+ 4. Factor r*i**3 + 6*i**3 - 12*i**4 + 3*i**5 + 4*i**3 - 5*i**3.
3*i**3*(i - 3)*(i - 1)
Let h(n) = n**2 - n. Let g be h(3). Suppose b - 5*v = 7, -7 = -5*b - g*v + 3*v. What is k in b*k**2 + 7*k**2 + 9*k - 27 + 6*k**2 + 3*k**3 = 0?
-3, 1
What is b in -6 + 1/3*b**2 + 17/3*b = 0?
-18, 1
Let t(b) be the first derivative of 5*b**4/8 - 55*b**3/6 + 75*b**2/4 + 135*b/2 - 1869. Factor t(l).
5*(l - 9)*(l - 3)*(l + 1)/2
Let u(s) = -s**5 + 25*s**4 - 35*s**3 - 73*s**2 + 4. Let a(k) = 2*k**5 - 29*k**4 + 37*k**3 + 71*k**2 - 5. Let m(j) = 4*a(j) + 5*u(j). Solve m(h) = 0 for h.
-3, 0, 3
Let a(p) be the first derivative of p**4/2 - 326*p**3/3 + 7031*p**2 - 62410*p - 3003. Determine n, given that a(n) = 0.
5, 79
Let t = -29164/3 + 9722. Let j(v) be the first derivative of 11/5*v**5 + 12 - 46/3*v**3 + 8*v - 10*v**2 + t*v**6 - 11/4*v**4. Let j(c) = 0. Calculate c.
-2, -1, 1/4, 2
Let v(w) = -w**2 - w - 1. Let j(n) = 4*n**2 + 3*n + 5. Let i = 257 + -267. Let p(c) = i*v(c) - 2*j(c). Solve p(a) = 0 for a.
-2, 0
Factor 19/3*t + 0*t**2 + 10 - 1/3*t**3.
-(t - 5)*(t + 2)*(t + 3)/3
Let d(z) be the first derivative of -2*z**3 + 0*z - 9/20*z**5 + 7/2*z**2 - 3/2*z**4 - 1/20*z**6 + 5. Let w(y) be the second derivative of d(y). Factor w(j).
-3*(j + 2)**2*(2*j + 1)
Let d = 7665 + -252919/33. Let l = 1235/66 + d. Find o, given that 0 + 72*o**2 - 54*o - l*o**3 + 3/2*o**4 = 0.
0, 1, 6
Suppose -a + 68 = a. Let b(r) = 2*r + 54. Let j be b(-17). Suppose -a*k**3 + 17*k**3 + 12*k**3 - j*k**2 + 10*k**3 = 0. What is k?
0, 4
Suppose -619*h - 228 = -733*h. Factor 25/2*t**3 - 20 - 98*t - 115*t**h.
(t - 10)*(5*t + 2)**2/2
Let k(f) be the third derivative of 2*f**7/105 - 17*f**6/240 + f**5/60 + 5*f**2 + 5*f. Factor k(m).
m**2*(m - 2)*(8*m - 1)/2
Let q(m) be the second derivative of 0*m**3 + 13/60*m**6 + 0*m**2 + 1/12*m**4 + 1/21*m**7 + 11/40*m**5 + 0 - 52*m. Suppose q(p) = 0. Calculate p.
-2, -1, -1/4, 0
Let g(i) = i**3 + 380*i**2 + 376*i - 1134. Let x be g(-379). Let 36/7*t + 108/7 - 4/7*t**x - 12/7*t**2 = 0. Calculate t.
-3, 3
Let d(i) be the third derivative of -i**6/24 - 23*i**5/6 + 725*i**4/24 - 245*i**3/3 - 10*i**2 - 70*i. Factor d(j).
-5*(j - 2)*(j - 1)*(j + 49)
Solve 3*l**2 - 3734*l + 11226*l - 3743*l - 3728*l - 132 = 0 for l.
-11, 4
Suppose -7*w = 16 + 5. Let y be (-3)/2*w*1/9. Factor -k**2 + y*k + 1/2*k**3 + 0.
k*(k - 1)**2/2
Let h = 9910/3 - 59263/18. Let a = h + -58/9. Factor 3/4*m**2 - a*m + 27/4.
3*(m - 3)**2/4
Suppose -981*c - 136 = -1049*c. Factor -1/7*z + 1/7*z**c + 0.
z*(z - 1)/7
Let i = 1858 + -1770. Let w be i/12 - (-30 + 37). Factor -w*x**2 + 0 + 0*x + 1/6*x**3.
x**2*(x - 2)/6
Suppose 6*h = -4*y + 74, 0 = 3*h - 3*y + 16 - 43. Suppose 3*a + 3 = 5*n, 12*n - 4*a = h*n - 13. Suppose -9/2 + 3/2*j**2 - n*j = 0. What is j?
