et p be (-21)/(-18)*(-2 + 144/56). Let k(l) be the first derivative of p*l - 1/3*l**3 - 1/12*l**4 + 1/6*l**2 - 1 + 1/15*l**5. Solve k(r) = 0 for r.
-1, 1, 2
Let t(m) be the third derivative of -m**8/1848 + m**7/165 + 9*m**6/220 + 29*m**5/330 + 5*m**4/66 + 62*m**2 - m. Suppose t(k) = 0. What is k?
-1, 0, 10
Let w(i) be the third derivative of -1/45*i**5 + 1/315*i**7 - 1/72*i**4 + 0 + 1/180*i**6 - 1/1008*i**8 + 1/9*i**3 - 14*i**2 + 0*i. Let w(d) = 0. What is d?
-1, 1, 2
Let p(j) be the second derivative of 3*j**5/140 - j**4/7 - 11*j**3/14 - 9*j**2/7 - 101*j. Factor p(x).
3*(x - 6)*(x + 1)**2/7
Let k(h) be the third derivative of h**5/240 + 7*h**4/48 + 49*h**3/24 - 17*h**2 - 1. Find z such that k(z) = 0.
-7
Factor -190/9*m**2 + 374/9*m + 2/9*m**3 - 62/3.
2*(m - 93)*(m - 1)**2/9
Suppose 50*o - 46*o = 0. Let r(y) = 4*y**2 - 2*y + 3. Let z be r(o). Let 8/7*f**z - 6/7*f - 2/7*f**5 - 4/7 + 4/7*f**2 + 0*f**4 = 0. What is f?
-1, 1, 2
Let x(a) be the third derivative of a**6/60 - 103*a**5/210 - 5*a**4/14 - 11*a**2 - 11. Factor x(g).
2*g*(g - 15)*(7*g + 2)/7
Suppose 3*c = -3*f + 138 + 138, 4*c - 107 = -f. Let i = f + -603/7. Find v, given that -2/7*v**4 - 6/7*v**2 + 2/7*v + i*v**3 + 0 = 0.
0, 1
Factor 1/4*q**5 + 0*q**3 + 0*q + 0 + 0*q**2 + 0*q**4.
q**5/4
Suppose -19 - 17 = -3*r. Suppose 4*y + 2*y = r. Solve -5*x - y*x + 3*x - 42 + x**2 + 38 + x**3 = 0.
-2, -1, 2
Suppose -2*s + 6 + 8 = 2*v, 5*s = -4*v + 32. What is i in -3 + 6*i**2 - 3/2*i - 3/2*i**5 + v*i**3 - 3*i**4 = 0?
-2, -1, 1
Suppose -2*p - 1 = 5*i, 17 = 5*i - 5*p - 3. Let l be (-15)/(-24) - i/4*2. What is n in -1/2 + l*n**2 + 3/8*n = 0?
-4, 1
Let r(m) be the third derivative of 0 + 0*m**3 - 11*m**2 - 1/72*m**6 - 1/45*m**5 - 1/315*m**7 + 0*m - 1/72*m**4. Factor r(w).
-w*(w + 1)**2*(2*w + 1)/3
Let h(o) = o**3 - 4*o**2 - 11*o - 2. Let w be h(6). Find c such that 3*c**2 - 4*c**2 - w*c + 2*c - 5*c = 0.
-7, 0
Let i(k) = 3*k - 11. Let o be i(6). Let t(m) = -6*m + 2. Let a(y) = y**2 - 19*y + 7. Let h(u) = o*t(u) - 2*a(u). Factor h(g).
-2*g*(g + 2)
Suppose -4*k = h - 1 + 9, 3*k + 31 = -2*h. Let l be (-2 - -3) + -4 + (-92)/h. Factor -l*j**2 + 18/5*j - 4/5.
-2*(j - 2)*(4*j - 1)/5
Let j(p) = p**3 + 1. Suppose 0 = -10*m + 12*m - 10. Suppose 5*h - 6*h = -m. Let f(c) = -c**4 + 9*c**3 - 3*c**2 - 4*c + 9. Let u(b) = h*j(b) - f(b). Factor u(w).
(w - 2)**2*(w - 1)*(w + 1)
Solve 3/5*x**3 + 93/5*x + 18 + 6*x**2 = 0.
-5, -3, -2
Let b(y) be the second derivative of -3*y**5/40 - 3*y**4/4 - 9*y**3/4 - 3*y**2 + 65*y - 1. Let b(h) = 0. What is h?
-4, -1
Factor 1/3*m**2 + 363 + 22*m.
