 Let s be u(-15). Let v = s + -4. Factor -4*l**3 + 0 - 2*l**v + 16/3*l**4 + 2/3*l + 0*l**2.
-2*l*(l - 1)**3*(3*l + 1)/3
Suppose 20 = 5*z + 5*j, -3*z + 2*j - 2 = -4. Determine i, given that -18 - z*i - 15*i**2 + 17*i + 18*i**2 = 0.
-6, 1
Factor -240*l + 3362 - 81*l + 2*l**2 + 157*l.
2*(l - 41)**2
Let r be (-10)/(-55) - (0 - 10/(-55)). Let s(b) be the second derivative of -7*b + r - 1/48*b**4 - 1/8*b**2 + 1/12*b**3. Factor s(t).
-(t - 1)**2/4
Let r(s) be the third derivative of -2*s**7/105 + s**6/12 + 7*s**5/15 - 2*s**4/3 - 247*s**2. Let r(b) = 0. What is b?
-2, 0, 1/2, 4
Let o(y) be the third derivative of -y**7/35 - 43*y**6/180 - 31*y**5/45 - 5*y**4/9 + 8*y**3/9 - 323*y**2 + 2*y. Determine w so that o(w) = 0.
-2, -1, 2/9
Let k = 340 + -6115/18. Let c(v) be the second derivative of 1/20*v**5 - 7/36*v**4 + k*v**3 + 5*v - 1/6*v**2 + 0. Factor c(t).
(t - 1)**2*(3*t - 1)/3
Let k(f) = 2*f**3 + 53*f**2 + 101*f + 24. Let r(h) = -26*h**2 - 50*h - 12. Let j(g) = -6*k(g) - 13*r(g). Solve j(o) = 0 for o.
-1, -1/3, 3
Factor -85*a**2 - 20*a + 216*a**3 - 733*a**3 + 236*a**3 + 25*a**2 + 236*a**3.
-5*a*(3*a + 2)**2
Let z be -3*(-5 - 94/(-18)) + 10. Let i be -2*2/16*-12. Determine y so that -92/3*y**4 + 36*y**i + 0 + z*y**5 + 8/3*y - 52/3*y**2 = 0.
0, 2/7, 1
Let l = -5 - -7. Let f be -1 + l + (-3)/1. Let w(s) = -2*s**2 + 3*s - 13. Let u(v) = v + 1. Let d(k) = f*w(k) - 10*u(k). Factor d(o).
4*(o - 2)**2
Let f = 9 + -7. Let h = f - 0. Solve -h*u**3 + 8 + 2*u**4 - 6*u**2 + 0*u**3 - 4 + 2*u = 0 for u.
-1, 1, 2
Let y(m) be the first derivative of 0*m - 1/30*m**4 + 0*m**2 + 10 + 2/45*m**3. Suppose y(f) = 0. What is f?
0, 1
Let t = -89 + 85. Let n be 4 + t + 4/5. Find s, given that -2/5*s**3 + 3/5*s**2 - n - 1/5*s**4 + 4/5*s = 0.
-2, 1
Suppose 3*d + 0*d - 54 = 0. Let x = -162 + 169. Determine k, given that 2 + 1 + d*k**2 - x*k**3 - 5*k**3 - 12*k + 3*k**4 = 0.
1
Solve 40/3 + 8/3*g**2 + 54*g = 0 for g.
-20, -1/4
Let p(h) be the first derivative of h**7/210 - h**6/90 - h**5/30 + h**4/6 - 2*h**3/3 + 19. Let j(i) be the third derivative of p(i). Solve j(o) = 0 for o.
-1, 1
Factor -66/5*o - 3*o**2 - 48/5 + 3/5*o**3.
3*(o - 8)*(o + 1)*(o + 2)/5
Let x(y) be the third derivative of -16*y**6/255 - 8*y**5/255 + y**4/51 + y**3/51 + 66*y**2. Find a, given that x(a) = 0.
-1/4, 1/4
Let b(u) be the second derivative of 0 + 22*u - 3*u**2 - u**4 - 9/2*u**3. Solve b(y) = 0.
-2, -1/4
Factor 1/2*s**3 + 8 - 11*s + 5/2*s**2.
(s - 2)*(s - 1)*(s + 8)/2
Suppose 10 - 9 = -39*j + 79. Factor 0 - 1/2*u**j + 3*u.
-u*(u - 6)/2
Let r(s) be the second derivative of s**6/180 + s**5/120 - s**4/36 + 61*s + 1. Factor r(u).
u**2*(u - 1)*(u + 2)/6
Let a(d) = -4*d + 1 - d**3 + 14*d**2 + 4*d + 1 - 13*d. Let y be a(13). Factor -p**2 - p - y + 3*p**2 - 2 - p.
