2
Let g(r) be the first derivative of -2*r**3/21 - 32*r**2/7 - 62*r/7 + 1. Factor g(x).
-2*(x + 1)*(x + 31)/7
Let j(z) = z**3 + 3*z**2 - z + 3. Let s be j(0). Determine t, given that -t**2 + 3*t - s*t**4 - 4*t**3 + 2*t**5 + 0*t**3 - 25*t**3 + 20*t**3 = 0.
-1, 0, 1/2, 3
Factor -3*s**5 - 4*s**4 - 5*s**4 + 448531*s**3 - 448537*s**3.
-3*s**3*(s + 1)*(s + 2)
Let p = 20937/5 + -4187. Let s be ((-108)/(-20) - 5)*1. Factor -p*f + 4/5 - s*f**2.
-2*(f - 1)*(f + 2)/5
Let q(p) be the second derivative of 0 + 4*p**2 + 5/6*p**4 - 17*p - 1/12*p**5 - 10/3*p**3. Let u(z) be the first derivative of q(z). Factor u(w).
-5*(w - 2)**2
Let n(z) = -z**3 - 37*z**2 + 44*z + 207. Let h be n(-38). Let v = 235/11 + h. Let -2/11*w**3 + 0*w**2 - v + 6/11*w = 0. What is w?
-2, 1
Find t such that -455 - 204*t**2 + 2338 + 342*t + 207*t**2 + 364 = 0.
-107, -7
Let o = 20781949 + -14235632031/685. Let r = o + -4/137. Let 24/5*g**2 - r*g - 2/5 = 0. What is g?
-1/12, 1
Let b be (-2 - 0) + 3 + -1. Factor 3*m**3 - 13*m - 148*m**2 + 123*m**2 - 5*m + b*m**3.
m*(m - 9)*(3*m + 2)
Suppose -5*i + 725 = -3*p - 285, 0 = 2*p. Let y = i + -200. Factor 24/11*x**y - 12/11*x + 2/11 - 20/11*x**3 + 6/11*x**4.
2*(x - 1)**3*(3*x - 1)/11
Let v be (68/(-154))/((-50)/35 + 1). Let u = v - -158/231. Factor u + 867/7*k**2 - 204/7*k.
3*(17*k - 2)**2/7
Let p(i) be the first derivative of 0*i - 60 + 2/27*i**3 + 14/9*i**2. Suppose p(g) = 0. Calculate g.
-14, 0
Let k(m) = m**3 - 20*m**2 + 37*m + 30. Let y be k(18). Suppose -45*s - y = -57*s. Factor 0*l**3 - 1/7*l**5 + 2/7*l**2 + 1/7*l - 2/7*l**s + 0.
-l*(l - 1)*(l + 1)**3/7
Let b(q) be the third derivative of 2*q**7/315 + 637*q**6/90 + 101123*q**5/45 - 101761*q**4/18 - q**2 + 104*q + 2. Let b(n) = 0. Calculate n.
-319, 0, 1
Let p(r) = -9*r**3 - 141*r**2 + 94*r + 35. Let h(l) = 3*l**3 + 46*l**2 - 31*l - 12. Let c be (5/(-2))/(-1)*(-456)/570. Let o(y) = c*p(y) - 7*h(y). Factor o(t).
-(t - 1)*(t + 14)*(3*t + 1)
Let a(i) = 3*i + 8. Suppose 15 = 3*y, 7*n - 12*n + y - 15 = 0. Let t be a(n). Factor 1 - 1/2*q**t + 1/2*q.
-(q - 2)*(q + 1)/2
Factor 2*x**4 + 185*x**2 + 1122 + 482 - 36 + 1344*x - 74*x**3 - 9*x**2 + 26*x**3.
2*(x - 14)**2*(x + 2)**2
Let k = -741 - -741. Suppose 5*j - 25 = -k*r + 5*r, 2*j = 4*r + 14. Factor 1/10*s + 0 - 1/10*s**j + 0*s**2.
-s*(s - 1)*(s + 1)/10
Let b = 279963 - 279878. Suppose 0 - 5*o + b*o**2 - 1445/4*o**3 = 0. What is o?
0, 2/17
Let b(m) = 3*m**4 - 6*m**3 - 74*m**2 - 188*m - 115. Let h(k) = -28*k**4 + 54*k**3 + 665*k**2 + 1693*k + 1034. Let u(v) = 57*b(v) + 6*h(v). Factor u(s).
3*(s - 13)*(s + 1)*(s + 3)**2
Let b(t) be the first derivative of t**7/735 - t**6/120 - t**5/105 - 145*t**2 + 70. Let o(c) be the second derivative of b(c). Let o(x) = 0. What is x?