-1, 3
Let u(j) be the second derivative of j**4/36 + 19*j**3/6 - 29*j**2/3 + 2395*j. Let u(l) = 0. What is l?
-58, 1
Let o(g) be the third derivative of -g**7/105 - 43*g**6/84 - 263*g**5/105 + 2*g**4 - 2421*g**2. Suppose o(u) = 0. Calculate u.
-28, -3, 0, 2/7
Let n = -89284 + 178569/2. Solve 2*w - 21/2*w**2 + 14 - n*w**4 - 5*w**3 = 0.
-7, -2, 1
Suppose 61*b = 66*b - 25. Let h be (-1 + -5)*b/(-15). Factor -2*u**4 + 2*u + 0*u**3 + 1 + 6*u**3 - 1 - 6*u**h.
-2*u*(u - 1)**3
Let s = 45255 - 45255. Let c = -44 + 222/5. Suppose 0 - c*t**2 + 2*t**3 + s*t = 0. What is t?
0, 1/5
Let u(a) be the second derivative of a**4/12 - 55*a**3/2 + 163*a**2 - 7064*a. Suppose u(t) = 0. Calculate t.
2, 163
Let f(v) be the first derivative of 2*v**5/25 - 6*v**4/5 + 58*v**3/15 - 18*v**2/5 - 3066. Suppose f(q) = 0. What is q?
0, 1, 2, 9
Let b(f) be the second derivative of -75/7*f**3 + 6*f**2 + 0 - 11/14*f**4 - 159*f. Factor b(s).
-6*(s + 7)*(11*s - 2)/7
Let k = 959 - 955. Let n be (0 - (-1)/7) + 60/21. Factor 4/3*s**4 + k*s**n + 4/3*s + 4*s**2 + 0.
4*s*(s + 1)**3/3
Let b be ((-1340)/804)/(1/(-3)). Let p(t) be the third derivative of 0 + 0*t**3 + 5/24*t**4 + 1/12*t**b + 0*t + 14*t**2. Let p(d) = 0. Calculate d.
-1, 0
Let b(o) be the second derivative of 2*o**6/25 + 429*o**5/100 + 231*o**4/5 + 776*o**3/5 - 672*o**2/5 - o + 1367. Suppose b(l) = 0. Calculate l.
-28, -4, 1/4
Let h = -151088 + 1359794/9. Factor 5/3 + h*y - 1/9*y**2.
-(y - 5)*(y + 3)/9
Factor 1/5*m**2 - 28/5*m + 132/5.
(m - 22)*(m - 6)/5
Let j(f) be the second derivative of 41/114*f**4 - 17 - 3/95*f**6 - 2/19*f**5 + 64/57*f**3 + 2*f + 12/19*f**2. Solve j(k) = 0 for k.
-3, -1, -2/9, 2
Factor -9674 - 270315 - 289786 + 0*f**2 + 89575 - 2*f**2 + 1960*f.
-2*(f - 490)**2
Let j(t) be the first derivative of 0*t**2 + 0*t**4 - 2/3*t**3 + 1/180*t**6 + 0*t**5 + 0*t + 6. Let a(q) be the third derivative of j(q). Factor a(i).
2*i**2
Let g be (6/5)/(54 + (-37548)/700). Factor -5*y**2 - 5*y**3 + 35/3*y**4 + 0 - 5*y**5 + g*y.
-5*y*(y - 1)**3*(3*y + 2)/3
Let n(k) be the first derivative of -121/5*k**3 + 132/5*k**2 - 48/5*k + 161. Suppose n(t) = 0. What is t?
4/11
Let b be -52*(-54)/(-1170)*(-10)/16. Find l such that 6 - 3/4*l**2 - b*l = 0.
-4, 2
Let y = 569 + -567. Let 25 + 9*t - t**2 - y*t**2 - 31 = 0. What is t?
1, 2
Suppose 24*j - 627*j = -4337*j - 1667*j - 1244*j. Factor -16/5*t - 2/5*t**3 - 18/5*t**2 + j.
-2*t*(t + 1)*(t + 8)/5
Solve -339*z**3 + 912 - 8 + 468 + 1848*z**2 - 4704*z + 12*z**4 + 83*z**3 = 0.
1/3, 7
Let u = 8 + -4. Suppose -3 = -4*m + i, -m + 2*i = -2*i + 18. Determine z, given that 301 + 3*z**2 + z**m - 309 + u*z = 0.
-2, 1
Let d(l) be the second derivative of -l**7/210 - l**6/15 + l**5/50 + l**4/3 - l**3/30 - l**2 + 3055*l. What is p in d(p) = 0?
