**k - 8*f - f**4. Factor h(b).
-4*(b + 1)**2*(b + 2)
Let o(u) be the third derivative of 52*u**2 + 0 - 17/3*u**3 + 0*u + 53/24*u**4 - 1/20*u**5. Factor o(j).
-(j - 17)*(3*j - 2)
Let h(d) = 22*d + 178. Let q be h(-8). Factor 29*y**q + 10*y**2 - 12*y - 12*y + 12*y.
3*y*(13*y - 4)
Determine t so that 16*t**4 + 1519*t**5 - 34*t**2 + 32*t - 6*t**4 - 1521*t**5 - 6*t**2 = 0.
-2, 0, 1, 2, 4
Suppose 70 = 7*y - 2*y. Factor -9*u**3 + y*u**3 - 15*u**4 + 13*u**3 - 3*u**5.
-3*u**3*(u - 1)*(u + 6)
Let m(w) be the second derivative of 59*w + 0*w**2 + 1/3*w**4 + 2/3*w**3 + 0. Factor m(s).
4*s*(s + 1)
Let u(g) = -g**3 + g - 6. Suppose -4 = -w + 5. Suppose 23 = 2*j + w. Let x(k) = k**3 - k + 7. Let a(d) = j*u(d) + 6*x(d). Factor a(q).
-q*(q - 1)*(q + 1)
Let t(h) be the first derivative of h**4/26 + 50*h**3/39 + 72*h**2/13 - 504*h/13 + 9223. Factor t(d).
2*(d - 2)*(d + 6)*(d + 21)/13
Suppose -61 = -15*o - 1. Solve -27*l**o - 12*l**2 + 4*l**3 - 49*l**3 - 9*l**2 - 3*l**5 = 0.
-7, -1, 0
Let o(l) be the first derivative of 3/200*l**5 + 0*l**3 - 1/300*l**6 + 0*l**2 + 24*l - 19 - 1/60*l**4. Let k(d) be the first derivative of o(d). Factor k(b).
-b**2*(b - 2)*(b - 1)/10
Let i = 116 + -121. Let a(g) = 13*g**4 + 24*g**3 - 3*g**2 - 24*g + 5. Let k(x) = -7*x**4 - 12*x**3 + x**2 + 12*x - 3. Let r(m) = i*k(m) - 3*a(m). Factor r(p).
-4*p*(p - 1)*(p + 1)*(p + 3)
Let l be -16 + 6/(-7) + (-6921852)/(-13965). Factor 1083/5*p**3 + 468/5*p + 24/5 + l*p**2.
3*(p + 2)*(19*p + 2)**2/5
Let u(t) = -t**3 - 5*t**2 - t - 18. Let k be u(-6). Find v such that 5 + v + 7 - k*v + 4*v**2 + 4*v**3 + 3*v = 0.
-3, 1
Let j = -10774 + 10778. Let h(v) be the third derivative of -1/3*v**3 - 1/105*v**7 + 0*v + 11*v**2 + 1/15*v**5 + 0*v**6 + 0 + 0*v**j. Factor h(d).
-2*(d - 1)**2*(d + 1)**2
Let u(p) be the second derivative of -p**7/4620 - p**6/198 - 5*p**5/132 - 11*p**3/6 - 58*p. Let n(o) be the second derivative of u(o). Factor n(s).
-2*s*(s + 5)**2/11
Suppose -305 = -8*d - 177. Let -21*a + 0*a - 20*a + 17*a - d*a - 52*a**2 = 0. What is a?
-10/13, 0
Let r(z) = 10*z**2 - 13 - 19 - 52 - 10*z - 6. Let u(t) = t**2 - t + 2. Let s(g) = r(g) - 5*u(g). Factor s(i).
5*(i - 5)*(i + 4)
Let b(f) = -f**3 - 21*f**2 + 11*f + 933. Let j be b(-19). Factor q**4 + 2*q**3 - 4*q**j - 1/2*q**5 + 0*q + 0.
-q**2*(q - 2)**2*(q + 2)/2
Suppose 132*w - 350 = -2*w + 186. Let o(v) be the first derivative of 7/27*v**3 + 17 - 4/9*v**2 - 16/9*v - 1/36*v**w. Determine h, given that o(h) = 0.
-1, 4
Let z(j) be the first derivative of 0*j - 16/11*j**2 + 63 + 16/33*j**3 + 15/22*j**4 - 16/55*j**5 + 1/33*j**6. Suppose z(h) = 0. What is h?
-1, 0, 1, 4
Suppose 2*w + 34 = -5*h + 2, h = -5*w - 57. Let l(j) = 26*j**2 + 72*j - 16. Let n(k) = -76*k**2 - 215*k + 48. Let f(x) = w*l(x) - 4*n(x). Factor f(i).
