**4/5 + 15552*z**3/5 + 15*z**2 - 3*z. Factor a(u).
2*(u + 36)**3/5
Let q be 7 + (-4 - -1) + 2. Let v be -3 - (-4)/4*q. Let u**5 + 3*u - 3*u - 10*u**v + 9*u**3 = 0. Calculate u.
-1, 0, 1
Let g(f) be the second derivative of f**6/90 - 3*f**5/20 + 3*f**4/4 - 31*f**3/18 + 2*f**2 - 810*f. Factor g(s).
(s - 4)*(s - 3)*(s - 1)**2/3
Let h(q) be the second derivative of q**7/273 - q**6/39 + 3*q**5/130 + 3*q**4/26 - 242*q. Factor h(o).
2*o**2*(o - 3)**2*(o + 1)/13
Let 13/4*p**3 - 7/2*p**2 + 0 - 6*p + 1/2*p**4 - 1/4*p**5 = 0. What is p?
-3, -1, 0, 2, 4
Let g(y) be the first derivative of 1/10*y**5 + 0*y - 3 + 0*y**3 - 1/8*y**4 + 1/2*y**2. Let w(i) be the second derivative of g(i). Factor w(u).
3*u*(2*u - 1)
Let m(f) be the third derivative of f**7/945 + 7*f**6/540 + f**5/18 + 13*f**4/108 + 4*f**3/27 + 852*f**2. Find a, given that m(a) = 0.
-4, -1
Suppose 723 = 122*t + 357. Factor 13/3*b - 1/3*b**t - 5*b**2 + 5/3*b**4 - 2/3.
(b - 1)**2*(b + 2)*(5*b - 1)/3
Let a(s) be the first derivative of 2/15*s**3 + 0*s + 2/5*s**2 + 13. What is v in a(v) = 0?
-2, 0
Suppose 2*t + 5*x - 689 = -634, 86 = 3*t + 4*x. Factor 0 - 5/2*r**4 + 0*r**3 + 65/2*r**2 + t*r.
-5*r*(r - 4)*(r + 1)*(r + 3)/2
Let c(g) be the second derivative of g**5/20 + 13*g**4/6 + 70*g**3/3 - 196*g**2 - 475*g. Solve c(z) = 0 for z.
-14, 2
Let f be (-3 - 4) + (-120)/16*(-1 + 0). Factor f*c**3 - 1/3 - 5/6*c + 2/3*c**2.
(c - 1)*(c + 2)*(3*c + 1)/6
Let h(u) be the third derivative of -u**6/300 - 13*u**5/150 - 43*u**2. Find q such that h(q) = 0.
-13, 0
Let g(r) be the second derivative of r**5/60 - 5*r**4/36 - 11*r**3/9 + 28*r**2/3 - 308*r. Let g(k) = 0. Calculate k.
-4, 2, 7
Let b(z) be the first derivative of -5*z**4/4 - 595*z**3/3 - 17995*z**2/2 - 17405*z + 57. Factor b(u).
-5*(u + 1)*(u + 59)**2
Factor -2 + 561*i**3 - 570*i**3 + 147*i**2 + 101*i + 19.
-(i - 17)*(3*i + 1)**2
Let j(s) be the third derivative of 0*s + 1/112*s**8 + 0*s**4 + 0 + 0*s**3 + 0*s**6 - 18*s**2 + 0*s**5 - 1/70*s**7. Solve j(p) = 0 for p.
0, 1
Let h(a) = 3*a**2 + 11*a - 18. Let m be h(-5). Factor -29*u**3 - 11 - 64*u - 7*u**3 + 96*u**m + 4*u**4 + 11.
4*u*(u - 4)**2*(u - 1)
Let c(i) be the third derivative of i**7/42 + i**6/2 - i**5/12 - 5*i**4/2 + 116*i**2. Factor c(w).
5*w*(w - 1)*(w + 1)*(w + 12)
Let y(o) = -o**5 + o**4 - o**3 - o**2. Let i(u) = 5*u**5 + 10*u**4 + 11*u**3 - 10*u**2 - 12*u. Let c(g) = i(g) + 2*y(g). Factor c(b).
3*b*(b - 1)*(b + 1)*(b + 2)**2
Let c be (21 - 10) + -3 + 10*(-4)/8. What is o in c*o + 4/5 + 7/10*o**2 = 0?
-4, -2/7
Let s(y) be the third derivative of y**9/272160 - y**8/15120 + y**7/2520 - y**5/20 + y**2 + 20*y. Let i(h) be the third derivative of s(h). Factor i(d).
2*d*(d - 3)**2/9
Let w(i) = 1389*i - 1387. Let u be w(1). Find j, given that -6/17*j + 10/17*j**u - 4/17 = 0.
