**3 + 5*y**2 + 2*y**4. Let d(t) = 3*q(t) - 5*z(t). Factor d(b).
b**3*(b + 1)
Let o(f) be the first derivative of -f**3 - 24*f**2 - 192*f - 19. Factor o(r).
-3*(r + 8)**2
Let h be ((-48)/64)/(9/(-24)). Let m(p) be the second derivative of 0 + 6*p - 7/6*p**4 - p**3 + 3/10*p**5 + 2*p**h + 1/3*p**6. Let m(s) = 0. Calculate s.
-1, 2/5, 1
Let v(t) be the first derivative of 2*t**3/3 - 5*t**2 + 12*t - 69. Find s such that v(s) = 0.
2, 3
Let d(o) = 14*o**2 + 906*o - 895. Let a(k) = 6*k**2 + 452*k - 448. Let i(n) = -5*a(n) + 2*d(n). Factor i(b).
-2*(b - 1)*(b + 225)
Let k(t) be the first derivative of t**4/40 - t**3/5 - 52. Factor k(m).
m**2*(m - 6)/10
Let 5 + 23/5*q**3 + 81/5*q**2 + 2/5*q**4 + 17*q = 0. What is q?
-5, -1, -1/2
Let m = -100/13 - -1513/195. Let g(h) be the first derivative of m*h**6 + 1/5*h**2 + 5 + 4/15*h**3 - 1/5*h**4 - 2/5*h - 2/25*h**5. Factor g(r).
2*(r - 1)**3*(r + 1)**2/5
Let -26*q + 2*q**2 - 231 + 105 + 98 = 0. What is q?
-1, 14
Factor f**2 + 18/7*f + 0 - 1/7*f**3.
-f*(f - 9)*(f + 2)/7
Let h(k) be the first derivative of -5/3*k**2 + 1/9*k**3 + 3*k + 6. Factor h(m).
(m - 9)*(m - 1)/3
Factor -3*u**3 + 3*u**2 - 3 + 12*u - 23*u + 14*u.
-3*(u - 1)**2*(u + 1)
Let d be -1 + (-2)/4*424/(-36). Factor 16/3*r**4 + d*r**3 + 2/9*r + 16/9*r**2 + 2*r**5 + 0.
2*r*(r + 1)**2*(3*r + 1)**2/9
Let j(a) = 12*a**2 + 672*a - 279. Let v(c) = 5*c**2 + 334*c - 139. Let b(f) = 5*j(f) - 9*v(f). Let b(i) = 0. Calculate i.
-24, 2/5
Let x(f) = -19*f**2 + 59*f - 87. Let o(a) = 9*a**2 - 29*a + 42. Let i(k) = 9*o(k) + 4*x(k). Factor i(b).
5*(b - 3)*(b - 2)
Let l(c) be the first derivative of -5*c**6/6 - 17*c**5 - 75*c**4/2 + 10*c**3/3 + 155*c**2/2 + 75*c - 4. Let l(i) = 0. What is i?
-15, -1, 1
What is m in -196*m**4 + 56*m**4 - 140*m - 349*m**3 - 38*m**5 + 634*m**3 + 260*m**2 + 13*m**5 = 0?
-7, -1, 0, 2/5, 2
Let a = -26 - -31. Suppose -7*c = -a - 30. Determine t so that 13/4*t**2 - 1/2*t - 13/4*t**4 - 9/4*t**3 + 11/4*t**c + 0 = 0.
-1, 0, 2/11, 1
Let y(v) = -v**5 - 8*v**4 + 6*v**3 - v. Let k(m) = 3*m**5 + 14*m**4 - 13*m**3 + 3*m. Let n(j) = -4*k(j) - 7*y(j). Factor n(g).
-5*g*(g - 1)**2*(g + 1)**2
Suppose 0 = 4*j + t - 13, 0*j + 4*j + 7 = 3*t. Let f be 3/4 + 0 + 2 - j. Factor -13/4*a**3 - 17/4*a**2 - 3/4*a + 1/2 + f*a**4 + a**5.
(a - 2)*(a + 1)**3*(4*a - 1)/4
Let r be 6/6*((-20)/4 + 7). Factor 3*z - 1/2*z**r - 9/2.
-(z - 3)**2/2
Suppose -v = 4*v + 4*v. Let f(k) be the first derivative of 4/3*k**6 + k**2 + 15/2*k**4 + 26/5*k**5 + v*k + 3 + 14/3*k**3. Factor f(q).
2*q*(q + 1)**3*(4*q + 1)
Let o be 160/220 + 64/(-88). Suppose 0 - 1/6*b**4 + o*b - 1/3*b**3 - 1/6*b**2 = 0. Calculate b.
-1, 0
Let q(f) be the third derivative of -1/2*f**4 - 4/3*f**3 - 14*f**2 - 1/15*f**5 + 0*f + 0. Factor q(r).