2*(i + 4)*(9*i - 2)
Let p(b) = b**3 + 11*b**2 + 16*b - 8. Let i be p(-9). Let n be 2/(-4)*0/(4 - i). Factor 1/2*t + n - 1/4*t**2.
-t*(t - 2)/4
Find c such that -2/11*c**3 + 36/11*c**2 - 192/11*c + 256/11 = 0.
2, 8
Suppose j - 115 = -4*v, 149 = -0*v + 5*v + 3*j. Let h be (-4)/14 + 64/v. Suppose -22 + 2*a**2 + 3*a + 8 + 0*a**h + 12 = 0. Calculate a.
-2, 1/2
Let l(j) = j**2 + 3*j - 1. Let v(t) = 6*t**2 + 38*t + 121. Let c(y) = -5*l(y) + v(y). Let q be c(-14). Factor 0*p + 0 + 25/3*p**3 - 5/3*p**4 + q*p**2.
-5*p**3*(p - 5)/3
Let h(g) = 14*g**2 - 94*g - 3. Let k(i) be the first derivative of 74*i**3/3 - 235*i**2 - 16*i - 148. Let j(t) = 16*h(t) - 3*k(t). Factor j(r).
2*r*(r - 47)
Let v be -3 + 4/(-4 - 0). Let x be (40/(-12))/(v/6). Solve -l**4 + 7*l**2 - 6*l - 2*l**2 + x*l**3 - 4*l**4 + l = 0 for l.
-1, 0, 1
Let f(j) be the third derivative of -j**5/20 - 95*j**4/8 - 632*j**3 + 325*j**2 - 3*j - 1. Factor f(n).
-3*(n + 16)*(n + 79)
Let z(a) be the first derivative of 29/9*a**2 - 4/9*a**3 + 10/9*a - 93. Factor z(g).
-2*(g - 5)*(6*g + 1)/9
Let y(p) be the third derivative of p**6/720 + p**5/45 + 5*p**4/48 - 137*p**2 + 7. Suppose y(l) = 0. What is l?
-5, -3, 0
Suppose 18/5*g**4 + 183/5*g + 237/5*g**3 + 9 - 483/5*g**2 = 0. Calculate g.
-15, -1/6, 1
Find x, given that 1043*x**2 + 502*x + 532*x - 729*x + 2 = 0.
-2/7, -1/149
Suppose 3*t = -4*w - 24 - 4, -w - 7 = -4*t. Let g(k) be the second derivative of 0 + 1/6*k**4 + 0*k**2 + 47*k + 3/20*k**5 + t*k**3 + 1/30*k**6. Factor g(s).
s**2*(s + 1)*(s + 2)
Let u(r) be the third derivative of r**8/672 + 31*r**7/1260 - 29*r**6/360 + r**5/15 + 2093*r**2. Find n such that u(n) = 0.
-12, 0, 2/3, 1
Let c be (3/32)/(417/7784). Factor -1/4*p**2 - c*p - 3.
-(p + 3)*(p + 4)/4
Let c be ((-2)/(-12))/(94/3948). Suppose -43*a - 70*a**2 - 78*a - 137*a - c*a**3 - 67*a - 500 + 2*a**3 = 0. What is a?
-5, -4
Let p(h) be the second derivative of 4/3*h**4 - 2/15*h**6 + 0*h**2 - 4/5*h**5 + 0*h**3 + 2/21*h**7 - 37*h + 0. Factor p(f).
4*f**2*(f - 2)*(f - 1)*(f + 2)
Suppose 58*p = 57*p - 136. Let i be 10 - (-17)/(p/60). Factor -1/2*l**5 + 0 - i*l**3 + 0*l + 2*l**4 + l**2.
-l**2*(l - 2)*(l - 1)**2/2
Let g = 5849 + -29242/5. Let v(n) be the first derivative of 14 + g*n**2 + 0*n - 2/5*n**3. Factor v(s).
-6*s*(s - 1)/5
Suppose -1/4*i**4 - 1/2*i**3 + 7/4*i**2 - i + 0 = 0. What is i?
-4, 0, 1
Suppose 11*v + 573 + 527 = 0. Let i be 0*(5/(v/35) + 2). Factor -10/3*q**4 - 11/6*q**3 + 0*q + i + 2/3*q**2.
-q**2*(4*q - 1)*(5*q + 4)/6
Let k(a) be the first derivative of 5*a**6/72 - 59*a**5/24 - 5*a**4/2 - 8*a**3/3 - 3*a + 134. Let c(z) be the third derivative of k(z). Let c(l) = 0. What is l?
