 first derivative of 1/2*x**3 + 15*x**2 + 150*x - 1. Determine t, given that u(t) = 0.
-10
Let p = -381092/9 + 381122/9. Let -1/6*n**2 + p*n - 19/6 = 0. What is n?
1, 19
Let t(c) be the second derivative of c**6/150 - c**5/20 - 47*c**4/60 - 13*c**3/10 + 9*c**2 + 212*c + 7. Factor t(m).
(m - 10)*(m - 1)*(m + 3)**2/5
Suppose -182*w + 3 = 2*o - 181*w, 0 = 4*w + 4. Let i(y) be the third derivative of 0*y - 2*y**o + 1/3*y**3 + 1/120*y**5 + 0 + 1/12*y**4. Factor i(z).
(z + 2)**2/2
Let c(l) = 7*l**2 - 68*l + 1227. Let m(q) = 38*q**2 - 337*q + 6136. Let f(h) = 22*c(h) - 4*m(h). Factor f(g).
2*(g - 49)*(g - 25)
Factor 54/5 - 11/2*h**2 + 26/5*h + 1/10*h**3.
(h - 54)*(h - 2)*(h + 1)/10
Let c(d) = -6*d**3 + 5*d**2 + d - 8. Let u(w) = w**3 - w**2 + 4. Let l(q) = c(q) + 2*u(q). Factor l(g).
-g*(g - 1)*(4*g + 1)
Find b, given that 56*b**3 - 31*b**3 - 5*b**3 - 21*b**3 - 792*b**2 - 791*b = 0.
-791, -1, 0
Suppose -3*j - 8724 = 14*g - 8*g, 2*g + 4*j + 2896 = 0. Let q = 1458 + g. Factor -14/9*p**q + 0 + 4/9*p.
-2*p*(7*p - 2)/9
Suppose -12*x - 31 - 89 = 0. Let i(y) = -80*y**3 - 45*y**2 + 85*y + 40. Let l(p) = p**3 + p**2 - p - 1. Let q(r) = x*l(r) + i(r). Determine f so that q(f) = 0.
-10/9, -1/2, 1
Let z(u) be the first derivative of 0*u**2 - 5/12*u**4 - 3 - 7*u - 5/3*u**3. Let j(q) be the first derivative of z(q). Factor j(f).
-5*f*(f + 2)
Let r(y) be the first derivative of y**5/5 + y**4/4 - 2*y**3/3 - 102. Let j(x) = 7*x**4 + 9*x**3 - 16*x**2. Let h(u) = j(u) - 6*r(u). Factor h(z).
z**2*(z - 1)*(z + 4)
Let a(r) = -r**3 + 60*r**2 + 17*r - 111. Let k be a(40). Let 2*n**2 + 9*n**4 - k + 32569 - 27*n**2 + 18*n + n**5 - 3*n**3 = 0. Calculate n.
-9, -2, 0, 1
Let u(w) be the second derivative of -1/48*w**4 - 2/3*w**3 - 15/8*w**2 + 189*w + 0. Factor u(n).
-(n + 1)*(n + 15)/4
Factor 24*f**2 + 0 - 74*f**3 + 60*f**4 - 9/2*f**5 + 0*f.
-f**2*(f - 12)*(3*f - 2)**2/2
Let x = -844008 + 10972126/13. Let -2/13*a**4 - 4*a**2 + x*a**3 + 0 + 32/13*a = 0. Calculate a.
0, 1, 2, 8
Let v = -741 + 746. Let b(t) be the third derivative of 5/6*t**4 + 37*t**2 + 0 + 1/30*t**6 + 0*t + 4/3*t**3 + 4/15*t**v. Suppose b(x) = 0. What is x?
-2, -1
Factor 9/5*z**2 + 21/5*z - 1/5*z**3 + 11/5.
-(z - 11)*(z + 1)**2/5
Find j such that 39/2*j**2 + 21/4*j - 3/8*j**4 - 153/8 - 21/4*j**3 = 0.
-17, -1, 1, 3
Factor 6675*h - 3660*h**2 + 52842 - 3647*h**2 + h**3 + 2605 + 7136*h**2.
(h - 89)**2*(h + 7)
Determine y, given that -1/5*y**3 + 0 + 1872/5*y**2 - 876096/5*y = 0.
0, 936
Let i be (-1 - (-132)/8)*2. Suppose 465 = 34*x - i*x. Find q, given that -5*q**5 + x*q**3 + 4*q**5 + 2*q**4 - 156*q**3 = 0.
0, 1
Suppose 40 = 2*y - 3*a, a = 4*y - a - 80. Suppose -k = -f - 3*k + 10, -2*f = -k - y. Solve 9*g**2 - 15*g - 2*g**4 - 142 + 145 - f*g**4 + 15*g**3 = 0.
