Let g be -5 - (50/p - 3/2). Factor g*s**2 + 8/3 + 8/3*s.
2*(s + 2)**2/3
Let q = 1671/2 + -831. Suppose -3*j**3 + q*j**2 + 3/4*j**4 - 3*j + 3/4 = 0. What is j?
1
Let v be 0 + 0/(16/4). Suppose v = 4*a + a - 20. Let -a*z - z**3 - 3*z**2 - 2*z**3 + 4*z = 0. What is z?
-1, 0
Factor p**5 - 30*p + 46*p**3 - 9*p**4 - 23*p**3 - 3*p**2 - 6*p.
p*(p - 4)*(p - 3)**2*(p + 1)
Let s(t) be the second derivative of -t**5/80 - t**4/48 + 74*t. Factor s(r).
-r**2*(r + 1)/4
Solve 2/5*s - 18/5*s**2 - 2/5*s**3 + 18/5 = 0 for s.
-9, -1, 1
Let t(z) be the second derivative of -2*z**6/75 + 3*z**5/25 + 3*z**4/5 + 2*z**3/3 + 66*z. Determine g so that t(g) = 0.
-1, 0, 5
Let n(u) = -85*u**2 - 255*u. Let v(c) = 5*c**2 + 15*c. Let i(w) = w**2 + 23*w + 11. Let a be i(-24). Let h(l) = a*v(l) + 2*n(l). Factor h(g).
5*g*(g + 3)
Let a(j) = 49*j**4 + 75*j**3 + 36*j**2 - 9*j - 18. Let m(c) = 12*c**4 + 19*c**3 + 9*c**2 - 2*c - 4. Let o(g) = -4*a(g) + 18*m(g). Find s such that o(s) = 0.
-3/2, -3/5, 0
Let z(r) be the first derivative of -9*r**2 + 18*r**3 + 3/2*r - 18. What is f in z(f) = 0?
1/6
Factor 2/11*r**4 + 0 - 4/11*r**3 + 2/11*r**2 + 0*r.
2*r**2*(r - 1)**2/11
Let m(u) be the first derivative of -2/3*u**3 + 0*u - 1/24*u**4 + 6 + 0*u**2 - 1/360*u**6 + 1/60*u**5. Let f(b) be the third derivative of m(b). Factor f(p).
-(p - 1)**2
Let c(k) = 2*k + 3. Let t(a) = 22*a**3 - 744*a**2 + 6202*a + 1126. Let s(p) = -10*c(p) - t(p). Suppose s(n) = 0. Calculate n.
-2/11, 17
Let g(t) be the third derivative of -t**7/21 + 11*t**6/24 + 5*t**5/3 + 35*t**4/24 + 150*t**2. Determine s so that g(s) = 0.
-1, -1/2, 0, 7
Let b = -2710 - -2710. Suppose 9/4*r**3 + b*r + 0 + 3/2*r**2 + 3/4*r**4 = 0. What is r?
-2, -1, 0
Suppose 26 = -2*a + 36. Let o be a/(-25) - (2 - 42/10). Factor 0 + 2*v**o - 4/3*v.
2*v*(3*v - 2)/3
Let y be ((-16)/5 + -2)*999/(-54). Let a = -96 + y. Factor 1/5*o**2 + 3/5*o**4 - 3/5*o**3 + 0 - a*o**5 + 0*o.
-o**2*(o - 1)**3/5
Factor -16*x - x**3 - 4*x**3 + 20*x**2 - x + 2*x.
-5*x*(x - 3)*(x - 1)
Suppose -3*h = -3*a - 6*h + 57, 5*h = 25. Suppose 0 = 4*k + p - a, 2*k + p - 6 = -0*k. Let -3*s**2 + k*s**3 + 3*s**2 - 25*s + 13*s + 8 = 0. What is s?
-2, 1
Let t(d) be the second derivative of -d**5/220 + 2*d**4/33 - 3*d**3/22 - 9*d**2/11 - 82*d + 2. Factor t(s).
-(s - 6)*(s - 3)*(s + 1)/11
Let g(m) be the second derivative of m**5/48 + 5*m**4/96 + 11*m**2/2 + 9*m. Let j(d) be the first derivative of g(d). Determine l, given that j(l) = 0.
-1, 0
Let m(x) be the third derivative of 2/105*x**7 - 13*x**2 + 0*x**3 + 0*x**4 + 1/84*x**8 - 1/15*x**5 - 1/30*x**6 + 0*x + 0. Factor m(j).
4*j**2*(j - 1)*(j + 1)**2
Factor 99*u - 97*u + 24*u**2 - 23*u**2 - 15.
(u - 3)*(u + 5)
Let 1/4*a**2 - 18*a + 71/4 = 0. What is a?