-2/5, 1
Let h(x) be the second derivative of -7*x**6/1800 + x**5/50 + x**4/30 + 6*x**3 + 45*x. Let d(b) be the second derivative of h(b). Factor d(v).
-(v - 2)*(7*v + 2)/5
Let s(o) be the first derivative of -o**3/5 + 9*o**2/10 + 54*o/5 - 163. Let s(k) = 0. What is k?
-3, 6
Let i(r) be the third derivative of -r**6/120 + r**5/20 + 3*r**4/8 - 5*r**3/3 + 3*r**2. Let c(l) be the first derivative of i(l). What is h in c(h) = 0?
-1, 3
Let q(m) be the third derivative of m**6/840 - m**5/84 - 15*m**2. Factor q(t).
t**2*(t - 5)/7
Suppose 540 = -11*z - 285. Let s = 75 + z. Factor -4/5*f**3 + 2/5*f**4 + 2/5*f**2 + s + 0*f.
2*f**2*(f - 1)**2/5
Let q = 25 + -23. Let w(i) = -i - 7 + 4*i**q + 7 - 3*i**2. Let s(x) = 2*x**3 + 8*x**2 - 10*x. Let c(l) = s(l) - 10*w(l). Factor c(b).
2*b**2*(b - 1)
Let w(n) = -4*n**2 + 668*n - 52486. Let o(x) = 9*x**2 - 1346*x + 104971. Let p(a) = -2*o(a) - 5*w(a). Find z, given that p(z) = 0.
162
Let g(l) = 11*l**2 + 54*l. Let i(o) = 3*o**2 + 18*o. Let c(b) = 2*g(b) - 7*i(b). Suppose c(r) = 0. What is r?
0, 18
Let b be 2/(-3) + (-628)/(-936). Let n = b + 2101/1170. Factor -6/5*j + n - 3/5*j**2.
-3*(j - 1)*(j + 3)/5
Let v be -3*(-2)/12 - 10/4. Let x be (v + -1)/(45/(-6)). Solve 4/5*c + 2/5*c**2 + x = 0.
-1
Suppose 200/11*l + 1250/11 + 8/11*l**2 = 0. Calculate l.
-25/2
Let a(k) be the second derivative of 0*k**3 + 0*k**4 - 2/45*k**6 + 0*k**2 + 1/30*k**5 - 5/252*k**7 + 0 + 6*k. Suppose a(f) = 0. Calculate f.
-2, 0, 2/5
Let v(m) be the second derivative of -7/48*m**4 + 1/2*m**2 + 1/2*m**3 + 12*m + 0. Suppose v(s) = 0. What is s?
-2/7, 2
Suppose 2*w = s + 11, 5*w - 15 = 4*s + 17. Suppose 0 = 3*v + m - 10, -w*v - m + 2*m + 18 = 0. Factor -1 + 2*c**2 - 1 - v*c**2 + 4.
-2*(c - 1)*(c + 1)
Find m such that 48*m**2 - 15*m**3 + 3499*m - 3379*m - 5*m**4 - 3*m**2 + 5*m**2 = 0.
-4, -2, 0, 3
Let a(f) be the first derivative of -2*f**5/45 - 11*f**4/18 + 2*f**3 + 11*f**2/9 - 52*f/9 + 209. Suppose a(n) = 0. What is n?
-13, -1, 1, 2
Let k(w) be the second derivative of 5*w**4/48 - w**3/24 - 4*w + 3. Factor k(d).
d*(5*d - 1)/4
Let u = 213/260 - 10/13. Let q(i) be the second derivative of -u*i**5 + 1/4*i**4 + 0 - 1/3*i**3 - 6*i + 0*i**2. Suppose q(s) = 0. What is s?
0, 1, 2
Let k(o) be the first derivative of -5*o**5/3 + 115*o**4/4 - 88*o**3/3 + 26*o**2/3 - 8. Determine q, given that k(q) = 0.
0, 2/5, 13
Let u be 12 - 5 - 3*1. Suppose 0*m = -2*x + m + 10, u*m + 31 = 5*x. Factor -4/11*c**x + 0*c**2 + 4/11*c - 2/11 + 2/11*c**4.
2*(c - 1)**3*(c + 1)/11
Factor -4*k**3 - 112*k + 2*k**2 + 56*k + 55*k + 3*k**3.
-k*(k - 1)**2
Let f(z) be the third derivative of -z**9/24192 + z**8/13440 + 23*z**3/6 - 15*z**2. Let g(l) be the first derivative of f(l). Let g(i) = 0. Calculate i.
0, 1
Let l be (-238)/40 - (-17 + 11). Let d(k) be the second derivative of -l*k**4 - 6/5*k**2 + 3*k + 0 - 2/5*k**3. Factor d(v).