-4*(r + 1)*(r + 2)
Let x = -22 - -27. Factor -5*u**5 - x*u**3 + 2*u**3 + 4*u**3 + 4*u**3.
-5*u**3*(u - 1)*(u + 1)
Let n(q) be the third derivative of 1/120*q**6 + 1/1008*q**8 + 0*q**3 - 2*q**2 + 2/315*q**7 + 0*q - 1/45*q**5 + 0 - 1/18*q**4. Factor n(r).
r*(r - 1)*(r + 1)*(r + 2)**2/3
Factor -15/2*u**3 + 0 - 18*u - 48*u**2.
-3*u*(u + 6)*(5*u + 2)/2
Let h = 2193 - 2193. Factor 0*j - 3/5*j**5 + h + 0*j**2 + 0*j**3 + 1/5*j**4.
-j**4*(3*j - 1)/5
Let i(c) be the third derivative of c**8/4032 + c**7/840 - c**6/1080 - 5*c**4/4 - 10*c**2. Let d(r) be the second derivative of i(r). Factor d(g).
g*(g + 2)*(5*g - 1)/3
Let r = -2565 + 12841/5. Factor -2/5*n**2 + r*n - 32/5.
-2*(n - 4)**2/5
Find u, given that -12*u**3 + 0*u - 35/2*u**4 + 0 - 2*u**2 = 0.
-2/5, -2/7, 0
Suppose -201 = -3*r + 2*r. Let p = r - 197. Determine j, given that -2/3*j - 4/3*j**2 + 2/3*j**5 + 0 + 0*j**3 + 4/3*j**p = 0.
-1, 0, 1
Factor 96/5 + 3/5*i**3 + 36/5*i**2 + 108/5*i.
3*(i + 2)**2*(i + 8)/5
Let l be (-2)/(2/(-5*(-9)/(-90))). Suppose -1/8 - 1/8*r**4 + 1/4*r**2 + r**3 - 1/2*r**5 - l*r = 0. Calculate r.
-1, -1/4, 1
Let r(h) = 13*h**3 + 2*h**2 - 7*h - 11. Let g(s) = 2*s**3 - 3. Let x(q) = 6*g(q) - 2*r(q). Factor x(j).
-2*(j - 1)*(j + 1)*(7*j + 2)
Suppose -4/9 - 2/9*k**2 + 2/3*k = 0. What is k?
1, 2
Let t(g) be the second derivative of -2/7*g**3 + 1/35*g**5 + 0*g**4 + 35*g + 0 - 4/7*g**2. Factor t(q).
4*(q - 2)*(q + 1)**2/7
Suppose 3*b - 16 = v, 5*b - 10 = -4*v + 11. Suppose 13*h**3 + 3*h**2 - 5*h**b + 7*h**3 - 4*h**4 - 8*h + h**2 - 7*h**5 = 0. What is h?
-1, 0, 2/3, 1
Let r be 504/480 + 3/(-12). Factor r - 4/5*u**2 - 3*u.
-(u + 4)*(4*u - 1)/5
Let v(n) be the third derivative of -169/60*n**6 + 371293/30*n**3 + 0*n - 1/1680*n**8 + 13/210*n**7 - 28561/24*n**4 - 34*n**2 + 0 + 2197/30*n**5. Factor v(p).
-(p - 13)**5/5
Suppose 21*u + 3581 = 3581. Let p(h) be the second derivative of -1/12*h**3 + 3/8*h**2 - 1/48*h**4 + u - 2*h. Suppose p(t) = 0. What is t?
-3, 1
Suppose 5*m - 300 = 5*n, 0 = -3*m + 1 + 2. Let c = n - -181/3. Factor 1/3*s**2 - 4/3*s + c.
(s - 2)**2/3
Let m be -2*-1*3 - 0. Let k = 270 - 269. Suppose k + 3 + m*v - 18*v**2 + 8*v = 0. Calculate v.
-2/9, 1
Let o(u) be the third derivative of u**8/336 - u**7/105 - u**6/8 + 2*u**5/15 + 17*u**4/6 + 8*u**3 + 59*u**2. Determine f so that o(f) = 0.
-2, -1, 3, 4
What is r in 222/13*r**2 + 24/13 - 112/13*r**3 + 18/13*r**4 - 152/13*r = 0?
2/9, 1, 2, 3
Suppose 2/7*s - 27/7*s**3 + 0 + 18/7*s**4 + s**2 = 0. Calculate s.
-1/6, 0, 2/3, 1
Let x be 4/2 + 6/(-2). Let q(f) = f**2 - f + 1. Let d(p) = -16*p**2 - 29*p + 5. Let b(h) = x*d(h) - 4*q(h). Determine w, given that b(w) = 0.
-3, 1/4
Let s(r) be the third derivative of r**8/336 + 19*r**7/525 + 13*r**6/75 + 28*r**5/75 + 2*r**4/15 - 16*r**3/15 - 72*r**2. Factor s(w).