-1/2, 0, 4
Let u(z) be the third derivative of -z**6/420 + 79*z**5/210 - 13*z**4/14 + z**2 + z + 209. Factor u(t).
-2*t*(t - 78)*(t - 1)/7
Let -338*k**2 + 3 + 880*k + 4*k**3 - 2 + 210*k**2 - 1 = 0. Calculate k.
0, 10, 22
Let h be (-866)/4 + ((-13)/2)/13. Let j = -217 - h. Suppose j*f + 1/4*f**4 + 0 + 0*f**3 - 1/4*f**2 = 0. What is f?
-1, 0, 1
Suppose 28*k + 20 = 32*k. Suppose -2*p - 10 = 2*l - 5*l, -4*p + 24 = k*l. Determine g, given that -4*g**5 - 103*g + 95*g - 4*g**2 + 12*g**3 + 3*g**4 + g**l = 0.
-1, 0, 1, 2
Let k(x) = -x**2 - 20*x. Let v(y) = 50*y - 21*y - 13*y - 11*y. Let z(n) = -5*k(n) - 35*v(n). Factor z(a).
5*a*(a - 15)
Let w(g) be the second derivative of -g**5/30 + g**4/2 + g**3/9 - 3*g**2 + 177*g. Factor w(y).
-2*(y - 9)*(y - 1)*(y + 1)/3
Factor 1302/5*y + 0 + 3/5*y**2.
3*y*(y + 434)/5
Let f = 664 - 665. Let m(t) be the third derivative of -t**5/20 + t**4/12 + t**3 - t**2. Let k(x) = -1. Let j(u) = f*m(u) - 5*k(u). What is g in j(g) = 0?
-1/3, 1
Let q(k) be the first derivative of -25/14*k**4 - 287 + 0*k + 12/7*k**3 + 1/21*k**6 + 12/35*k**5 + 0*k**2. Let q(c) = 0. What is c?
-9, 0, 1, 2
Let v(w) = -3*w**2. Let p(i) = -i**3 + 118*i**2 - 129*i. Let a(s) = -3*p(s) + 12*v(s). Factor a(h).
3*h*(h - 129)*(h - 1)
Let t(o) be the first derivative of -o**6/18 + 17*o**5/15 + 19*o**4/6 + 2*o**3/9 - 37*o**2/6 - 19*o/3 + 111. Solve t(q) = 0 for q.
-1, 1, 19
Determine j so that -80*j + 0 - 2/9*j**3 + 92/9*j**2 = 0.
0, 10, 36
Suppose 77*f - 75*f + 3*g = -42, -3*g = 5*f + 42. Factor 8/7*n**4 - 2/7*n**5 + 24/7*n**3 + 0*n + 0 + f*n**2.
-2*n**3*(n - 6)*(n + 2)/7
Let s(p) = 396*p + 4766. Let y be s(-12). Let r(v) be the first derivative of -10/27*v**3 + 2/9*v**4 + y + 2/15*v**5 + 0*v - 2/9*v**2. Solve r(k) = 0.
-2, -1/3, 0, 1
Let b(r) be the second derivative of 0*r**2 - 4/9*r**3 + 0*r**5 - 2/45*r**6 + 0 - 55*r + 1/3*r**4. Factor b(x).
-4*x*(x - 1)**2*(x + 2)/3
Let k(f) be the third derivative of -f**6/60 - 41*f**5/30 - 299*f**4/12 + 2645*f**3/3 - 1463*f**2. Let k(o) = 0. Calculate o.
-23, 5
Let g(j) be the third derivative of -19/180*j**5 - 2/9*j**3 - 5/144*j**6 - 7/36*j**4 + 0 - 2/315*j**7 + 0*j - 1/2016*j**8 - 21*j**2. Factor g(b).
-(b + 1)**2*(b + 2)**3/6
Let c be -40 + ((4 + -6)/(-2))/(-1). Let j be (-8)/2 - (-47 - c). Factor 1/2*o**j + 0 + 2*o.
o*(o + 4)/2
Determine z, given that 130*z - 5/2*z**2 + 265/2 = 0.
-1, 53
Let p(l) = 3*l**2 + 4*l - 2. Suppose 4 = -2*s - 0*s - g, -4*g - 2 = s. Let a be p(s). What is h in 80 + 16*h + 5*h**a - 22*h + 46*h = 0?
-4
Let t(o) = -o**3 + 9*o**2 - 15*o + 9. Let v be t(7). Factor 1388 - 709 - 698 - 18*u + u**v.
(u - 19)*(u + 1)
Let k(u) be the third derivative of u**8/2520 + u**7/315 + u**6/225 - 721*u**2. Factor k(c).
2*c**3*(c + 1)*(c + 4)/15
Let t(z) be the second derivative of -5*z**4/12 + 155*z**3/6 + 255*z**2 - 26*z + 21. Factor t(b).
