b**2 + 4*b - 15*b**2 - 22*b**3 + 4*b**2.
-2*b*(b + 1)*(11*b - 2)
Let m(q) be the third derivative of q**6/600 + q**5/75 + q**4/120 - q**3/5 - 31*q**2. What is l in m(l) = 0?
-3, -2, 1
Let u(z) be the third derivative of -z**5/510 + 8*z**4/17 - 768*z**3/17 - 76*z**2. Determine x so that u(x) = 0.
48
Let r = -19 + 21. Suppose -7*l + l**r - 6*l**2 - 3*l - 2 - 3 = 0. What is l?
-1
Let y(l) be the second derivative of l**4/24 - 5*l**3/4 - 4*l**2 + 79*l + 1. Factor y(z).
(z - 16)*(z + 1)/2
Determine q, given that -15/4*q**4 + 0 + 0*q + 17/4*q**5 - 1/2*q**3 + 0*q**2 = 0.
-2/17, 0, 1
Let h = -20 + 22. What is k in -4*k**h - 6 + 4*k**2 + 3*k + 4*k**2 - k**2 = 0?
-2, 1
Let k be 14/12 - (-2)/6. Factor k*r + 3/2*r**2 - 3.
3*(r - 1)*(r + 2)/2
Let u(y) be the second derivative of y**5 + 45*y**4/4 - 65*y**3/2 + 20*y**2 + y + 214. Suppose u(q) = 0. What is q?
-8, 1/4, 1
Solve 0 + 2/15*z**4 - 2/15*z**3 + 0*z**2 + 0*z = 0.
0, 1
Let h(d) be the third derivative of -d**5/105 + 2*d**4/21 + 10*d**3/21 - 3*d**2 + 98*d. Solve h(p) = 0 for p.
-1, 5
Let r(u) be the third derivative of -u**8/112 - u**7/10 - 7*u**6/40 + 23*u**5/20 + u**4 - 8*u**3 + 504*u**2. Solve r(q) = 0.
-4, -1, 1
Let a(l) = -14*l**2 + 7*l - 30. Let y(o) = -3*o**2. Let r(h) = 3*a(h) - 15*y(h). Factor r(n).
3*(n - 3)*(n + 10)
Let r(g) be the third derivative of 0 + 1/90*g**4 + 0*g**3 + 0*g - 1/900*g**6 - 7*g**2 - 1/450*g**5. What is s in r(s) = 0?
-2, 0, 1
Let l(b) be the first derivative of 2*b**3/3 - 12*b**2 + 22*b + 289. Factor l(j).
2*(j - 11)*(j - 1)
Let b(a) be the second derivative of 35*a**4/4 + 12*a**3 + 6*a**2 - 75*a. Factor b(f).
3*(5*f + 2)*(7*f + 2)
Let f be (-6)/5*(-580)/(-174) + 240/22. Factor 16/11*l**4 - 56/11*l + f*l**2 + 16/11 - 2/11*l**5 - 50/11*l**3.
-2*(l - 2)**3*(l - 1)**2/11
Let r = 260 - 257. Let p(g) be the first derivative of 4/9*g**r + 0*g**2 - 16/3*g - 8. Factor p(b).
4*(b - 2)*(b + 2)/3
Let t(k) be the third derivative of -k**5/480 + 61*k**4/192 - 5*k**3/4 + 482*k**2. Factor t(q).
-(q - 60)*(q - 1)/8
Let l(f) be the third derivative of 0*f - 1/10*f**5 + 0 + 0*f**4 + 0*f**6 + 2*f**3 + 1/280*f**7 - 6*f**2. Determine g, given that l(g) = 0.
-2, 2
Factor -22*v + 2*v + 9*v**2 + 296*v**3 - 291*v**3 + 6*v**2.
5*v*(v - 1)*(v + 4)
Suppose n + 2*n - 6 = 3*c, 0 = 2*c + 3*n - 16. Factor -29*a**c + 54 + 18*a - a**4 + 3*a**4 + 90*a + 101*a**2 + 20*a**3.
2*(a + 1)*(a + 3)**3
Let l(d) = -4*d**2 + 9*d**2 + 8 - d - 5*d - 3*d. Let y(w) = 9*w + 2*w**2 - 3*w**2 - 9 - 5*w**2. Let b(m) = -3*l(m) - 2*y(m). Let b(c) = 0. What is c?
1, 2
Find k such that 38/9*k**4 + 64/9*k - 128/9*k**2 + 2/3*k**5 + 20/9*k**3 + 0 = 0.
-4, 0, 2/3, 1
Let u(b) = b**3 + 6*b**2 + 28*b - 24. Let p(i) = -3*i**3 - 10*i**2 - 57*i + 49. Let n(g) = 2*p(g) + 5*u(g). Let d be n(12). Factor -3/5*s**d + 6/5*s + 0.