-1, 1/4, 1
Suppose 0 = f + 4*y - 28, -4*y + 34 = 14. Let m be 2/f*(-128)/(-160). Determine q, given that 0 + 1/5*q**3 - m*q + 2/5*q**4 - 2/5*q**2 = 0.
-1, -1/2, 0, 1
Suppose 2*l + 489 = 3*s, s - 1255 = 104*l - 99*l. Let c = l + 256. Determine b, given that 10/3*b**5 + 8/3*b**3 - 26/3*b**c + 0*b + 0 + 8/3*b**2 = 0.
-2/5, 0, 1, 2
Let z(a) be the second derivative of -3*a**5/100 - 51*a**4/20 - 5*a**3 - 1099*a. Factor z(t).
-3*t*(t + 1)*(t + 50)/5
Let r(l) = -214*l + 645. Let d be r(3). Let k(o) be the second derivative of 1/120*o**6 - 1/16*o**4 + 0 + 1/12*o**d + 20*o + 0*o**2 + 0*o**5. Factor k(v).
v*(v - 1)**2*(v + 2)/4
Let t(a) be the third derivative of -75*a**8/112 + 137*a**7/42 + 29*a**6/4 - 2*a**5/3 + 52*a**2 - a. Determine y so that t(y) = 0.
-1, 0, 2/45, 4
Let m = -2542 - -2544. Let r(c) be the third derivative of -7*c**m - 1/2*c**5 - 25/24*c**4 - 1/24*c**6 + 0 + 0*c + 0*c**3. Factor r(j).
-5*j*(j + 1)*(j + 5)
Let w(s) be the second derivative of s**5/160 + 5*s**4/48 + 17*s**3/48 + s**2/2 + 959*s. Factor w(k).
(k + 1)**2*(k + 8)/8
Let y(g) = 199*g + 20499. Let o be y(-103). Factor 1/5*k**o + 1/5*k - 12/5.
(k - 3)*(k + 4)/5
Let p be ((-2)/5)/(31/(-465)). Determine c so that 1332*c + 9 + 0*c**2 - 1335*c - p*c**2 = 0.
-3/2, 1
Let a(s) be the first derivative of -19*s**3/9 + 35*s**2/2 + 124*s/3 + 6046. Determine w, given that a(w) = 0.
-1, 124/19
Suppose 2 + 16 = 6*z. Suppose -2264*t - 1024 - t**2 - z*t**2 + 2136*t = 0. Calculate t.
-16
Let w(g) = g**3 - 2*g**2 + g + 2. Let o(m) = 5*m**3 - 5*m**2 + 7*m + 9. Suppose 0 = 13*z + 27*z + 160. Let y(k) = z*w(k) + o(k). Find x, given that y(x) = 0.
-1
Let p = 15604 - 15604. Let q(d) be the first derivative of -36 + p*d + 6/7*d**2 - 1/7*d**4 + 8/21*d**3. What is y in q(y) = 0?
-1, 0, 3
Let h(s) be the first derivative of -9/7*s - 1/21*s**3 + 3/7*s**2 - 16. Factor h(w).
-(w - 3)**2/7
Let o = -181/28 + 2047/308. Let k = -4 + 6. Factor 6/11 + 7/11*f - o*f**3 - f**k.
-(f - 1)*(f + 6)*(2*f + 1)/11
Let a = 2/5371 + 5355/42968. Let g(q) be the second derivative of 1/56*q**7 - 2*q + 0*q**6 + 0*q**4 + 0*q**2 + 7 - 3/40*q**5 + a*q**3. Factor g(f).
3*f*(f - 1)**2*(f + 1)**2/4
Let v = -241/22 + 23/2. Let y be 7/(-14)*-8 - 4. Solve 0*q + y - v*q**5 + 10/11*q**4 - 4/11*q**3 + 0*q**2 = 0 for q.
0, 2/3, 1
Suppose -123627 - 1219/3*d**2 - 124033*d - 1/3*d**3 = 0. Calculate d.
-609, -1
Let x(a) be the second derivative of 0 - 1/195*a**6 - 5/13*a**2 - 5*a - 3/13*a**4 + 16/39*a**3 + 4/65*a**5. Factor x(t).
-2*(t - 5)*(t - 1)**3/13
Let m(j) = 2*j**3 - 4*j**2 - 17*j + 24. Let h(y) = 2*y**2 - 8*y - 13*y + 0*y**2 + 22*y. Let i(s) = h(s) + m(s). Factor i(p).
2*(p - 2)**2*(p + 3)
Suppose 5*n = 2*z + 109, -3*z - 14 = n - 2*n. Let j = -19 + n. Find u, given that 0 + 5*u**2 - 2 - j + 1 = 0.