(m + 33)**2/3
Let v(a) be the first derivative of 0*a**3 + 0*a + 0*a**4 - 1/25*a**5 + 0*a**2 + 1/10*a**6 + 31. Factor v(p).
p**4*(3*p - 1)/5
Factor -7 - 1 - 21*w + 0 + 89*w + 76*w**2.
4*(w + 1)*(19*w - 2)
Let d(a) be the second derivative of -a**9/3780 + a**7/210 - a**6/90 - 11*a**4/12 - 4*a. Let f(x) be the third derivative of d(x). Determine j so that f(j) = 0.
-2, 0, 1
Let n(v) be the first derivative of 8*v - 6 + 2/27*v**3 + 4/3*v**2. Find z, given that n(z) = 0.
-6
Let w(h) be the first derivative of h**5/2 + 43*h**4/8 + 39*h**3/2 + 81*h**2/4 - 27*h - 321. Factor w(d).
(d + 3)**3*(5*d - 2)/2
Let u = 1988 + -1988. Let h(v) be the second derivative of 9*v + 1/18*v**3 + u + 1/9*v**4 - 1/20*v**5 - 1/3*v**2. Let h(n) = 0. Calculate n.
-2/3, 1
Let -24/5*h**2 + 0 + 3/5*h**4 - 3/5*h**3 + 36/5*h = 0. What is h?
-3, 0, 2
Let f be 11*1 + (330/11)/(-15). Let b(n) be the first derivative of -2/21*n**3 - 1/7*n**2 + 0*n + f. Determine i, given that b(i) = 0.
-1, 0
Suppose 2/5*d**4 + 26/5 - 28/5*d**2 - 24/5*d + 24/5*d**3 = 0. What is d?
-13, -1, 1
Suppose 4*c = -3*d + 1, 2*c + 50 = 5*d - c. Suppose 0 = d*m - 2*m. Factor -1/2*i**4 + 0*i + 0*i**3 + 1/2*i**5 + m + 0*i**2.
i**4*(i - 1)/2
Let m be (15/120)/(70/112). Find s such that -m*s**2 + 1/5*s + 6/5 = 0.
-2, 3
Determine a so that 12/7*a**3 + 0 - 74/7*a**2 + 2/7*a**4 + 60/7*a = 0.
-10, 0, 1, 3
Let v(k) be the second derivative of 0*k**2 + 0 + 13*k - 1/4*k**5 + 0*k**3 + 5/12*k**4. Factor v(q).
-5*q**2*(q - 1)
Let w(k) = 8*k**2 - 15*k - 20. Let h(o) = -o**2 + o. Let q(y) = -28*h(y) - 4*w(y). Factor q(c).
-4*(c - 10)*(c + 2)
Let t(h) be the second derivative of h**4/28 + 93*h**3/7 + 25947*h**2/14 - 165*h. Let t(c) = 0. Calculate c.
-93
Let x(z) be the first derivative of z**4/4 + 20*z**3/3 + 50*z**2 + 77. Factor x(a).
a*(a + 10)**2
Let w(f) be the third derivative of f**6/90 - f**4/18 + 26*f**2 - 1. Factor w(t).
4*t*(t - 1)*(t + 1)/3
Factor 166*f + 0*f + 4*f**3 - 3*f**3 - 30*f**2 - 392 - 51*f + 137*f.
(f - 14)**2*(f - 2)
Determine b so that -442*b - 28141 - 4*b**2 - 240*b - 638 + 2535 + 34*b = 0.
-81
Let z(y) be the third derivative of 5*y**6/216 + y**5/18 + y**4/18 + 5*y**3/3 - 15*y**2. Let j(o) be the first derivative of z(o). Factor j(l).
(5*l + 2)**2/3
Let g(c) be the first derivative of -19*c**4 - 92*c**3/3 - 8*c**2 + 90. Factor g(w).
-4*w*(w + 1)*(19*w + 4)
Let b(p) be the first derivative of -3*p**4/4 + 84*p**3 - 3528*p**2 + 65856*p + 56. Determine g, given that b(g) = 0.
28
Let a(s) be the second derivative of s**5/25 + s**4/6 + 4*s**3/15 + 15*s**2/2 + 24*s. Let c(w) be the first derivative of a(w). Determine r so that c(r) = 0.
-1, -2/3
Let p(x) = -4*x - 10. Let d be p(-3). Let u be (-34)/(-3) + 4/6. Factor -3*b + u*b**4 + 15*b**3 + 4*b + 3*b**5 + 6*b**d - b.
3*b**2*(b + 1)**2*(b + 2)
Let y(u) be the third derivative of u**8/420 + u**7/140 + u**6/180 - u**3 + 2*u**2. Let b(n) be the first derivative of y(n). Factor b(h).