-1/5, 12
Let j(v) = v**5 - v**4 - v**3 - v**2 + 2*v - 1. Let m(u) = 2*u**5 - u**4 - 8*u**3 - 7*u**2 + 2*u - 1. Let f(b) = -5*j(b) + 5*m(b). Factor f(x).
5*x**2*(x - 3)*(x + 1)*(x + 2)
Let m(w) be the second derivative of -w**7/2520 + 7*w**6/720 + 3*w**5/20 - 7*w**4/6 - w + 29. Let y(b) be the third derivative of m(b). Let y(l) = 0. What is l?
-2, 9
Let w(b) be the first derivative of -1/5*b**2 - 28 - 8/15*b**3 + 12/5*b - 1/10*b**4. Factor w(c).
-2*(c - 1)*(c + 2)*(c + 3)/5
Let g(d) = 5*d + 52. Let w be g(-10). Factor -h**2 + 2*h + 11*h + 0*h + 20 - h + 2*h**w.
(h + 2)*(h + 10)
Solve 2179/3*n**2 - 1090/3 + n**4 - 1639/3*n**3 + 547/3*n = 0.
-2/3, 1, 545
Factor -54729/5*x**2 + 474/5*x**3 - 1/5*x**4 - 103680 - 68256*x.
-(x - 240)**2*(x + 3)**2/5
Let o(h) be the second derivative of -7*h**6/600 + 3*h**5/100 + h**4/10 - 2*h**3/15 + 65*h**2/2 - 51*h. Let f(z) be the first derivative of o(z). Factor f(i).
-(i - 2)*(i + 1)*(7*i - 2)/5
Let s(h) = -6*h**2 - 212*h - 459. Let m be s(-33). Factor 8/11 + 16/11*r**4 - 2/11*r**5 + 56/11*r**2 - 34/11*r - 4*r**m.
-2*(r - 4)*(r - 1)**4/11
Let v(s) be the third derivative of -13*s**8/2016 - 5*s**7/84 - 47*s**6/720 + s**5/24 + 153*s**2 - 8*s. Find w, given that v(w) = 0.
-5, -1, 0, 3/13
Suppose 484*k + 0*k**2 - 1/3*k**3 - 21296/3 = 0. What is k?
-44, 22
Suppose -5*l - 25 = -c, 5*l + 30 = -4*c + 6*c. Suppose -12*r**3 + 360*r**2 - 4*r**c - 17*r**3 + 44*r**4 - 324*r - 155*r**3 + 108 = 0. Calculate r.
1, 3
Let w(b) be the first derivative of -5/12*b**4 + 0*b + 8/9*b**3 - 36 - 2/3*b**2 + 1/15*b**5. Determine u so that w(u) = 0.
0, 1, 2
Let u be (-2)/18*3 - -3. Suppose 502*g - 53 - 2818 = -455*g. Let -14/3*r**g - 8/3*r**4 + 2*r**5 + 0 + 8/3*r + u*r**2 = 0. Calculate r.
-1, -2/3, 0, 1, 2
Suppose 1/2*p**4 + 11*p**3 + 38*p**2 + 0 + 36*p = 0. What is p?
-18, -2, 0
Let k(j) be the second derivative of -j**4/3 + 52*j**3/3 + 8254*j. Factor k(x).
-4*x*(x - 26)
Let o(m) be the third derivative of 0 + 20/3*m**3 - 19/30*m**5 - 1/105*m**7 + 20*m**2 - 1/168*m**8 + 0*m + 17/60*m**6 - 4/3*m**4. Suppose o(w) = 0. Calculate w.
-5, -1, 1, 2
What is y in -1/5*y**5 - 3630*y**3 + 44*y**4 - 1830125*y + 0 + 133100*y**2 = 0?
0, 55
Let l(z) be the second derivative of z**5/35 - z**4/3 + 72*z**2/7 + 1939*z. Factor l(r).
4*(r - 6)*(r - 3)*(r + 2)/7
Determine l, given that 2*l**4 + 132*l + 584/5*l**3 + 0 + 1882/5*l**2 = 0.
-55, -3, -2/5, 0
Find w, given that 1273 - 7/2*w**2 - 8909/2*w = 0.
-1273, 2/7
Let m(y) = y**4 + y**3 + y**2 - 4*y + 6. Let p(l) = 42*l**4 - 2262*l**3 + 1773*l**2 + 4848*l + 870. Let a(x) = 9*m(x) - p(x). Solve a(f) = 0.
-1, -2/11, 2, 68
Let c(h) be the second derivative of 37/15*h**3 + 0 + 52*h + 1/10*h**5 + 2*h**2 + 16/15*h**4. Factor c(y).
2*(y + 1)*(y + 5)*(5*y + 2)/5
Let i(g) = -16*g**2 + 11*g - 29. Suppose 30 = 2*j - 2*s, -j - 9 = -2*s - 25. L