-5*(b - 34)*(b + 3)
Let n(o) = -3*o**4 + o**3 + o**2 - o - 2. Let u(v) = -14*v**4 - 2*v**3 + 10*v**2 + 2*v - 16. Let h(q) = -20*n(q) + 4*u(q). Factor h(w).
4*(w - 6)*(w - 1)**2*(w + 1)
Determine l, given that 6*l**2 + 823*l + 11*l**4 - 13*l**4 - 867*l + 16*l**3 - 32 = 0.
-1, 2, 8
Let l(u) be the first derivative of 22 + 105*u**2 - 3599*u**3 + 3600*u**3 + 207*u + 45. Factor l(b).
3*(b + 1)*(b + 69)
Let a be -41*((-4)/(-5))/((-6)/15). Let g = a + -79. Find z such that 22/3*z**g + 14/3*z**4 + 0 - 4/3*z - 6*z**5 - 14/3*z**2 = 0.
-1, -2/9, 0, 1
Let t(s) be the second derivative of -s**9/52920 + 4*s**7/2205 - 4*s**4/3 - s**2 - 209*s. Let i(j) be the third derivative of t(j). Factor i(l).
-2*l**2*(l - 4)*(l + 4)/7
Let q be -10 + -1 + (-1185)/45 + 46. Determine m, given that -2/3*m**4 - 70/3*m**2 - q*m**3 + 0 + 98/3*m = 0.
-7, 0, 1
Let l(n) be the first derivative of -1/3*n**3 + 24 + 0*n + 3/2*n**2. Suppose l(k) = 0. Calculate k.
0, 3
Suppose -22 = -3*b + n - 6*n, 2*b = -3*n + 14. Factor 21*p - 22*p - b*p**3 - 31*p + 16*p**2 + 2*p**3.
-2*p*(p - 4)**2
Let d(m) = -4*m**4 - 8*m**3 + 88*m**2 + 95*m - 422. Let w(n) = 5*n**4 + 4*n**3 - 87*n**2 - 96*n + 420. Let v(b) = 6*d(b) + 5*w(b). Solve v(a) = 0 for a.
-2, 3, 24
Suppose -44*d = 9*p - 42*d + 3, 0 = 4*p + 5*d + 63. Factor 3/7*q**5 + 72/7*q**2 + 66/7*q**p + 24/7*q**4 + 27/7*q + 0.
3*q*(q + 1)**2*(q + 3)**2/7
Let a(y) be the third derivative of 1/240*y**5 + 1/24*y**3 - 1/48*y**4 + 0*y + 21 - 2*y**2. What is z in a(z) = 0?
1
Let k be 124/66 + 5436/(-9966). Solve -1/3*v**3 + 0 + k*v + v**2 = 0 for v.
-1, 0, 4
Let r(l) be the third derivative of l**5/15 - 610*l**4/3 + 744200*l**3/3 - 1989*l**2. Factor r(g).
4*(g - 610)**2
Let s(n) = 24 - 153*n**2 - 105 - 54*n - 179*n**2 + 354*n**2 - 7. Let z(j) = 4*j**2 - 11*j - 18. Let a(v) = -3*s(v) + 16*z(v). Factor a(t).
-2*(t + 3)*(t + 4)
Suppose 2*b + 44 - 38 = -2*v, 4*b - 5*v - 15 = 0. Let k(n) be the third derivative of 0*n**5 + 0*n + 1/60*n**4 + 0*n**3 + b - 1/300*n**6 - 7*n**2. Factor k(j).
-2*j*(j - 1)*(j + 1)/5
Let t(x) be the first derivative of 2*x**3/9 + 238*x**2/3 - 320*x + 15143. Factor t(g).
2*(g - 2)*(g + 240)/3
Let l = -55649 - -55652. Solve 5/6*u**2 + 0*u + 1/6*u**l + 0 = 0 for u.
-5, 0
Suppose 25 - 17 = 2*d - 5*q, -5*d + 4*q + 54 = 0. Let o be (d/(-4))/(266/(-228)). Find k such that 0*k**2 - 2/9*k**5 + 0*k + 2/3*k**o - 4/9*k**4 + 0 = 0.
-3, 0, 1
Factor 3/2*o**2 - 372*o + 741/2.
3*(o - 247)*(o - 1)/2
Factor 565 + 8*w**2 - 4066*w - 160 + 611.
2*(w - 508)*(4*w - 1)
Suppose 0 = -4*s - 4*g + 32, 5*s = 5*g - 36 - 4. Let y(v) be the second derivative of -1/7*v**3 + 18*v + 1/28*v**4 - 12/7*v**2 + s. Factor y(p).
3*(p - 4)*(p + 2)/7
Let