Let n(s) = 0*s**2 + 1 - s + 3 - s**2 + 3*s. Let i(p) = k*n(p) - b(p). Factor i(m).
(m - 4)*(m + 1)
Determine g, given that -213 - 219/2*g - 3/2*g**2 = 0.
-71, -2
Find n such that 368440/3*n + 91204 + 4/3*n**4 + 32016*n**2 + 408*n**3 = 0.
-151, -3, -1
Factor -325*t**4 + 74743*t**5 - 2*t**2 + 2*t**2 + 330*t**3 - 74748*t**5.
-5*t**3*(t - 1)*(t + 66)
Let l(n) be the second derivative of -n**6/30 - 157*n**5/20 + n**4/12 + 157*n**3/6 + 35*n + 1. Factor l(y).
-y*(y - 1)*(y + 1)*(y + 157)
Let d(f) be the third derivative of 1/40*f**5 + 5/16*f**4 + 3/2*f**3 + 0*f + 8 + f**2. Factor d(h).
3*(h + 2)*(h + 3)/2
Let b = -1622/185 - -1918/185. Factor -1/5*g**2 + 9/5 + b*g.
-(g - 9)*(g + 1)/5
Let w(g) = -2*g**2 - 4*g + 4. Let p(v) = -58 - 8*v + 138 - 72 - 3*v**2. Let j(u) = 3*p(u) - 5*w(u). Find y such that j(y) = 0.
2
Let m = 232 - 226. Factor 124*d**2 - 2 - 4*d**3 + 118*d**2 - 362*d**2 + 116*d**2 + m*d**4 + 6*d - 2*d**5.
-2*(d - 1)**4*(d + 1)
Suppose 5*l - l + b - 399 = 0, l = -b + 102. Let i be 3/(-18) - l/(-54). Factor 10/3*g - 5/3*g**3 - i*g**2 + 0.
-5*g*(g - 1)*(g + 2)/3
Let z(l) be the second derivative of 5/12*l**4 - 29/40*l**5 - 1 + 7/60*l**6 - 125/4*l**2 + 275/24*l**3 + 105*l - 1/168*l**7. Determine b so that z(b) = 0.
-2, 1, 5
Let q(j) be the third derivative of j**7/420 - 27*j**6/40 + 6397*j**5/120 + 1107*j**4/4 + 1681*j**3/3 + 4*j**2 + 142. Suppose q(p) = 0. What is p?
-1, 82
Suppose 0 = -22*z - 14*z + 1836. Let i(k) = -k**3 + 53*k**2 - 99*k - 149. Let o be i(z). Determine c, given that -o*c + 0 - 4/3*c**2 = 0.
-3, 0
Let b(c) be the third derivative of -c**6/120 + 9*c**5/20 - 22*c**4/3 - 4590*c**2. What is g in b(g) = 0?
0, 11, 16
Suppose 63*j - 8*j - 275 = -0*j. Let v(z) be the second derivative of -1/5*z**j + 8*z**2 + 14/3*z**3 + 48*z + 2/3*z**4 + 0. Solve v(m) = 0.
-1, 4
Factor 2358*y**2 + 567*y + 363*y**3 + 5109*y**4 + 5066*y**4 - 10163*y**4.
3*y*(y + 9)*(y + 21)*(4*y 