1, 71
Let f(u) be the third derivative of u**7/70 + u**6/20 - u**5/20 - u**4/4 + 32*u**2. Factor f(x).
3*x*(x - 1)*(x + 1)*(x + 2)
Let y(i) be the first derivative of i**5/190 + i**4/57 + 5*i - 5. Let x(v) be the first derivative of y(v). What is r in x(r) = 0?
-2, 0
Let i(y) be the second derivative of -y**4/2 + 19*y**3/3 - 6*y**2 + 92*y. Factor i(x).
-2*(x - 6)*(3*x - 1)
Factor 0 + 2/5*r + 3/5*r**2 + 1/5*r**3.
r*(r + 1)*(r + 2)/5
Let m(n) = -5*n**3 - n**2 + n + 1. Let i be m(-1). Suppose 0*t + t - i = 0. Factor -5 + 5 - t*q**2 + 3*q + 5*q.
-4*q*(q - 2)
Let k(z) be the third derivative of 2*z**7/105 + 7*z**6/60 - z**5/15 - 7*z**4/12 - 8*z**2 + 8. Factor k(t).
2*t*(t - 1)*(t + 1)*(2*t + 7)
Let i(r) be the third derivative of -r**7/490 + 9*r**6/280 + r**5/140 - 9*r**4/56 - r**2 - 30*r. Factor i(l).
-3*l*(l - 9)*(l - 1)*(l + 1)/7
Suppose -5*o - 49*o + 184 = -8*o. Solve -8/3*i**3 + o*i + 8/3*i**2 + 4/3 - 4*i**4 - 4/3*i**5 = 0.
-1, 1
Suppose -4*d**2 - 34/9*d + 0 - 2/9*d**3 = 0. Calculate d.
-17, -1, 0
Let h(l) be the third derivative of -l**7/70 + l**6/10 + 13*l**5/20 - 5*l**4 - 24*l**3 + 434*l**2. Factor h(i).
-3*(i - 4)**2*(i + 1)*(i + 3)
Let u(x) = 11*x - 2. Let l be u(2). Suppose l = -4*k, -p + 0*k + 7 = -k. Factor 2/5*n - 4/5 - 2/5*n**3 + 4/5*n**p.
-2*(n - 2)*(n - 1)*(n + 1)/5
Let r(x) = -12*x**4 - 63*x**3 + 99*x**2 + 6*x - 135. Let l(q) = -7*q**4 - 32*q**3 + 49*q**2 + 2*q - 67. Let o(h) = 9*l(h) - 5*r(h). Factor o(v).
-3*(v - 6)*(v - 2)**2*(v + 1)
Factor 1/2*w**2 + 3025/2 + 55*w.
(w + 55)**2/2
Let v = -34 - -34. Let p(b) be the third derivative of v*b + 0*b**5 + 1/1155*b**7 + 0*b**3 + 0*b**4 + 0 - 5*b**2 + 1/660*b**6. Factor p(r).
2*r**3*(r + 1)/11
Let q(b) be the first derivative of -b**3/3 + b**2/2 + 6*b + 81. What is v in q(v) = 0?
-2, 3
Let j(w) be the second derivative of -w**5/60 - w**4/12 - w**3/6 + 9*w**2/2 - 12*w. Let x(i) be the first derivative of j(i). Factor x(d).
-(d + 1)**2
Suppose -16*j = 283 - 347. Factor 5*g**j - 1/2*g**2 + 0 + 0*g + 3/4*g**3.
g**2*(4*g - 1)*(5*g + 2)/4
Let a(i) = -i**3 + i + 1. Let y(p) = 21*p**3 - 5*p**2 - 6*p - 6. Suppose -5*s = 3*s - 8. Let g(u) = s*y(u) + 6*a(u). Find z such that g(z) = 0.
0, 1/3
Let m(u) = -3*u**2 - 5*u**3 - 10 - 4*u**2 + 10*u**2 + 18*u. Let i(c) = -65*c**3 + 40*c**2 + 235*c - 130. Let s(z) = -3*i(z) + 40*m(z). Factor s(j).
-5*(j - 1)**2*(j + 2)
Let i(q) = -q**2 - 19*q - 7. Let t(g) = g + 1. Let s(j) = i(j) + 4*t(j). Let r be s(-14). Factor 31*f**2 - 10*f + r*f**2 - 3*f**4 + 9 - 3*f**5 + 18*f**3 + 43*f.
-3*(f - 3)*(f + 1)**4
Let r(y) be the second derivative of y**5/50 - 31*y**3/15 + 6*y**2 + 221*y. Solve r(p) = 0.
-6, 1, 5
Let u(l) = 698*l - 2092. Let b be u(3). Factor 1/5 - 3/5*i - 1/5*i**3 + 3/5*i**b.