2*(p - 2)*(p + 1)
Let n(b) = -2*b**2 - 8*b - 42. Let t(a) = -5*a**2 - 15*a - 84. Let f(y) = 7*n(y) - 3*t(y). Suppose f(s) = 0. Calculate s.
-3, 14
Let y(h) be the second derivative of 5*h**4/8 + 125*h**3/12 + 10*h**2 - 95*h - 1. Factor y(f).
5*(f + 8)*(3*f + 1)/2
Let d(l) be the first derivative of -l**6/720 + l**5/120 - l**4/72 - 9*l**2/2 + 17. Let z(x) be the second derivative of d(x). Factor z(y).
-y*(y - 2)*(y - 1)/6
Factor 644/3*o + 5508*o**3 + 1908*o**2 + 8 - 972*o**4.
-4*(o - 6)*(9*o + 1)**3/3
Let v(x) be the first derivative of 3*x**3 - 75*x**2/2 - 54*x - 111. Solve v(o) = 0 for o.
-2/3, 9
Let l be (0 - (0 + 0))/3. Let a(i) be the first derivative of -4/3*i**3 + i**4 + l*i - 2 - 2/3*i**6 + 0*i**2 + 4/5*i**5. What is v in a(v) = 0?
-1, 0, 1
Suppose 42*c - 37*c = 15. Suppose 3*w - 24 = -3*x, -c*x - 2*w + 13 = -2*x. Factor 2/13*h**5 + 0 + 0*h + 0*h**x + 2/13*h**4 + 0*h**2.
2*h**4*(h + 1)/13
Let y(x) be the third derivative of -x**5/180 + 25*x**4/72 - 4*x**3/3 + 39*x**2 - x. Factor y(w).
-(w - 24)*(w - 1)/3
Let f(c) = -c**3 + 12*c**2 + 112*c + 26. Let y be f(-6). Factor 1/5 - 1/5*r**y + 0*r.
-(r - 1)*(r + 1)/5
Let y(r) be the first derivative of -7/24*r**4 + 1/12*r**5 + 1/2*r**3 - 3/2*r**2 - 1/120*r**6 + 5 + 0*r. Let l(g) be the second derivative of y(g). Factor l(b).
-(b - 3)*(b - 1)**2
Let i(w) be the second derivative of -w**5/10 - 2*w**4/11 - 137*w. Factor i(m).
-2*m**2*(11*m + 12)/11
Let a be (104/24 - -3)/(122/3). Let z = a + 1021/427. Factor 2/7*q**3 + 54/7 + 54/7*q + z*q**2.
2*(q + 3)**3/7
Let k(m) be the second derivative of -m**10/2520 + m**9/1008 - m**8/2240 - 5*m**4/6 + 11*m. Let n(r) be the third derivative of k(r). Factor n(c).
-3*c**3*(c - 1)*(4*c - 1)
Let m be (512/(-24))/4*(-9)/(-4). Let u be 6/m - 5/(-2). Suppose 0 + 1/6*n**u + 1/3*n = 0. Calculate n.
-2, 0
Let h be (-5 + (-231)/(-51))/(4/(-8)). Find a, given that -4/17*a**3 - 2/17*a**4 + h*a + 8/17 + 6/17*a**2 = 0.
-2, -1, 2
Let p(j) be the first derivative of -j**4/8 - 3*j**3/2 - 27*j**2/4 + 4*j + 7. Let h(l) be the first derivative of p(l). Find u, given that h(u) = 0.
-3
Let n(d) = -2*d - 8. Let z be 1/(4 - (-84)/(-20)). Let v be n(z). Let -w**3 + 12*w**v - 27*w - 2*w**3 + 9 - 3 + 12*w = 0. What is w?
1, 2
Let b be 24/(-38)*(198/44 + -5). Factor b - 8/19*w + 2/19*w**2.
2*(w - 3)*(w - 1)/19
Let g(o) = 2*o**4 + 2*o**3 + 5*o**2 - 18*o + 3. Let p(n) = -11*n**4 - 12*n**3 - 31*n**2 + 108*n - 20. Let c(v) = 34*g(v) + 6*p(v). Suppose c(r) = 0. What is r?
-3, 1, 3
Let s(o) = -2*o**4 - o**2 - o + 1. Let z(r) = -12*r**4 + 12*r**3 - 4*r**2 - 4*r + 4. Let t(g) = -4*s(g) + z(g). Determine v so that t(v) = 0.
0, 3
Let v = -29390 - -175933/6. Let o = 68 + v. Determine f, given that 1/2*f**4 - 1/2*f**2 + 0 - 1/3*f**5 + o*f + 1/6*f**3 = 0.
-1, 0, 1/2, 1
Let y(x) be the first derivative of 11 + 2/5*x**3 - 6/5*x + 3/20*x**4 - 3/10*x**2. Factor y(d).
