r(h) = 3*h**3 + 34*h**2 + 10*h - 9. Let s be r(-11). Let q(j) be the first derivative of -2*j**s + 8 + 0*j - 2/3*j**3. Solve q(l) = 0.
-2, 0
Factor -16/7 - 18/7*v**2 - 44/7*v.
-2*(v + 2)*(9*v + 4)/7
Let s(w) be the third derivative of w**6/1980 + w**5/660 - w**4/66 - w**3/2 + 6*w**2. Let j(n) be the first derivative of s(n). Determine r so that j(r) = 0.
-2, 1
Let p = -10 - -9. Let v be -2*p*(-18)/(-4). Factor -7*n**5 + 4*n**5 - 6*n**4 + v*n**4.
-3*n**4*(n - 1)
Suppose 5*l + 1 = 4*m, 5*l - 4*m - 3 = -m. Determine t so that t**4 - t**4 + t**4 - 3*t**l + 4*t**3 = 0.
-1, 0
Let n(z) be the second derivative of 0 - 10/3*z**3 + 4/3*z**4 + 20*z - 1/5*z**5 + 4*z**2. Let n(r) = 0. Calculate r.
1, 2
Suppose 15*i = 10*i + 90. Suppose 17 - i = -h. Determine s so that 19/4*s**2 + 2*s - h + 7/4*s**3 = 0.
-2, -1, 2/7
Let w be 0*3/24*((-8)/(-3))/(-8). Factor -45/4*u**2 - 5/2*u + w.
-5*u*(9*u + 2)/4
Let g be 2/(1 - 6/2). Let j be (-2)/g - (-92)/161. Factor -10/7*f**2 + j - 2/7*f**3 - 6/7*f.
-2*(f - 1)*(f + 3)**2/7
Let o(l) = 36*l**3 - 36*l**2 - 126*l. Let j(p) = -5*p**3 + 5*p**2 + 18*p. Let u(a) = 15*j(a) + 2*o(a). Find s such that u(s) = 0.
-2, 0, 3
Suppose 6*u = 16 - 4. What is i in i**2 + 5*i + i**2 + 5*i**3 - 12*i**u = 0?
0, 1
Let u(i) be the first derivative of -i**4/24 + 4*i**3/9 + 19*i**2/12 + 5*i/3 - 229. Factor u(g).
-(g - 10)*(g + 1)**2/6
Let h(j) be the first derivative of -j**5/150 + j**4/30 - j**3/15 - 5*j**2 - 11. Let i(x) be the second derivative of h(x). Determine r, given that i(r) = 0.
1
Let c(j) be the third derivative of -j**7/315 - j**6/60 - j**5/30 - j**4/36 - 19*j**2 + j. Factor c(f).
-2*f*(f + 1)**3/3
Let a = -71 - -69. Let h be ((-2)/(-10)*-9)/(a/2). Factor h*n**2 + 2/5 - 7/5*n + 1/5*n**4 - n**3.
(n - 2)*(n - 1)**3/5
Let f = -50773 - -50775. Find u such that 4/13 + 8/13*u**f - 14/13*u + 8/13*u**3 = 0.
-2, 1/2
Let m be (24/(-16))/(6/(-16)). Let k be (-3)/m*(-1 + -3). Find a, given that -4*a**4 + 0*a**5 + 6*a**2 - k*a**3 + 2*a**5 - 2*a**4 + a**5 = 0.
-1, 0, 1, 2
Let j(u) be the first derivative of -u**3/9 - 4*u**2/3 - 5*u - 56. Determine t so that j(t) = 0.
-5, -3
Let y(m) = -5*m**2 - 12*m - 2. Let p(j) = -6*j**2 - 12*j - 3. Let n(f) = 2*p(f) - 3*y(f). Solve n(a) = 0 for a.
-4, 0
Suppose -11*u = -16 - 39. Let r be (-2 - -3) + u*1/5. Let -2/9*d - 22/3*d**3 - 32/9*d**5 + 20/9*d**r + 0 + 80/9*d**4 = 0. Calculate d.
0, 1/4, 1
Let f = 107 + -103. Let q(m) be the second derivative of -18*m**2 - 8*m + 0 + 4*m**3 - 1/3*m**f. Factor q(y).
-4*(y - 3)**2
Let p(c) = c**5 - c**4 - c**3 - c**2 - c. Let o(z) = 27*z**4 + 69*z**3 + 75*z**2 + 30*z. Let l(y) = -o(y) - 3*p(y). Factor l(q).
-3*q*(q + 1)**2*(q + 3)**2
Let r = -10376266/13299 + 24290/31. Let y = r - -2/143. Determine w, given that -y*w**2 - 2 + 2/3*w**3 + 14/3*w = 0.