(w + 2)**4*(5*w - 2)/5
Let u be 150/105*(-3 - -1 - -9). Suppose 4*d - 5*d + 5*h + 10 = 0, 0 = 2*h + 4. Factor -5*t**3 + 141*t - 10 + u*t**2 + d*t**3 - 136*t.
-5*(t - 2)*(t - 1)*(t + 1)
Let g = 261690/7 - 37301. Let o = g - 83. Factor 2/7*t**2 - o*t + 0.
2*t*(t - 1)/7
Let q(l) = -l**3 - 10*l**2 - 8*l + 3. Let f be q(-9). Let n = f + 9. Factor -12*u + 18*u - u**3 + 3*u**3 + u**n + 9*u**2.
3*u*(u + 1)*(u + 2)
Let d(k) = -20*k**2 + 12*k - 3. Let z = -16 - -10. Let a(n) = 5*n**2 - 3*n + 1. Let f(m) = z*d(m) - 22*a(m). What is j in f(j) = 0?
-2/5, 1
Let h(g) be the first derivative of -g**4/4 - g**3 + g**2/2 + 3*g - 85. Suppose h(m) = 0. Calculate m.
-3, -1, 1
Let h(b) be the second derivative of 5/126*b**7 + 5/18*b**3 + 6*b + 0*b**6 + 0*b**2 - 1/6*b**5 + 0*b**4 + 0. Factor h(n).
5*n*(n - 1)**2*(n + 1)**2/3
Let b(v) = -v**2 - 5*v - 3. Let w be b(-2). Let c be 4/11*1518/92. Find j, given that -6 - c*j + 3/2*j**w + 3/2*j**2 = 0.
-2, -1, 2
Suppose -4*j + 13 = 333. Let x = -77 - j. Determine l so that -4/9*l**2 + 0 + 2/9*l + 2/9*l**x = 0.
0, 1
Let x(l) be the second derivative of -l**5/60 + 16*l**4/9 - 1085*l**3/18 + 961*l**2/3 + 176*l. What is a in x(a) = 0?
2, 31
Let c be (30/(-96))/(24/(-192)). Factor -25/4 - 1/4*m**2 + c*m.
-(m - 5)**2/4
Let 3*x + 5/4*x**4 + 0 - 7/4*x**3 - 7*x**2 = 0. Calculate x.
-2, 0, 2/5, 3
Suppose 24 + 18 = 27*s - 6*s. Factor -1/5*y**s + 0 - 3/5*y.
-y*(y + 3)/5
Suppose 157212*h = 157219*h. Find c such that 8/5*c**4 + 2/5*c**2 + 0 + 2*c**3 + h*c = 0.
-1, -1/4, 0
Suppose -6*b - 11 = -17. Let u(j) = -j**2. Let y(l) = -5*l**2 - 8*l. Let w(h) = b*y(h) - 3*u(h). Factor w(f).
-2*f*(f + 4)
Let o(d) = -d**3 + d**2 + 3*d. Let f be o(2). Factor -l**2 + 3*l**f + 0*l**2.
2*l**2
Let i be 12/(-32) + (-842)/(-112) + -6. Solve 4/7*a**2 - i - 4/7*a = 0 for a.
-1, 2
Let g be (-6)/(-2)*((-4)/(-6) + 0). Let s = 447/5 - 4857/55. Determine n so that -24/11*n - s*n**g - 2/11*n**3 - 16/11 = 0.
-2
Factor -37*x**2 + 223*x**2 + 5400 - 1912*x - 3*x**3 - 893*x - 255*x.
-3*(x - 30)**2*(x - 2)
Let p(s) = -2*s**3 + s**2 + s. Let h be p(-1). Let u = 2 - -1. Factor o + u*o**2 + 3*o**h - 3*o**3 - 4*o.
-3*o*(o - 1)**2
Suppose 57*a**3 + a**5 + 104*a**3 - 16*a**3 + 216 + 142*a + 20*a**4 + 398*a + 0*a**5 + 450*a**2 = 0. Calculate a.
-6, -1
Let m(h) be the third derivative of h**5/30 - 67*h**4/6 + 4489*h**3/3 - 58*h**2 + 2*h. Factor m(u).
2*(u - 67)**2
Let l(v) be the first derivative of -4*v**3/15 - 6*v**2/5 + 105. Factor l(b).
-4*b*(b + 3)/5
Let o(l) be the first derivative of l**5/10 - l**4/8 - 5*l**3/6 - 3*l**2/4 + 195. Factor o(s).
s*(s - 3)*(s + 1)**2/2
Let g(d) be the first derivative of -7*d**3/12 - 2*d**2 - d - 87. Find t, given that g(t) = 0.
-2, -2/7
Factor -56/13*k - 8/13*k**2 