-3*(v + 2)**2/5
Determine i so that 34 - 2/5*i**2 + 24/5*i = 0.
-5, 17
Let x(i) be the second derivative of 0*i**2 + 5/3*i**3 + 0 + 8*i + 1/6*i**6 - 3/4*i**5 + 5/42*i**7 - 5/12*i**4. Find y, given that x(y) = 0.
-2, -1, 0, 1
Suppose 0 = 64*l + 35*l - 20*l - 237. What is s in -2/13*s**l - 4/13 + 2/13*s + 4/13*s**2 = 0?
-1, 1, 2
Let q(l) = -l**2 - 3*l - 1. Let p(o) = -2*o**2 - 4*o - 1. Let d(x) = 2*p(x) - 3*q(x). Let w(s) = 18*s**2 - 21*s - 15. Let b(i) = 15*d(i) + w(i). Factor b(h).
3*h*(h - 2)
Let p = -7288 - -7290. Find t, given that -4/3 + 16/9*t - 4/9*t**p = 0.
1, 3
Suppose 24*h + 121 = 289. Let k(t) be the third derivative of 0 + 0*t - 1/180*t**6 + 0*t**5 - t**2 + 0*t**3 + 0*t**4 + 1/315*t**h. Factor k(m).
2*m**3*(m - 1)/3
Let b(z) be the third derivative of -z**8/896 + 33*z**7/560 - 29*z**6/160 - 33*z**5/40 + 31*z**4/8 + 3*z**2 - 69*z. Solve b(s) = 0 for s.
-2, 0, 2, 31
Suppose -3*i + 1 - 10 = -j, 21 = 2*j - 3*i. Let -j*g**3 - 2*g**4 - 2*g - 8*g**2 - 2*g**5 + 0*g**5 - 6*g**4 = 0. What is g?
-1, 0
Factor 2/15*t**2 + 0 + 2/15*t - 2/15*t**3 - 2/15*t**4.
-2*t*(t - 1)*(t + 1)**2/15
Let x be (129/(-3440))/(14/8 + -2). Let n(w) be the second derivative of 1/4*w**4 - x*w**5 + 3*w + 0 + 1/2*w**3 - 3/2*w**2. Factor n(f).
-3*(f - 1)**2*(f + 1)
Let y(j) be the first derivative of -13 - 1/16*j**4 - 1/10*j**5 + 0*j**3 - 1/24*j**6 + 0*j + 0*j**2. Factor y(c).
-c**3*(c + 1)**2/4
Let o be ((-25)/15*-3)/1. Suppose 0*y - y + 20 = 5*v, 2*v = -o*y + 31. Factor -38 - 4*i**4 - v*i - 5*i + 42 + 8*i**3.
-4*(i - 1)**3*(i + 1)
Let x(t) be the second derivative of -t**5/4 + 5*t**4/12 + 5*t**3 + 95*t. Let x(q) = 0. Calculate q.
-2, 0, 3
Let t = -16350 + 408696/25. Let j = 84/25 + t. Let j*o**3 + 0*o**2 + 0 - 8/5*o - 2/5*o**4 = 0. What is o?
-1, 0, 2
Let o(h) be the third derivative of -1/200*h**6 + 1/40*h**4 + 0*h - 1/5*h**3 + 1/50*h**5 + 0 - 34*h**2. Factor o(v).
-3*(v - 2)*(v - 1)*(v + 1)/5
Let i(n) = -6*n**3 + 753*n**2 - 4839*n + 9873. Let y(v) = -v**3 + 137*v**2 - 880*v + 1795. Let k(w) = -5*i(w) + 27*y(w). Factor k(u).
3*(u - 12)*(u - 5)**2
Let o = -2922 - -2924. Factor -3 + 3/2*h + 6*h**o - 9/2*h**3.
-3*(h - 1)**2*(3*h + 2)/2
Let h be 5 + (5 - 1)/(-4). Factor 6*m + 17*m**2 - 9*m**3 + 3*m**5 - h*m**4 - 14*m**2 + m**4.
3*m*(m - 2)*(m - 1)*(m + 1)**2
Let z(g) = -1128*g - 6768. Let y be z(-6). Let y + 1/2*m + m**2 + 1/2*m**3 = 0. Calculate m.
-1, 0
Let u(j) be the second derivative of 38*j**7/105 - 41*j**6/15 + 377*j**5/50 - 131*j**4/15 + 44*j**3/15 + 8*j**2/5 + 2*j - 33. What is a in u(a) = 0?
-2/19, 1/2, 1, 2
Let l(n) = 3*n**2 + 2*n - 8. Let c be l(-4). Let o = -32 