3*(d - 1)*(d + 1)*(d + 2)/5
Let o(l) = -6*l**3 - 114*l**2 - 1206*l - 1080. Let y(v) = 11*v**3 + 229*v**2 + 2409*v + 2161. Let f(r) = 5*o(r) + 3*y(r). Suppose f(z) = 0. What is z?
-19, -1
Find x, given that 18*x**3 - 3*x**4 + 15 - 13*x**3 + 111*x**2 + 7*x**3 + 93 + 204*x = 0.
-2, -1, 9
Let q(c) be the first derivative of 2/35*c**5 - 2/21*c**3 + 0*c - 1/14*c**2 - 17 + 1/28*c**4. Suppose q(k) = 0. Calculate k.
-1, -1/2, 0, 1
Factor -4/5*a**3 - 24/5 + 2/5*a**4 - 38/5*a**2 - 56/5*a.
2*(a - 6)*(a + 1)**2*(a + 2)/5
Suppose -l + 8 = -3*y, y = 6*l + 5*y - 4. What is m in -7/4*m**3 - 19/4*m**l + 1 - 2*m = 0?
-2, -1, 2/7
Let c be 1*(5 - 2)/((-9)/261). Let a = -87 - c. Suppose 0 + 2/7*k**2 + 2/7*k**3 + a*k = 0. Calculate k.
-1, 0
Suppose -47*k + 42 = -41*k. Let l(j) be the first derivative of j**2 + k - 2/3*j**3 + 0*j. Factor l(g).
-2*g*(g - 1)
Let d be 5/2*54/45. Suppose n - 20 = -d*n. Factor -n*j**3 - j**3 + 5*j**3 + j**5.
j**3*(j - 1)*(j + 1)
Suppose 24*q - 104 = 5*q + 6*q. Factor -q*b - 4/7*b**2 - 28.
-4*(b + 7)**2/7
Let f(b) = -11*b**2 - 130*b - 265. Let n(z) = -5*z**2 - 66*z - 133. Let v(w) = -6*f(w) + 14*n(w). Factor v(s).
-4*(s + 2)*(s + 34)
Let m(h) be the first derivative of 23*h**3/5 + 3*h**2/5 - 25. Factor m(q).
3*q*(23*q + 2)/5
Suppose 3*q + 7 = 13. Factor -2 + i**3 - 4 - 4*i**2 - 8*i**2 + q*i**3 + 15*i.
3*(i - 2)*(i - 1)**2
Let i(g) = -g**3 - 8*g**2 - 6*g - 1. Let b be i(-8). Let 36 + 59*y + 6*y + 11*y**4 + b*y**3 + 77*y**2 + 31*y + 20*y**2 + y**5 = 0. Calculate y.
-3, -2, -1
Let h(s) = s**3 + 387*s**2 - 379*s + 9. Let c(a) = -a**3 - 192*a**2 + 189*a - 4. Let z(b) = -9*c(b) - 4*h(b). Factor z(l).
5*l*(l - 1)*(l + 37)
Let u = -6/113 + 125/226. Let h(o) be the first derivative of 1/6*o**6 - 3/5*o**5 + u*o**4 + 1 + o + 2/3*o**3 - 3/2*o**2. What is s in h(s) = 0?
-1, 1
Let n(j) be the third derivative of 18*j**2 + 0*j - 2/7*j**3 - 1/7*j**4 + 0 - 1/140*j**5 + 3/280*j**6. Suppose n(a) = 0. Calculate a.
-1, -2/3, 2
Factor -12/11*y**2 - 8/11*y - 2/11*y**4 - 2/11 - 8/11*y**3.
-2*(y + 1)**4/11
Factor 7/6*w**5 + 0 + 1/3*w**2 + 1/2*w**3 - 2*w**4 + 0*w.
w**2*(w - 1)**2*(7*w + 2)/6
Let u(c) = -7*c**3 + 3*c**2 - 6. Let r(z) = z + 1. Let d(m) = 6*r(m) + 2*u(m). Let s(w) = -5*w**3 + 2*w**2 + 2*w - 2. Let t(x) = 3*d(x) - 8*s(x). Factor t(j).
-2*(j - 1)**2*(j + 1)
Factor 1912*a**3 - 199 + 78*a - 1914*a**3 + 55 - 4*a**2.
-2*(a - 3)**2*(a + 8)
Let o(y) be the first derivative of y**4/18 - 7*y**3/27 + 2*y**2/9 - 9*y - 30. Let l(c) be the first derivative of o(c). Factor l(r).
2*(r - 2)*(3*r - 1)/9
Factor 9*x**2 + 160*x + 163*x - 293*x - 3*x**3.
-3*x*(x - 5)*(x + 2)
Let 