1, 3
Let m(c) be the third derivative of -c**5/15 - 4*c**4 - 46*c**3/3 - 32*c**2. Factor m(u).
-4*(u + 1)*(u + 23)
Let z(j) be the third derivative of 0*j**3 - 1/84*j**8 - 3/35*j**7 - 3/10*j**5 + 0*j + 0 + 4*j**2 - 7/30*j**6 - 1/6*j**4. What is y in z(y) = 0?
-2, -1, -1/2, 0
Let m(y) be the second derivative of y**7/168 - 3*y**6/40 + 23*y**5/80 - 7*y**4/48 - y**3 + 2*y**2 + 7*y + 17. Suppose m(p) = 0. What is p?
-1, 1, 4
Let j(b) be the second derivative of 0*b**2 - 15*b - 1/5*b**5 + 1/6*b**4 + 0 + 1/15*b**6 + 0*b**3. Find p, given that j(p) = 0.
0, 1
Let n(c) = c**3 - 37*c**2 - 37*c - 36. Let j be n(38). Factor -13/8*d**j + 3/4*d**3 - 1/8*d**4 - 1/2 + 3/2*d.
-(d - 2)**2*(d - 1)**2/8
Factor 7*v - 39*v**2 - 36*v**3 + 3*v**4 - 4*v - 3*v.
3*v**2*(v - 13)*(v + 1)
Let k(c) be the third derivative of -c**6/48 - 23*c**5/24 - 215*c**4/48 - 35*c**3/4 + 74*c**2 - 3. Find d, given that k(d) = 0.
-21, -1
Let d(l) be the first derivative of l**3/9 + 2*l**2/3 - 5*l/3 - 23. Suppose d(g) = 0. Calculate g.
-5, 1
Let r(q) be the third derivative of 0*q - 1/570*q**5 + 0 + 27*q**2 + 4/57*q**3 + 0*q**4. Let r(h) = 0. Calculate h.
-2, 2
Suppose -4*g + 6 = 42*r - 39*r, r - 4*g - 2 = 0. Factor 4*z + 8/3 + 1/3*z**3 + r*z**2.
(z + 2)**3/3
Let t(m) be the first derivative of -m**6/2 - 54*m**5/5 - 129*m**4/2 + 56*m**3 + 2205*m**2/2 - 2058*m + 164. Find u, given that t(u) = 0.
-7, 1, 2
Suppose 0 = 381*g - 382*g. Let s(j) be the third derivative of 0*j**3 + 1/3*j**4 + 0 - 1/15*j**5 + 5*j**2 + g*j - 1/30*j**6. Determine k so that s(k) = 0.
-2, 0, 1
Let m(x) = x**3 - 22*x**2 + 4*x + 17. Let n(g) = -2*g**3 + 34*g**2 - 6*g - 26. Let r(s) = -8*m(s) - 5*n(s). Solve r(o) = 0 for o.
-3, -1, 1
Let s(i) be the third derivative of 0*i + 0 + 0*i**3 + 1/390*i**5 + 21*i**2 + 2/39*i**4. Factor s(y).
2*y*(y + 8)/13
Suppose 18*a - 27*a = 59*a. Let i be 12/(-15) - 1*-1. Factor i*t**3 + 1/5*t**2 - 2/5*t + a.
t*(t - 1)*(t + 2)/5
Factor -108 - 123*y**3 - 2*y**5 + 252*y**3 + 17*y + 9*y**4 + y**5 - 152*y**3 - 9*y**2 + 91*y.
-(y - 3)**3*(y - 2)*(y + 2)
Factor 4/3*d + 0 - 1/3*d**2.
-d*(d - 4)/3
Factor 2*c**5 - 5*c - c**5 - 20*c**4 - 30*c**3 - 6*c**5 + 310*c**2 - 330*c**2.
-5*c*(c + 1)**4
Let n(p) = 3*p**2 + 21*p + 30. Let d be n(-5). Let m(h) be the second derivative of 3/130*h**5 + d*h**2 + 5/78*h**4 + 0 + 2/39*h**3 - h. What is u in m(u) = 0?
-1, -2/3, 0
Let f = -1322 - -1322. Let x(o) be the third derivative of f*o + 1/105*o**5 + 0 + 1/210*o**6 + 8*o**2 + 0*o**4 + 0*o**3. Solve x(c) = 0 for c.
-1, 0
Let f(y) = y**2 - 15*y - 1. Let v be f(15). Let b be 2*2/16*(0 - v). Determine u, given that b*u**2 + 9/4 - 3/2*u = 0.
3
Let l(d) be the second derivative of 0 + 10/27*d**3 - d**2 - 1/54*d**4 + 11*d. Factor l(n).