-1, 1
Let t be (7 - 1) + ((-41)/((-246)/(-36)))/1. Factor -9/7*j**2 - 6/7*j**3 + t + 3/7*j**4 + 0*j.
3*j**2*(j - 3)*(j + 1)/7
Let m(v) be the first derivative of -178 - 136*v**4 + 16/5*v**5 + 1541*v**3 + 17*v**2 - 289*v. Find x such that m(x) = 0.
-1/4, 1/4, 17
Let s = 46091 - 46091. Let -3/7*n**3 + 18/7 + s*n**2 + 3*n = 0. Calculate n.
-2, -1, 3
Suppose -2*p - 2*p + 231 = 3*i, 3*p = 2*i + 152. Factor -p*l + 5*l**2 + 49*l - 66 + 36.
5*(l - 3)*(l + 2)
Let b be (-8)/(-44) - (634/(-22) - 4). Factor b*r**4 - 12*r**4 + 58*r**3 + 3*r**5 + 66*r**3 - 106*r**3.
3*r**3*(r + 1)*(r + 6)
Let h(v) be the third derivative of -2*v**7/105 - 13*v**6/30 - 8*v**5/3 - 6*v**4 + 318*v**2. Factor h(t).
-4*t*(t + 2)**2*(t + 9)
Let z(a) be the third derivative of -19*a**6/150 - 157*a**5/25 - 178*a**4/15 + 64*a**3/5 + 8*a**2 - 3*a + 3. Suppose z(w) = 0. What is w?
-24, -1, 4/19
Let b = 1 + -1. Let a be 18/24*8/3 + b. Factor 2*p - 4*p**2 + 14*p**a - 3*p**2 - 8*p**2.
-p*(p - 2)
What is o in -36*o**4 + 610*o**3 + 540 - 4*o**5 - 616*o - 540*o**2 + 311*o**3 - 409 + 445 - 301*o**3 = 0?
-18, -1, 1, 8
Suppose 4*o - 29 = -4*m + 11, -2*o - 10 = -4*m. Find f, given that -84*f**o - 3*f**2 - 7*f + 78*f**5 - 3*f**4 + 6 - 8*f + 21*f**3 = 0.
-2, -1, 1/2, 1
Let m(y) be the second derivative of 21/16*y**7 - 11/16*y**4 + 3/4*y**3 - 19 - 7/40*y**6 + 2*y - 377/160*y**5 + 1/2*y**2. Solve m(q) = 0.
-2/3, -2/7, 1/3, 1
Let y be ((-29532)/(-207))/(4/(-6)). Let p = 214 + y. Factor 1/2*c**3 + 1/8*c**4 + p + 5/8*c**2 + 1/4*c.
c*(c + 1)**2*(c + 2)/8
Let u = -2/3055 + 631/30550. Let y(r) be the third derivative of -1/300*r**6 + 0 + u*r**5 + 0*r + r**2 + 0*r**4 - 4/15*r**3. Factor y(m).
-2*(m - 2)**2*(m + 1)/5
Let u(v) = 49*v - 370*v - 95*v + 14680 + 3*v**2. Let x(a) = 3*a**2 - 415*a + 14675. Let l(q) = -5*u(q) + 4*x(q). Find b, given that l(b) = 0.
70
Let n(f) be the third derivative of -f**6/60 - 4*f**5/15 + 19*f**4/12 - 10*f**3/3 - 5083*f**2. Factor n(b).
-2*(b - 1)**2*(b + 10)
Let j be (-4)/150 + (-41528)/8700 + 6. Let 0 + 11/5*p**2 + 3/5*p**3 + j*p = 0. Calculate p.
-3, -2/3, 0
Let s = 26987 + -26987. Suppose -1/3*k + s + 1/6*k**2 = 0. What is k?
0, 2
Let m(r) be the second derivative of r**7/4410 - 2*r**6/315 - r**4/6 + 3*r**2/2 + 37*r. Let o(p) be the third derivative of m(p). Factor o(a).
4*a*(a - 8)/7
Let z(d) be the first derivative of -3*d**4/4 - 59*d**3/3 + 7*d**2/2 + 55*d - 15. Let a(n) = -n**3 + 2*n**2 - n. Let q(h) = -2*a(h) - z(h). Factor q(f).
5*(f - 1)*(f + 1)*(f + 11)
Let j be 5 + 6/(-12)*-246. Suppose 0 = 48*u - j - 352. Factor 4/5*i**2 - 2/5 - u*i**5 - 92/5*i**3 + 14/5*i - 26*i**4.
-2*(i + 1)**3*(5*i - 1)**2/5
Let r(y) be the second derivative of -y**4/30 - 19*y**3/15 + 462*y**2/5 + 1188*y. Fact