et s(k) = k + 1. Let g be s(2). Factor 9*y**3 - 10*y**2 - 5*y**g - p*y**2.
4*y**2*(y - 3)
Let h(z) be the second derivative of -z**5/110 + 7*z**3/33 + 6*z**2/11 - 15*z. Factor h(r).
-2*(r - 3)*(r + 1)*(r + 2)/11
Let b(y) = 5*y + 34. Let x be b(-7). Let z be (-3 + 9/(-3))/(-3 - x). Find k, given that -7*k**z + 0 - 2/3*k + 13/3*k**2 = 0.
0, 2/7, 1/3
Let n(p) be the third derivative of 0*p - 13*p**2 - 1/420*p**6 - 1/35*p**5 + 0 - 8/21*p**3 - 1/7*p**4. Factor n(x).
-2*(x + 2)**3/7
Let p = -41 + 43. Suppose -p = 5*c + 4*u, -u = -3*u - 6. Suppose 1/7*k**5 + 0 + 0*k**3 - 1/7*k - 2/7*k**c + 2/7*k**4 = 0. What is k?
-1, 0, 1
Let f = -158 - -158. Let j(m) be the second derivative of 0*m**4 + 1/15*m**6 + 0*m**2 + 0*m**5 + f*m**3 - 7*m + 0. Suppose j(d) = 0. What is d?
0
Let b(w) be the second derivative of w**5/10 - 57*w**4/2 + 3249*w**3 - 185193*w**2 + 131*w. Factor b(a).
2*(a - 57)**3
Factor 0 + 1/2*m + 1/2*m**3 + m**2.
m*(m + 1)**2/2
Factor -2 + 490*j**4 - 485*j**4 + 7 - 10*j**2.
5*(j - 1)**2*(j + 1)**2
Let 2/3*l**4 - 8/3*l + 4/3*l**2 - 2 + 8/3*l**3 = 0. Calculate l.
-3, -1, 1
Solve 12*j**2 - 12*j + 8 + 9*j**4 + 4 + 12*j**3 - 33*j**2 = 0.
-2, -1, 2/3, 1
Let g(q) be the third derivative of -q**6/60 - q**5/5 + 25*q**4/12 - 6*q**3 + 255*q**2. Factor g(l).
-2*(l - 2)*(l - 1)*(l + 9)
Let u = 67 + -172. Let s = -103 - u. Factor 0*k + 1/3*k**4 - 2/3*k**3 + 0 + 1/3*k**s.
k**2*(k - 1)**2/3
Let y(j) = -45*j**3 - 6*j**2 - 18. Let h(o) = -2*o**3 - 42 + 43 + 4*o**3. Let z(k) = -18*h(k) - y(k). Factor z(i).
3*i**2*(3*i + 2)
Suppose -3*w - 2*w - 30 = 0. Let u be -1 + 1 + w + 6. Let 0 + u*x + 2/9*x**2 + 2/3*x**3 = 0. What is x?
-1/3, 0
Let w(r) be the first derivative of -r**4/16 + r**3/6 - r**2/8 + 89. Factor w(y).
-y*(y - 1)**2/4
Let i = 673507425/999481 + -2/142783. Let d = 675 - i. Factor -4/7*b**4 + 4/7 + 0*b**2 - d*b**3 + 8/7*b.
-4*(b - 1)*(b + 1)**3/7
Let o(d) = d**3 + 2*d**2 - 4*d - 1. Suppose -6*y - 15 = -y. Let g be o(y). Factor 6*k**3 - 3*k**2 + 6*k**g + 12*k**2 - 15*k**4 - 6*k.
-3*k*(k - 1)*(k + 1)*(5*k - 2)
Let t(r) be the first derivative of -r**4/14 + 2*r**3/7 + 13*r**2/7 - 30*r/7 - 167. Factor t(h).
-2*(h - 5)*(h - 1)*(h + 3)/7
Factor 3/8 + 9/8*t**2 - 3/2*t.
3*(t - 1)*(3*t - 1)/8
Let p = -9799 - -9805. Factor 12 + 306/7*q + p*q**2.
6*(q + 7)*(7*q + 2)/7
Let d(b) = -b**2 - 3*b + 4*b + 0*b + 2 - 1. Let f(g) = 2*g**5 - 2*g**3 + 2*g**2 - 2*g - 2. Let y(l) = 4*d(l) + 2*f(l). Factor y(t).
4*t**3*(t - 1)*(t + 1)
Factor 2*i**2 - 4*i**4 + 5*i**4 - 12*i**4 + 14*i**3 - 14*i + 9*i**4.
-2*i*(i - 7)*(i - 1)*(i + 1)
Let n(w) = -w**2 + 2*w - 16. Let u be (4 - (2 - 0))/((-2)/(-1)). Let m(z) = z. Let l(p) = u*n(p) + 6*m(p). Let l(x) = 0. What is x?
