d(u) be the first derivative of u - 3 + 0*u**3 - 1/5*u**5 + u**2 - 1/2*u**q. Factor d(k).
-(k - 1)*(k + 1)**3
Let k be 5 + -2*6/(-16)*-4. Let q(p) be the second derivative of -8*p - 1/18*p**4 + 2/9*p**3 - 1/3*p**k + 0. What is n in q(n) = 0?
1
Let y(i) = -40*i**3 + 160*i**2 + 465*i + 265. Let o(v) = 23*v + 655 - 622 + 20*v**2 + v + 34*v - 5*v**3. Let b(s) = -25*o(s) + 3*y(s). Factor b(w).
5*(w - 6)*(w + 1)**2
Let k(x) be the third derivative of x**9/40320 + x**8/4480 + x**7/1120 + x**6/480 + 4*x**5/15 - 11*x**2. Let s(b) be the third derivative of k(b). Factor s(d).
3*(d + 1)**3/2
Let l(w) = -5*w + 122. Let o be l(24). Suppose -5*r = 5*u - 45 + 15, o*u - 21 = -5*r. Factor -1/4*t**4 - 4*t - 9*t**2 + 16 - 11/4*t**r.
-(t - 1)*(t + 4)**3/4
Let m be (-1 + 3)*1*1. Suppose -5*i + 30 = 5*y, -266*i = -262*i - 2*y - 12. Suppose 0 - 2/11*p**i - 2/11*p**5 + 2/11*p**m + 0*p + 2/11*p**3 = 0. Calculate p.
-1, 0, 1
Factor -8/5*k + 12/5*k**3 + 0 + 6/5*k**2 - 2*k**4.
-2*k*(k - 1)**2*(5*k + 4)/5
Suppose -15*d + 7 = 7*d - 37. Factor 76/13*h - 18/13*h**d - 16/13.
-2*(h - 4)*(9*h - 2)/13
Determine w so that 4/7*w - 2/7*w**4 - 30/7 + 32/7*w**2 - 4/7*w**3 = 0.
-5, -1, 1, 3
Solve -54007 - 763*t**4 - 12839*t**3 + 233692 + 16335*t - 3491*t**3 + 268*t**4 - 179190*t**2 - 5*t**5 = 0 for t.
-33, -1, 1
Suppose 124 - 347 = -5*f + 2*a, -4*f + 164 = 2*a. Suppose -17*x - 321 + 300 - 12*x**3 - f*x - 54*x**2 + 3*x**4 = 0. Calculate x.
-1, 7
Factor 196/5 - 238/5*t - 6/5*t**3 - 16*t**2.
-2*(t + 7)**2*(3*t - 2)/5
Suppose -2 + 0*x**2 - 5/2*x + 1/8*x**4 + 5/8*x**3 = 0. Calculate x.
-4, -2, -1, 2
Let t(k) be the first derivative of 3 + 4*k - 1/10*k**5 + 0*k**3 + 0*k**4 + 0*k**2. Let r(g) be the first derivative of t(g). Let r(p) = 0. What is p?
0
Suppose 9*r = 7*r + 2*i, 2*i + 2 = 3*r. Let t = 4 - 4. Factor -2/9*u**4 - 2/9*u**3 + t*u**r + 0 + 0*u.
-2*u**3*(u + 1)/9
Let d(g) be the first derivative of -g**4 - 112*g**3/3 - 392*g**2 - 373. Determine f, given that d(f) = 0.
-14, 0
Suppose -11*x = -10*x - 2. Factor p**4 + 23*p**3 - 47*p**3 + 24*p**3 - p**x.
p**2*(p - 1)*(p + 1)
Let n(i) be the second derivative of 1/6*i**3 + i**2 + 0 - 1/4*i**4 + 1/30*i**6 + 27*i - 1/20*i**5. Factor n(a).
(a - 2)*(a - 1)*(a + 1)**2
Let -30 + 87*y**3 - 40*y**2 - 70*y**2 + 115*y - 62*y**3 = 0. Calculate y.
2/5, 1, 3
Let g(p) = 5*p - 43. Let l be g(9). Let x(k) be the first derivative of 3*k**5 - 12*k**l + 0*k + 27/2*k**4 + 12*k**3 - 3. Factor x(i).
3*i*(i + 2)**2*(5*i - 2)
Let g(n) be the second derivative of 0 + 54*n + 9/7*n**2 + 1/28*n**4 - 5/14*n**3. Suppose g(l) = 0. Calculate l.
2, 3
Let s(l) = -49*l + 1078. Let u be s(22). Let h + 1/5*h**2 + u = 0. Calculate h.
-5, 0
Let l be (-10)/(-1) - (-3 - 0). Let m = 2 + l. Find w, given that -w**5 - 13 - 17*w + 4 - 46*w**2 - 3*w**5 - 31*w + m*w**4 + 12*w**3 = 0.