-10, -1, 1
Let n = 8 + -26. Let m = 21 + n. Factor -24*k**5 + 19*k**5 + 9*k**3 + 11*k**m.
-5*k**3*(k - 2)*(k + 2)
Factor 10/3*u**2 - 64/3 + 56/3*u - 2/3*u**3.
-2*(u - 8)*(u - 1)*(u + 4)/3
Let o(x) be the third derivative of x**6/120 - 11*x**5/15 + 63*x**4/8 + 39*x**3 - 11008*x**2. Find w such that o(w) = 0.
-1, 6, 39
Let y = -51073 - -510731/10. Factor 0 + 1/10*z**2 + 3/10*z**4 - 3/10*z**3 - y*z**5 + 0*z.
-z**2*(z - 1)**3/10
Let p(m) be the first derivative of 4*m**3/3 + 8792*m**2 + 19324816*m - 4608. Factor p(l).
4*(l + 2198)**2
Factor -4*p**2 + 2788 - 1117*p - 2182*p - 436*p + 951*p.
-4*(p - 1)*(p + 697)
Suppose -27*i = -5*i - 154. Let t = -30 - -45. Factor -11*b**4 - 10*b**2 + t*b**3 + 13*b**4 - i*b**3.
2*b**2*(b - 1)*(b + 5)
Let s(r) = 3*r**4 + 10*r**3 + 7*r**2 + 4*r - 6. Let g(b) = -8*b**4 - 30*b**3 - 22*b**2 - 14*b + 21. Let c(h) = -2*g(h) - 7*s(h). Factor c(v).
-5*v**2*(v + 1)**2
Let x = 45070 + -180265/4. Solve x*t**2 + 3/8*t**5 - 15/8*t**3 + 3/2*t - 3 - 3/4*t**4 = 0 for t.
-2, -1, 1, 2
Factor -81*v - 2*v**3 + 5*v**3 - 53 + 79*v + 132*v**2 - 79 - v**3.
2*(v - 1)*(v + 1)*(v + 66)
Let y(t) be the second derivative of -95*t**4/12 + 5885*t**3/3 + 620*t**2 + 3*t - 17. Find o, given that y(o) = 0.
-2/19, 124
Let l(j) be the first derivative of j**4/8 + 98*j**3 - 591*j**2 + 1184*j + 10630. Determine a so that l(a) = 0.
-592, 2
Let m = 434 + -194. Let u = m + -471/2. Factor -3/2*y - 3/2*y**4 - u*y**3 + 0 - 9/2*y**2.
-3*y*(y + 1)**3/2
Let u(m) be the first derivative of m**4/18 - 11*m**3/9 - 98*m + 6. Let z(n) be the first derivative of u(n). Factor z(b).
2*b*(b - 11)/3
Let v be (39/208)/(10/(-8))*(-4)/18. Let w(a) be the second derivative of -1/9*a**3 + 2*a - 1/18*a**4 + 0 + v*a**5 + 0*a**2 + 1/45*a**6. Factor w(p).
2*p*(p - 1)*(p + 1)**2/3
Suppose -164/3 - 2/9*y**3 - 322/9*y + 56/3*y**2 = 0. Calculate y.
-1, 3, 82
Let j be 2/19*(30 + (-4 - 7)). Let d(f) be the third derivative of 16*f**j - 1/156*f**4 + 0*f + 0 + 1/39*f**3 + 1/780*f**6 - 1/390*f**5. Factor d(r).
2*(r - 1)**2*(r + 1)/13
Let d be 38/(-95)*28695/33. Let i = d + 348. Determine k, given that 0*k**2 - i*k**3 + 0*k + 0 = 0.
0
Let v(o) be the third derivative of -o**5/30 - 479*o**4/6 - 229441*o**3/3 - 2*o**2 + 1033*o. Solve v(u) = 0.
-479
Let j(l) be the first derivative of l**5/10 + 2*l**4/3 - l**3/3 - 4*l**2 + 95*l + 27. Let d(x) be the first derivative of j(x). Factor d(n).
2*(n - 1)*(n + 1)*(n + 4)
Let x(t) = -3*t**3 + 116*t**2 - 1522*t + 6592. Let u(m) = -m + 8. Let o be u(6). Let g(r) = 689*r + o - 3 + r**2 - 688*r. Let f(a) = g(a) + x(a). Factor f(k).
-3*(k - 13)**3
Let w = 358 + -355. Let d(r) be the first derivative of -30*r + 5/3*r**w + 2 - 5/2*r**2. Find k such that d(k) = 0.
-2, 3
Solve 23*r**2 - 167*r**3 +