4
Suppose -6*y + 18 + 618 = 0. Suppose -5*m = -y - 89. Determine b so that -5 - 5 + 5*b**3 - m*b + 24*b = 0.
-1, 2
Suppose -5*c + 4 = -11. Suppose 0 = -2*s - 0*s + 8. Find q such that -s*q**c + 19*q**3 + 3*q + 13*q**2 + 11*q**2 - 6 = 0.
-1, 2/5
Let p(s) be the second derivative of -3*s**6/10 + 3*s**5/70 + 3*s**4/4 - s**3/7 - 446*s. Solve p(m) = 0.
-1, 0, 2/21, 1
Let m be (-2)/9 + 120/54. Suppose m*v - 32 = 3*o, -2*v + 3*o - 2*o + 28 = 0. Factor 6*q**2 - v*q**2 + 9 - 5*q**2 + 33*q.
-3*(q - 3)*(4*q + 1)
Find k, given that 3/2 + 3/4*k**3 - 1/4*k**4 + 3/4*k**2 - 11/4*k = 0.
-2, 1, 3
Let c(x) = -132*x + 2244. Let g be c(17). Factor -y**2 + 1/2*y**3 + g - 3/2*y.
y*(y - 3)*(y + 1)/2
Let r be ((-6)/21)/(36/(-14)). Let c(v) be the first derivative of 0*v + 5 + 1/24*v**4 - 1/30*v**5 + 0*v**2 + r*v**3. What is f in c(f) = 0?
-1, 0, 2
Suppose -4*y = 3*b + y - 7, 0 = 4*b - 5*y - 21. Factor -225 + 2*u**2 + 0*u**2 + b*u**2 + 30*u - 7*u**2.
-(u - 15)**2
Let -1/3*f**2 + 1/3 + 8/9*f = 0. Calculate f.
-1/3, 3
Let n(t) be the third derivative of t**6/480 + t**5/80 + t**3/3 + 6*t**2. Let j(w) be the first derivative of n(w). Factor j(g).
3*g*(g + 2)/4
Let u(k) be the third derivative of -7*k**5/360 + k**4/9 - k**3/9 + 3*k**2 - 35*k. Factor u(p).
-(p - 2)*(7*p - 2)/6
Let r = -1308/41 - -9238/287. Solve 4/7*t + r*t**4 - 4/7*t**2 + 2/7 - 8/7*t**3 + 4/7*t**5 = 0.
-1, -1/2, 1
Let y(r) be the first derivative of -r**4/30 + 2*r**3/45 + 4*r**2/15 - 8*r/15 - 121. What is g in y(g) = 0?
-2, 1, 2
Suppose -7*t - 79*t = 12*t. Let u(p) = -p**3 + 7*p**2 + 7*p + 11. Let j be u(8). Determine r so that 32/5 + 0*r + 2/5*r**4 + t*r**j - 16/5*r**2 = 0.
-2, 2
Let j(g) = -7*g**2 - 26*g - 10. Let k(o) = -7*o**2 - 9 - 4*o**2 - 27*o + 6*o**2 - o**2. Let w(s) = -2*j(s) + 3*k(s). Solve w(c) = 0.
-7, -1/4
Let o(b) be the first derivative of -b**4/4 + 40*b**3/3 - 357*b**2/2 - 882*b + 76. Factor o(p).
-(p - 21)**2*(p + 2)
Suppose 4*g = 12 + 24. Factor 2 - l**3 - g*l**2 - 27*l - 12 - 17.
-(l + 3)**3
Let l(p) be the second derivative of -2*p**7/735 - p**6/210 + p**5/105 + p**4/42 + 9*p**2/2 + 11*p. Let z(j) be the first derivative of l(j). Factor z(m).
-4*m*(m - 1)*(m + 1)**2/7
Let t(c) be the first derivative of -5 + 0*c**2 + 8/5*c**5 - 7/12*c**6 - 11/8*c**4 + 0*c + 1/3*c**3. Factor t(n).
-n**2*(n - 1)**2*(7*n - 2)/2
Let c(p) = -2*p - 7 + 22 - 12. Let m be c(0). Let -18 - w**2 - 5*w + 15 + 3*w**m - 2*w**3 = 0. Calculate w.
-1, 3
Suppose -2/17*r**4 + 0 + 6/17*r**3 - 80/17*r + 36/17*r**2 = 0. What is r?
-4, 0, 2, 5
Suppose -4*f - 36 = 8*f. Let y be 5*f/(-15) + -1. Factor y*n - 8/13 + 6/13*n**2 + 2/13*n**3.
2*(n - 1)*(n + 2)**2/13
Let 10 + 35*i**3 + 60*i**2 - 20*i - 13 + 3 = 0. Calculate i.