-3*s*(s - 2)/5
Let j(x) = -x + 3. Suppose 0 = -7*y + 3*y. Let v be j(y). Factor -3*g**2 + 0*g**3 - 12*g**v + 12*g**2 + 3*g**4 + 12*g - 12.
3*(g - 2)**2*(g - 1)*(g + 1)
Let k(g) = -g**3 + 2*g + 1. Let x be k(-2). Let f = 8 - x. Let -f*d**2 + d**5 - 2*d**5 + 3*d**3 + d**4 + 2*d**4 - 2*d**5 = 0. What is d?
-1, 0, 1
Let f(s) = s**2 - 3*s + 5. Let k(j) = j**2 - 3*j + 6. Let r be 10/15*(7 - 1). Let i be (-1 - -3)*(-6)/r. Let p(l) = i*k(l) + 4*f(l). Find o such that p(o) = 0.
1, 2
Let i(c) be the first derivative of 4*c**3/9 - 28*c**2/3 + 44*c + 89. Factor i(a).
4*(a - 11)*(a - 3)/3
Suppose -22 = -2*g + 4*z, -z + 50 + 5 = 5*g. Factor t**3 + 21 - 5*t**2 + 25*t - g*t**3 - 31.
-5*(t - 1)*(t + 2)*(2*t - 1)
Solve 404 + 71*r**3 - 404 - 91*r**3 + 16*r**2 + 4*r**4 = 0.
0, 1, 4
Suppose 28 = 4*y - 2*y - 4*r, -r = 1. Factor 2 + 4*b**3 + 4*b + 4*b - y*b - 4*b**2 + 2.
4*(b - 1)**2*(b + 1)
Let t(x) be the first derivative of -4*x**3 + 8*x**2/5 + 166. Factor t(w).
-4*w*(15*w - 4)/5
Let i(u) be the first derivative of -u**5/140 - u**4/84 + u**3/21 - 6*u + 9. Let s(q) be the first derivative of i(q). Factor s(f).
-f*(f - 1)*(f + 2)/7
Let y = 694 + -4843/7. Let r be (-2)/(-4) + 48/32. Suppose -y*z**5 + 0 + 9/7*z**4 + 3*z**3 - 9/7*z**r - 6/7*z = 0. Calculate z.
-1, -2/5, 0, 1
Suppose 9 = -5*y + 3*q, -18*y = -17*y - 4*q + 12. Let t be (0 + -3)*1/(-6). Factor y - t*f**2 - f.
-f*(f + 2)/2
Let r(u) be the first derivative of u**6/75 - 3*u**5/50 + u**4/10 - u**3/15 + 14*u + 16. Let p(d) be the first derivative of r(d). Factor p(k).
2*k*(k - 1)**3/5
Factor -2/7 + 4/7*r**2 - 2/7*r - 2/7*r**4 + 4/7*r**3 - 2/7*r**5.
-2*(r - 1)**2*(r + 1)**3/7
Let q = -24137 - -24140. Suppose -1/4*w**4 + 1/4*w**2 - 1/4*w**5 + 0 - 1/2*w + 3/4*w**q = 0. Calculate w.
-2, -1, 0, 1
Let w = 2038 - 8101/4. Let k = 13 - w. Factor 0*x + 1/4*x**4 + 0 - 1/4*x**2 - 1/4*x**5 + k*x**3.
-x**2*(x - 1)**2*(x + 1)/4
Let c(k) be the first derivative of -25*k**3/3 - 80*k**2 - 60*k - 151. Factor c(l).
-5*(l + 6)*(5*l + 2)
Let u(g) = g**4 - 41*g**3 - 24*g**2 - 18*g. Let o(v) = -20*v**3 - 12*v**2 - 8*v. Let h(m) = -9*o(m) + 4*u(m). Suppose h(j) = 0. What is j?
-3, -1, 0
Let a be (-4 - -10)/((-897)/(-260) + (-3)/(-4)). Let 2/7*b**2 - 12/7 + a*b = 0. Calculate b.
-6, 1
Solve 13/4*w**3 + 125/2 - 1/4*w**4 - 25/4*w - 45/4*w**2 = 0.
-2, 5
Factor -80/3*q**2 + 0 + 4/3*q**3 + 400/3*q.
4*q*(q - 10)**2/3
Let v(o) be the first derivative of 3*o**5/5 + 3*o**4/2 - 5*o**3 - 9*o**2 - 35. Find s such that v(s) = 0.
-3, -1, 0, 2
Let r be (-130)/70 + 2 - (-221)/21. Determine q, given that -6*q**3 - r*q + 0 + 2/3*q**4 + 16*q**2 = 0.
0, 1, 4
Let d = 599 + -23959/40. Let r(u) be the second derivative of 0 - 1/24*u**3 + d*u**5 + 1/120*u**6 - 6*u + 1/8*u**2 - 1/24*u**4 - 1/168*u**7. Factor r(p).