2*h**2*(h + 1)*(2*h + 1)
Let g(o) = -o**2 - 10*o + 9. Let v be g(-7). Find r such that 3*r**3 + 0*r**3 - r**2 + v + 73*r - 22*r + 25*r**2 = 0.
-5, -2, -1
Let j(o) = -2*o - 9. Let f be j(-10). Factor 25*b**2 - 20*b - 27 + f*b + 11*b**3 - b**2 + b**3.
3*(b - 1)*(2*b + 3)**2
Let z(a) = -a - 1. Let o(m) = 4*m**4 - 44*m**3 + 8*m**2 + 363*m - 485. Let j(c) = o(c) - 5*z(c). Determine n, given that j(n) = 0.
-3, 2, 10
Let j(q) be the third derivative of 0 - 13/48*q**4 + 2*q**2 + 1/30*q**5 + 0*q + 1/4*q**3. Find k such that j(k) = 0.
1/4, 3
Let g(x) = -x. Let w be g(0). Let s(p) be the second derivative of 4/21*p**7 + 0 + 1/5*p**5 + 0*p**3 + 0*p**2 + w*p**4 + 3*p + 3/5*p**6. Factor s(h).
2*h**3*(h + 2)*(4*h + 1)
Let m(x) be the third derivative of -21*x**2 + 0*x + 0 - 1/60*x**5 + 0*x**3 + 1/6*x**4. Solve m(h) = 0.
0, 4
Let s(y) = -3*y**3 - 3*y**2 + 96*y - 108. Let u(f) = 2*f**2. Let p(l) = -s(l) + 6*u(l). Suppose p(m) = 0. Calculate m.
-9, 2
Let q(z) be the second derivative of 5*z**5/8 + 15*z**4/4 + 35*z**3/12 - 15*z**2/2 + 12*z. Factor q(s).
5*(s + 1)*(s + 3)*(5*s - 2)/2
Let j(y) be the second derivative of -y**8/60480 - y**7/11340 - 5*y**4/6 + 7*y. Let b(f) be the third derivative of j(f). Factor b(w).
-w**2*(w + 2)/9
Let g be (-6)/(-105) - (-8)/(-168). Let v(d) be the second derivative of -g*d**6 - 3/70*d**5 - 1/14*d**4 + 0 + 0*d**2 + 4*d - 1/21*d**3. Factor v(m).
-2*m*(m + 1)**3/7
Suppose 2*t - 4 = c - 3*c, 4*t + 5*c - 7 = 0. Suppose -6*m + 6 = -4*m. Find p such that 8*p**5 + 7*p**2 + 3*p**3 - 7*p**5 - 4*p**m - 4 - t*p**4 = 0.
-1, 1, 2
Suppose 0*c + 8 = 4*c. Factor 0*l**3 + 2*l**3 + 7*l**3 - c*l**2 + 5*l**2.
3*l**2*(3*l + 1)
Let a(u) = -u**4 + u**3. Let y be (-2)/6 - (-4)/(-6). Let g(o) = -3*o**2 - 39*o**3 + o**4 + 36*o**3 + 3*o**2 + 2*o**2. Let t(b) = y*g(b) - 3*a(b). Factor t(x).
2*x**2*(x - 1)*(x + 1)
Factor 3 - 3*m**2 + 3/4*m**3 - 3/4*m.
3*(m - 4)*(m - 1)*(m + 1)/4
Factor -3/5*m**3 - 12/5 + 0*m + 9/5*m**2.
-3*(m - 2)**2*(m + 1)/5
Suppose -1 + 3 = t. Suppose 7 = 3*v - g, t*g + 2 = 4*v - 4. Suppose 9*q - 2*q**2 - v - 24*q + 9*q = 0. What is q?
-2, -1
Let b be (3 + 0 - -7)/((-4)/(-2)). Let 4*y**b - 9*y**3 + 14*y**3 + 8*y**2 - 9*y**3 - 8*y**4 = 0. What is y?
-1, 0, 1, 2
Let v(t) be the third derivative of t**7/11340 - t**6/3240 - 5*t**4/12 - 37*t**2. Let i(p) be the second derivative of v(p). Factor i(x).
2*x*(x - 1)/9
Let d(u) be the third derivative of 1/450*u**5 + 1/45*u**4 + 0*u + 0 + 22*u**2 + 1/15*u**3. Suppose d(z) = 0. Calculate z.
-3, -1
Factor 134/5 + 69/5*v + 1/5*v**2.
(v + 2)*(v + 67)/5
Factor 109 + 243 - m**3 + 210*m + 298 + 0*m**3 - m**3 + 6*m**2.
-2*(m - 13)*(m + 5)**2
Let r(z) = z**2 - 56*z - 141. Let h(n) = -14*n - 34. Let f(t) = -18*h(t) + 4*r(t). Let f(o) = 0. Calcu