-1, -1/4, 3
Let q be (1 - 1)*(-7)/14*1. Solve 5*a + q - 1/2*a**2 = 0 for a.
0, 10
Let b(z) = 16*z**5 - 39*z**4 - 114*z**3 + 95*z**2 + 34*z + 4. Let f(s) = s**5 + s**4 + s**3 - s - 1. Let u(t) = b(t) + 4*f(t). Solve u(o) = 0 for o.
-2, -1/4, 0, 1, 3
Factor 8*j**3 - 8*j**3 + 3*j**3 - 3*j.
3*j*(j - 1)*(j + 1)
Factor 2*i**3 + 36*i - 34*i**2 + 14*i - 18*i.
2*i*(i - 16)*(i - 1)
Let p(r) = r**2 + 17*r + 40. Let j be p(-23). Let c = j - 1240/7. Factor 2/7*t**4 + 0*t - c*t**3 + 4/7*t**2 + 0.
2*t**2*(t - 2)*(t - 1)/7
Let w be -1*((-87)/(-12) - (-3)/(-12)). Let n(l) = 6*l**2 - 12*l - 5. Let c(d) = 9*d**2 - 18*d - 7. Let g(k) = w*n(k) + 5*c(k). Factor g(a).
3*a*(a - 2)
Let p = -5/596 + 1207/1788. Let m(o) be the second derivative of p*o**3 + 2/3*o**4 - 2/21*o**7 + 0*o**2 + 0*o**5 + 0 - 4/15*o**6 + 6*o. Factor m(g).
-4*g*(g - 1)*(g + 1)**3
Factor 0*n - 1/5*n**5 + 3/5*n**4 + 1/5*n**2 - 3/5*n**3 + 0.
-n**2*(n - 1)**3/5
Let g = 22833 + -22830. Factor -2/7*r**g + 26/7*r + 20/7 + 4/7*r**2.
-2*(r - 5)*(r + 1)*(r + 2)/7
Let q(o) = o + 0 + 4*o - 6*o + 6. Let t be q(6). Suppose 0*r**2 + 0 - 16/7*r + 8/7*r**3 - 1/7*r**5 + t*r**4 = 0. Calculate r.
-2, 0, 2
Let s = -4/3719 + -2383863/14876. Let u = s - -161. What is r in u*r**2 - 3/4*r + 0 = 0?
0, 1
Let u be 51/15 + (-24)/(-192)*-24. Solve 0 + 6/5*d**2 + u*d = 0 for d.
-1/3, 0
Let h = -2 + 4. Factor 118*l**3 + 8*l + 107*l**3 + 12*l**h - 225*l**3 - 4*l**4.
-4*l*(l - 2)*(l + 1)**2
Let f = -302 + 302. Let a(r) be the second derivative of 1/12*r**3 + 1/2*r**2 + 8*r - 1/8*r**4 + f - 1/40*r**5 + 1/60*r**6. Suppose a(n) = 0. Calculate n.
-1, 1, 2
Suppose -5*h - 79 = -y + 18, 5*y - 459 = -h. Factor 24*d**2 + 48*d + 98*d**3 - 187*d**3 + y*d**3.
3*d*(d + 4)**2
Let i = -59/55 - -14/11. Let d = -1913 - -1915. Find w such that -3/5*w**3 + w**d - i - 4/5*w**4 + 3/5*w = 0.
-1, 1/4, 1
Let y(i) be the second derivative of -i**6/240 + 3*i**5/80 + 2*i**3/3 - 4*i. Let l(u) be the second derivative of y(u). Factor l(k).
-3*k*(k - 3)/2
Let f(t) = -3*t**2 - 2*t - 2. Let p be f(-2). Let z = p + 11. Find y such that 1/2*y**2 - 1/2*y - z = 0.
-1, 2
Factor -27/7*b**2 - 345/7*b + 78/7.
-3*(b + 13)*(9*b - 2)/7
Let g be 54/13 + 18/(-117). Factor -g*w**3 - 4*w**4 - w**2 + 4*w + 2*w**4 + 0*w + 3*w**2.
-2*w*(w - 1)*(w + 1)*(w + 2)
Let u(w) be the second derivative of 5*w**7/7 + 262*w**6/15 + 531*w**5/5 - 404*w**4/3 - 231*w**3 + 162*w**2 - 269*w - 1. Let u(v) = 0. Calculate v.
-9, -2/3, 1/5, 1
Let f = 998 + -993. Let y(t) be the third derivative of -1/15*t**f + 0 - 1/24*t**4 + 5*t**2 + 0*t + 0*t**3. Factor y(l).
-l*(4*l + 1)
Let u(f) be the third derivative of -f**7/840 + f**6/96 - f**5/48 - 5*f**4/96 + f**3/4 + 3*f**2 + 82. Find w such that u(w) = 0.