-2*(n - 9)*(n - 1)/9
Let r(z) = 26*z**2 + 6. Let s(y) = -4*y**2 - 1. Let v(k) = r(k) + 6*s(k). What is l in v(l) = 0?
0
Suppose 0 = 5*h - 39*h + 68. Let r(c) be the third derivative of 0*c + 0*c**3 + 0*c**4 - 1/10*c**5 - 2*c**h + 1/40*c**6 + 0. Factor r(t).
3*t**2*(t - 2)
Let 2/5*w**2 - 24/5 - 8/5*w = 0. What is w?
-2, 6
Factor 0 + 4/13*q + 2/13*q**3 - 6/13*q**2.
2*q*(q - 2)*(q - 1)/13
Let v(u) be the first derivative of -u**2/2 + 3*u - 7. Let b be v(1). Solve -3*p - 352 + 352 - 3*p**b = 0 for p.
-1, 0
Let c(a) be the third derivative of -a**5/15 - 100*a**4/3 + 134*a**3 + 246*a**2. Find m such that c(m) = 0.
-201, 1
Let y(n) be the third derivative of n**6/120 - n**5/15 - 43*n**2. Let y(v) = 0. What is v?
0, 4
Factor -4*b**3 + 41*b + 56*b**2 - 7*b**4 - b**5 - 57*b + 6*b**3 - 112 + 6*b**3 + 0*b**5.
-(b - 2)**2*(b + 2)**2*(b + 7)
Suppose -122*b + 558 = 64*b. Factor -3*q**2 + 3/2*q**b + 0 - 12*q.
3*q*(q - 4)*(q + 2)/2
Suppose -403*d + 200*d = 0. Solve 2/5*l**3 - 6/5*l + d*l**2 - 4/5 = 0 for l.
-1, 2
Let g(a) = -3*a**2 + 48*a - 626. Let d(w) = 2*w**2 + 2*w + 1. Let n(p) = -4*d(p) - 4*g(p). Suppose n(c) = 0. Calculate c.
25
Let w be 14*4/8 + -3. Factor -2*c**4 + 3 + 0*c**4 + w*c**3 - 4*c - 1 + 0*c.
-2*(c - 1)**3*(c + 1)
Factor 46/15*u**2 + 352/15*u + 2/15*u**3 + 896/15.
2*(u + 7)*(u + 8)**2/15
Let v = 23228 + -23225. Suppose 0 = 5*h - 5*z + 23 - 8, 15 = -h + 5*z. Factor 0*w + h*w**v + 2/7*w**4 - 16/7*w**2 + 32/7.
2*(w - 2)**2*(w + 2)**2/7
Let v(i) be the first derivative of -i**3/3 + 13*i**2/2 - 12*i + 102. Factor v(k).
-(k - 12)*(k - 1)
Let t(f) be the first derivative of -f**6/216 + 5*f**4/72 + 11*f**3/3 - 19. Let z(n) be the third derivative of t(n). Factor z(c).
-5*(c - 1)*(c + 1)/3
Let s(p) be the second derivative of 1/5*p**5 + 0*p**3 + 0 + 9*p + 0*p**2 - 1/3*p**4. Factor s(b).
4*b**2*(b - 1)
Suppose 64*s - 2*s - 248 = 0. Suppose -r**2 + 6*r - 1/2*r**5 - 11/2*r**3 - 3*r**4 + s = 0. What is r?
-2, -1, 1
Let g(r) be the first derivative of -1/8*r**3 + 0*r**2 - 13 + 0*r + 0*r**4 + 3/40*r**5. Solve g(y) = 0.
-1, 0, 1
Let o(s) be the first derivative of s**4/2 + 80*s**3/3 + 400*s**2 - 235. Suppose o(d) = 0. What is d?
-20, 0
Let s(v) be the second derivative of v**7/42 - 29*v**6/30 + 56*v**5/5 - 49*v**4/3 + 3*v + 29. Factor s(c).
c**2*(c - 14)**2*(c - 1)
Let h(o) be the second derivative of -7*o**7/900 + 7*o**6/150 - 3*o**5/25 + 11*o**4/12 + 30*o. Let i(u) be the third derivative of h(u). Factor i(l).
-2*(7*l - 6)**2/5
Let u(q) be the first derivative of -q**4/2 - 4*q**3/3 + q**2 + 4*q + 36. Determine c so that u(c) = 0.
-2, -1, 1
Let a be 13*-4*4/(-16). Suppose -a*y = -7*y. Solve 4/3*b**2 + 0 + y*b - 2/3*b**3 = 0 for b.
0, 2
Let h(i) = -2*i**2 - 11*i + 8. Let v be h(-6). Let 