-(i - 1)**3/5
Let x(g) be the third derivative of g**8/5040 + g**7/420 + g**6/90 - g**5/12 + 3*g**2. Let u(j) be the third derivative of x(j). Find o such that u(o) = 0.
-2, -1
Let l(v) be the second derivative of v**5/4 + 15*v**4/2 + 85*v**3/6 + 63*v. Factor l(q).
5*q*(q + 1)*(q + 17)
Let c(o) be the third derivative of 1/12*o**3 - 1/840*o**7 + 1/480*o**6 + 0 - 5/96*o**4 + 14*o**2 + 1/80*o**5 + 0*o. Suppose c(i) = 0. Calculate i.
-2, 1
Let i(m) = -m**3 - m**2 + m - 2. Let o(g) = -6*g**4 - 6*g**3 + 4*g**2 + 6*g - 19. Let u(q) = 21*i(q) - 3*o(q). What is t in u(t) = 0?
-1, -5/6, 1
Let j be (-2 - (5 - 1))/(-2). Suppose j*c + 38 = 50. Suppose -2*s + 2/3*s**5 + 8/3*s**2 + 0 - 8/3*s**c + 4/3*s**3 = 0. Calculate s.
-1, 0, 1, 3
Let i(u) be the first derivative of u**7/1470 + 11*u**6/630 + u**5/6 + 25*u**4/42 + 4*u**3 + 10. Let s(y) be the third derivative of i(y). Factor s(b).
4*(b + 1)*(b + 5)**2/7
Determine j so that 2/5*j - 92/5*j**2 - 2/5*j**3 + 92/5 = 0.
-46, -1, 1
Let m be 2 - (-7)/(28/(-8)). Let s(b) be the second derivative of -1/72*b**4 + 0*b**3 + 0 - 7*b + m*b**2. Factor s(v).
-v**2/6
Let b(f) be the third derivative of 0*f + 0 + 20*f**2 - 1/40*f**6 - 5/8*f**4 + f**3 + 1/5*f**5. Solve b(r) = 0 for r.
1, 2
Let v(w) be the first derivative of 6/7*w**2 - 12/7*w + 1/7*w**3 - 3/28*w**4 - 18. What is g in v(g) = 0?
-2, 1, 2
Suppose 7*k - 9 = 5. Factor -55*w**k - 2*w**4 - 3*w - w**3 + 57*w**2 + 4*w.
-w*(w - 1)*(w + 1)*(2*w + 1)
Let w = 5 + 71. Find d, given that 4*d**3 + w*d**2 - 138*d**2 + 4*d + 70*d**2 = 0.
-1, 0
Let l(m) be the third derivative of -m**6/240 - m**5/5 - 23*m**4/48 + 179*m**2. Factor l(b).
-b*(b + 1)*(b + 23)/2
Let z(d) = -d**3 - 7*d**2 + 21*d + 29. Let b be z(-9). Determine u so that -2*u**b - 15*u + 10*u + 12*u + 3*u**2 = 0.
-7, 0
Let a = 95 + -89. Let s be 40/(-30)*a/(-8). Solve 1/2*y**2 + 1/2*y - s = 0 for y.
-2, 1
Factor 51*k**3 + 84*k**3 + 6*k**4 - 137*k**3 - 6*k**2 + 2*k**5.
2*k**2*(k - 1)*(k + 1)*(k + 3)
Let j(x) be the first derivative of -1/70*x**5 + x + 1/7*x**3 + 0*x**4 - 4 + 2/7*x**2. Let r(k) be the first derivative of j(k). Factor r(c).
-2*(c - 2)*(c + 1)**2/7
Let t(a) = -2*a + 14. Let z be t(6). Let m(g) = g**3 - g**2 + g - 1. Let i be m(2). Find b, given that i*b + b**3 - 8 - 4*b**2 + 3*b**z - 5*b**2 + 7*b = 0.
2
Factor 36*j**2 - 4*j**2 - 7*j**2 - 16*j**2 - 27*j + 15 + 3*j**3.
3*(j - 1)**2*(j + 5)
Let i be (-264)/(-70) - 4/14. Let d = -16/5 + i. Solve 1/7*k**2 - d*k + 1/7 = 0.
1
Factor -z**3 + 1201 - 302 - 322 - 424 + 93*z + 11*z**2.
-(z - 17)*(z + 3)**2
Let q(n) be the first derivative of -n**6/11 - 164*n**5/55 - 837*n**4/22 - 2556*n**3/11 - 7020*n**2/11 - 3888*n/11 - 542. Find f such that q(f) = 0.
-9, -6, -1/3
Let i(r) be the second derivative of -r**6/120 + r**5/10 + 25*r**3/6 + 8*r. Let j(p) be th