-2, 0, 2/7
Suppose 2*o + 50 = -b, -4*b = -5*o - 40 - 85. Let h = 25 + o. Factor h*x + 0 + 2/13*x**4 + 0*x**2 - 2/13*x**3.
2*x**3*(x - 1)/13
Let c(d) be the second derivative of d**7/42 - d**6/30 + d - 152. Solve c(z) = 0 for z.
0, 1
Let t be 8/(-16)*2*-11. Factor 27*l**2 - t*l**2 + 4*l - 12*l**2.
4*l*(l + 1)
Let x(l) be the first derivative of -l**4/12 + 5*l**3/6 + 3*l**2 - 18*l + 20. Let d(n) be the first derivative of x(n). Solve d(i) = 0 for i.
-1, 6
Let i(v) = v**3 + 13*v**2 - 24*v - 128. Let b be i(-14). Factor -27/5*r**3 + b*r**2 + 6/5 - 39/5*r.
-3*(r - 1)**2*(9*r - 2)/5
Factor -100/7 - 290/7*t - 10/7*t**3 - 104/7*t**2.
-2*(t + 5)**2*(5*t + 2)/7
Let t(j) be the third derivative of -5*j**2 + 1/10*j**5 + 1/105*j**7 + 0 - 4/3*j**3 + 1/15*j**6 - 1/3*j**4 + 0*j. Suppose t(s) = 0. What is s?
-2, -1, 1
Let m(h) be the first derivative of -11 + 1/9*h**3 - 1/15*h**5 - 1/36*h**6 + 0*h**2 + 1/24*h**4 + 0*h. Solve m(n) = 0 for n.
-2, -1, 0, 1
Let o(t) be the third derivative of -t**6/780 - 4*t**5/195 + 3*t**4/52 - 394*t**2. Factor o(z).
-2*z*(z - 1)*(z + 9)/13
Let u(t) = 20*t**2 - 60*t - 158. Let n(y) = -11*y**2 + 30*y + 80. Let z(i) = -7*n(i) - 4*u(i). Suppose z(r) = 0. What is r?
-2, 12
Let h(n) be the third derivative of n**6/180 - n**5/45 + n**4/36 - 2*n**2 - 193*n. Find y, given that h(y) = 0.
0, 1
Let m = 215/117 + -21/13. Let b(d) be the first derivative of 1/9*d**2 - 2/27*d**3 - 4 + m*d - 1/18*d**4. Find z such that b(z) = 0.
-1, 1
Let u(k) = 4 + k + 16*k**2 + 4 - 17*k**2. Let o be u(3). Solve -10/9*r**3 - 4/9 + 10/9*r + 4/9*r**o = 0 for r.
-1, 2/5, 1
Let g be (-24)/((-4)/(-52) + 0). Let f be g/(-4)*3/9. Factor -18*q**3 + 2*q**2 - 15*q**3 + f*q**3.
-q**2*(7*q - 2)
Let x = 5661/20 - 283. Let j(q) be the second derivative of 1/6*q**3 + q - q**2 - 1/30*q**6 - x*q**5 + 0 + 1/4*q**4. Factor j(p).
-(p - 1)**2*(p + 1)*(p + 2)
Factor 2 - 9*y**3 + 14*y**3 - 6*y - 35*y**2 + 33 + y.
5*(y - 7)*(y - 1)*(y + 1)
Let w(o) be the second derivative of -o**4/72 + o**3/36 + o**2 + 87*o. Find i, given that w(i) = 0.
-3, 4
Let g = -510 + 513. Let d(q) be the first derivative of -17/3*q**g - 4*q + 5/4*q**4 + 8*q**2 + 7. Factor d(v).
(v - 2)*(v - 1)*(5*v - 2)
Let r(t) be the third derivative of 1/4*t**3 + 0*t**5 + 7/96*t**4 + 0*t + 0 - 1/480*t**6 - 15*t**2. Let r(b) = 0. Calculate b.
-2, -1, 3
Find c such that -1/4 + 2*c + 1/4*c**2 - 2*c**3 = 0.
-1, 1/8, 1
Let a(w) be the third derivative of w**8/1680 - 23*w**4/24 - 11*w**2. Let f(x) be the second derivative of a(x). Suppose f(p) = 0. What is p?
0
Let j(h) = -h**3 + h**2 - 2*h + 2. Let i be j(1). Suppose 0 = 2*c + c - 5*o + 19, 5*c + 4*o - 30 = i. Factor -3/2*t**4 + 6*t**3 - 15/2*t**c + 3*t + 0.
-3*t*(t - 2)*(t - 1)**2/2
Let o(c) = c**2 - c - 2. Let a(z) = 8*z**2 + 42*z - 116. Let v(d) = a(d) - 3*o(d). Factor v(g).
5*(g - 2)*(g + 11)
Factor -3/2*s**2 + 54*s + 