-1, 1, 2, 3
Let m(g) be the second derivative of 5*g**4/24 + 20*g**3 + 720*g**2 + 5*g + 4. Factor m(z).
5*(z + 24)**2/2
Find n such that 0 + 1/3*n**4 + 5/3*n**3 - 1/3*n**2 - 5/3*n = 0.
-5, -1, 0, 1
Let v = -2671 - -13367/5. Factor 363/5*u**2 + 132/5*u + v.
3*(11*u + 2)**2/5
Factor 1/3*r**2 - 1 + 2/3*r.
(r - 1)*(r + 3)/3
Suppose 7*h = 2*h + 20. Factor -28*d**h - 10*d + 2*d - 3*d + 48*d**3 - 12*d**2 + 3*d.
-4*d*(d - 1)**2*(7*d + 2)
Let l(o) be the second derivative of o**7/14 - 9*o**6/10 + 21*o**5/20 + 9*o**4/4 - 4*o**3 - 53*o. Factor l(r).
3*r*(r - 8)*(r - 1)**2*(r + 1)
Let f(d) = 13*d**2 - 23*d - 20. Let y(m) = m**2 - m. Let x(u) = -f(u) + 6*y(u). Let p(v) = -155*v**2 + 375*v + 440. Let i(n) = -2*p(n) + 45*x(n). Factor i(s).
-5*(s - 4)*(s + 1)
Let l(n) = n**5 + n**4 - 1. Let h(p) = 2*p**4 - 4 - 9*p + 2*p**3 - 2*p**5 - 22*p**2 - 15*p + 2*p**3 - 6*p**3. Let b(w) = -h(w) - 4*l(w). Factor b(x).
-2*(x - 2)*(x + 1)**3*(x + 2)
Let j be 4 - (-2 + 3)/1. Suppose 4*f - 3*g - 1 = 0, f + 1 = 815*g - 814*g. Suppose -1/3*r**f + 0*r**2 - 2/3*r**j + 1/3 + 2/3*r = 0. What is r?
-1, 1
Let g(d) = -8*d**2 - 59*d + 135. Let u(b) = -30*b**2 - 237*b + 539. Let k(w) = 22*g(w) - 6*u(w). What is l in k(l) = 0?
-33, 2
Let l(t) be the second derivative of 9/2*t**2 - 1/12*t**4 + 0 - 7*t + 0*t**3. Determine j so that l(j) = 0.
-3, 3
Let d(h) = 7*h + 10. Let b(w) = -2*w. Let n(p) = 6*b(p) + 2*d(p). Let r be n(-9). Factor -10*x - 4*x**2 + 5*x**2 - x**r + 5*x**2.
5*x*(x - 2)
Let j(y) be the third derivative of 1/42*y**4 - 1/140*y**5 - 1/420*y**6 + 0 - 8*y**2 + 2/21*y**3 + 0*y + 1/1470*y**7. Factor j(d).
(d - 2)**2*(d + 1)**2/7
Solve -50/3*f**2 - 2/3*f**3 + 338/3 - 286/3*f = 0 for f.
-13, 1
Factor -7*w**4 - 4*w**3 + 8643*w**5 - 8642*w**5 + 16*w**2 - 6*w**3.
w**2*(w - 8)*(w - 1)*(w + 2)
Let p = 29020/13 - 2232. Suppose -2 = 3*s - 8. Suppose -p*v - 2/13*v**s + 0 = 0. What is v?
-2, 0
Let g(y) be the first derivative of -3/8*y**4 + 0*y**2 + 1/3*y**3 + 0*y + 16 + 1/10*y**5. Find m, given that g(m) = 0.
0, 1, 2
Let j(h) be the third derivative of -h**5/180 + 5*h**4/24 - 2*h**3 + 196*h**2. Suppose j(a) = 0. What is a?
3, 12
Let w(a) be the second derivative of a**5/10 + a**4/2 + 2*a**3/3 + 247*a. Determine u so that w(u) = 0.
-2, -1, 0
Factor -8/5*f**2 - 16/5*f**3 + 9/5 + 3*f.
-(f - 1)*(4*f + 3)**2/5
Let f(j) be the first derivative of j**6/9 - 2*j**5/5 + j**4/3 + 4*j**3/9 - j**2 + 2*j/3 - 13. Factor f(b).
2*(b - 1)**4*(b + 1)/3
Let q(g) be the third derivative of -1/105*g**5 + 0*g**3 + 0 + 0*g + 2/21*g**4 + 16*g**2. Let q(t) = 0. Calculate t.
0, 4
Let r be -4 + 0 - (11 + -20). Let j = 8 - r. Factor -6*n**2 + 11*n**2 - n**4 - 2*n - 4*n**2 + 3*n**j - n**5.
-n*(n - 1)**2*(n + 1)*(n + 2)
Let p = 0 - -2. L