-(p - 1)**3*(p + 1)**2/4
Suppose 2*n + 14 - 4 = 0, n + 47 = h. Suppose -h*x + 14*x = 0. Factor 4/7*i**2 + x + 0*i - 4/7*i**3.
-4*i**2*(i - 1)/7
Let v be ((-5)/(20/(-256)))/2. Determine f, given that 6*f**3 + v*f**4 - 16*f**3 + 16*f - 32*f**2 + 6*f**3 - 12*f**5 = 0.
-1, 0, 2/3, 1, 2
Let y(p) = -2*p**2 - 7*p + 11. Let h be y(-6). Let k = -17 - h. Factor 4/3*x + 2/9 + k*x**2.
2*(3*x + 1)**2/9
Let i(p) = p**2 + 8*p + 12. Let f be i(-6). Let s be f + ((-2)/3 - 50/(-60)). Factor 0 - 1/6*v**2 + s*v**3 + 0*v.
v**2*(v - 1)/6
Determine i, given that -3/2*i**2 + 24 + 24*i - 3/2*i**3 = 0.
-4, -1, 4
Let n(t) be the first derivative of 13 + 15/7*t**2 + 3/14*t**4 - 9/7*t - 9/7*t**3. Factor n(c).
3*(c - 3)*(c - 1)*(2*c - 1)/7
Let m = 3504 - 3504. Factor m - 4/21*k**2 + 0*k - 2/21*k**3.
-2*k**2*(k + 2)/21
Let n(c) be the first derivative of 1/4*c**4 - 1/3*c**3 + 0*c - 32 + 0*c**2. Factor n(t).
t**2*(t - 1)
Let r(w) = w + 4. Let i be r(-2). What is c in -34*c**3 - 21*c**3 + 0*c**3 - 60*c**i + 10*c - 15*c**4 - 30*c = 0?
-2, -1, -2/3, 0
Let j(x) = 4*x**3 + 19*x - 227 + 0*x**3 + 23*x**2 + 13*x + 231. Let r(t) = -t**3 - t**2 - t. Let q(z) = 4*j(z) + 36*r(z). Factor q(s).
-4*(s - 4)*(s + 1)*(5*s + 1)
Let g(w) be the third derivative of w**6/72 + w**5/12 - w**3/3 - 15*w**2. Let n(k) be the first derivative of g(k). What is p in n(p) = 0?
-2, 0
Factor 9/4 + 9/2*g**3 - 7/4*g**4 - 1/4*g**5 - 17/4*g - 1/2*g**2.
-(g - 1)**3*(g + 1)*(g + 9)/4
Find v, given that 7500/7*v - 300/7*v**2 + 3/7*v**3 + 0 = 0.
0, 50
Find d, given that -35 - 118*d + 2487*d**2 + 155 - 2489*d**2 = 0.
-60, 1
Let o(m) be the third derivative of m**8/1344 - m**7/144 + m**6/72 + 7*m**5/30 - 10*m**2. Let z(a) be the third derivative of o(a). Factor z(k).
5*(k - 2)*(3*k - 1)
Let u = -29 - -23. Let p be 18/4*u/(-9). Factor 11*d**3 - 17*d**3 + 10*d**p.
4*d**3
Factor 2916*r + 26*r**3 + 2941*r + 43*r**2 - 5785*r + 37*r**2 + 2*r**4.
2*r*(r + 2)**2*(r + 9)
Let c = 3 + -7. Let x be 6/(-8) - 15/c. Suppose -q**x + 3*q**3 - 2*q - 3*q**2 - 6 + 9*q**2 = 0. Calculate q.
-3, -1, 1
Let y(p) = p + 6. Let b be y(-3). Let f(x) be the first derivative of 0*x + 3/16*x**4 + 0*x**2 + 5 - 1/24*x**6 + 0*x**5 - 1/6*x**b. Find q such that f(q) = 0.
-2, 0, 1
Let r(z) be the second derivative of 9*z + 1/10*z**4 - 3/100*z**5 + 0 + 0*z**3 + 0*z**2. Factor r(a).
-3*a**2*(a - 2)/5
Let n be (-20)/(-310) - 11072/(-5208). Suppose 26/21*s**2 + 0 + n*s**4 + 76/21*s**3 + 8/21*s**5 - 4/7*s = 0. Calculate s.
-3, -2, -1, 0, 1/4
Let n be ((-24)/(-16))/(1/(-12)). Let s be (-40)/n*(33/12 + -2). Factor 1/3*k**5 + 4/3*k**4 + 4/3*k**3 - s*k - 2/3*k**2 - 2/3.
(k - 1)*(k + 1)**3*(k + 2)/3
Factor -17 + 2*b**3 + 0*b**4 - 4*b + 44 + b**