r**4 + 1/2*r**2 + d.
-r**2*(r - 2)*(r + 1)**2/4
Let g(d) = d**3 - 21*d**2 + 20*d. Let b be g(20). Suppose b = 7*q + 7*q - 2*q. Factor 4/19*t**2 + q + 0*t + 6/19*t**3.
2*t**2*(3*t + 2)/19
Let a(d) = 21*d**3 - 54*d**2 + 30*d + 6. Let q(k) = k**4 - k**3 - k**2 + 2. Let j(z) = -a(z) + 3*q(z). Find x, given that j(x) = 0.
0, 1, 2, 5
Suppose 5*i = 4*z + 20, i - 4*z = -0*z - 12. Factor 33 - 4*f**2 + i*f - 4*f - 4*f**3 + 12*f - 17.
-4*(f - 2)*(f + 1)*(f + 2)
Let b(t) be the third derivative of t**7/1995 - t**6/190 + 11*t**5/570 - t**4/38 + 23*t**2 - 2*t. Let b(w) = 0. Calculate w.
0, 1, 2, 3
Suppose 2*a = -3*a - 5*n + 25, -a - 5*n = 11. Suppose 3 = -2*i + a. Factor f**i + 85*f**2 - 78*f**2 + f**3 - 5*f**3 - 4.
-(f - 2)*(f - 1)*(3*f + 2)
Let w(y) be the second derivative of -y**4/27 + 97*y**3/27 + 49*y**2/9 - 3*y - 12. Factor w(n).
-2*(n - 49)*(2*n + 1)/9
Let g(x) be the second derivative of -x**5/120 + x**4/16 + 25*x**2/2 - 9*x. Let w(p) be the first derivative of g(p). Solve w(i) = 0 for i.
0, 3
Let j(a) be the first derivative of a**3 - 9*a**2 + 126. Suppose j(s) = 0. Calculate s.
0, 6
Suppose 20 = 6*l - l. Factor 3 - 3*y + 4*y**2 - l + y**3 + 3 + 8*y.
(y + 1)**2*(y + 2)
Let v be (6/9)/(((-200)/(-6))/10). Factor -1/5 + 1/5*l**2 - v*l + 1/5*l**3.
(l - 1)*(l + 1)**2/5
Let h = 193 - 189. Let u(n) be the second derivative of -1/6*n**3 - n**2 - 6*n + 1/12*n**h + 0. Solve u(q) = 0 for q.
-1, 2
Factor 38*r - 51/2*r**2 - 8 - 1/2*r**4 + 49/8*r**3.
-(r - 4)**3*(4*r - 1)/8
Let u = 3/7 - 2/21. Let l be -5 + 4 - (116/(-60) - 6/(-10)). Determine k so that u*k**2 + 2/3*k + l = 0.
-1
Factor 11*d + 2*d - 6 + 22 + 4*d**2 + 3*d.
4*(d + 2)**2
Let i(w) be the second derivative of -w**8/2800 + w**7/1400 + w**6/120 + 3*w**5/200 + 3*w**3 - 4*w. Let v(b) be the second derivative of i(b). Factor v(h).
-3*h*(h - 3)*(h + 1)**2/5
Determine b, given that 124/5 + 2/5*b**2 + 126/5*b = 0.
-62, -1
Let p(b) be the first derivative of -1/20*b**5 + 0*b**2 + 1/24*b**6 + 0*b**3 - 1/8*b**4 + 0*b - 5. Factor p(i).
i**3*(i - 2)*(i + 1)/4
Let k(r) be the third derivative of -r**5/30 - 5*r**4/6 - 3*r**3 - 34*r**2. Solve k(y) = 0.
-9, -1
Let r(a) = 4*a**3 - 2*a**2 + 5. Let i(v) = 3*v**3 - 2*v**2 + 4. Let h(q) = -5*i(q) + 4*r(q). Find n such that h(n) = 0.
-2, 0
Let r(t) be the third derivative of t**5/300 - 49*t**4/120 - 324*t**2. Find v, given that r(v) = 0.
0, 49
Suppose -3*q = -4*u - 38, 7*q = 6*q - 4*u - 14. Let b(j) be the second derivative of -q*j - 2/5*j**2 + 4/15*j**3 - 1/15*j**4 + 0. Let b(c) = 0. What is c?
1
Suppose 3*c - 5*a = -43, -c - 3*a - 15 = 4*c. Let z be (c/4 + 2)*6. Solve -k**z - k**2 + k**5 - 2 - 3 + k**4 + 5 = 0 for k.
-1, 0, 1
Let o(a) = 27*a**2 - 3*a. Let h(k) = -41*k**2 + 4*k. Let l(v) = 2*h(v) + 3*o(v). Factor l(g).
-g*(g + 1)
Suppose -23 + 25 = n. Let v(k) = -k**5 + k. Let m(o) = -4*o**5 + o**4 - o**3 - o**2 + 5*o. Let u(r) = n*m(r) - 10*v(r). Suppose u(x) = 0. Calculate x.
-1, 0, 1
Let w(a) be the second derivative of a**4/60 + 11*a**3/10 - 7*a**2 - 583*a. Factor w(s).
(s - 2)*(s + 35)/5
Let i(x) = -x**3 - 6*x**2 + 28. Let p be i(-5). Let o(q) be the second derivative of 0 - 1/6*q**p - 1/36*q**4 - 4*q + 0*q**2. Suppose o(a) = 0. What is a?
-3, 0
Let u(h) = 2*h**2 + 12*h + 4. Let j(g) = -g**2 - 14*g - 6. Let a(m) = 2*j(m) + 3*u(m). Find p such that a(p) = 0.
-2, 0
What is s in -3/2*s**3 + 3*s**2 - 3/2*s**4 - 3/2 + 3/4*s**5 + 3/4*s = 0?
-1, 1, 2
Factor 0 + 4/9*o - 4/9*o**3 + 1/9*o**4 - 1/9*o**2.
o*(o - 4)*(o - 1)*(o + 1)/9
Let i = 16 - 14. Suppose 0 = i*q + 5 - 13. Factor 8 - q + b**3 + 3*b**3 + 4 + 12*b**2 - 4*b**4 - 20*b.
-4*(b - 1)**3*(b + 2)
Let h(l) = l - 15. Let i be h(17). Solve -4*g**3 + 2*g**2 - 5*g**5 + 15*g**4 - 9*g**3 - 2*g**3 + 3*g**i = 0.
0, 1
Let k(j) be the first derivative of -1/3*j**3 - 1/210*j**5 + 5 + 0*j**2 - 1/1260*j**6 + 0*j - 1/84*j**4. Let i(t) be the third derivative of k(t). Factor i(a).
-2*(a + 1)**2/7
Let x be ((-70)/(-15) - 5) + 411/45. Let f = 221/20 - x. Factor 11/4*q + f*q**2 + 1/2.
(q + 1)*(9*q + 2)/4
Let w = -15/197 + 833/591. Solve 2/9*c - w + 2/9*c**2 = 0.
-3, 2
Let z(c) = c**4 + c - 1. Let b(a) = -27*a**5 + 117*a**4 - 159*a**3 + 84*a**2 - 9*a - 3. Let j(l) = -b(l) + 3*z(l). Solve j(k) = 0 for k.
0, 2/9, 1, 2
Let u(x) = x**2 + 3*x + 3. Let a = 6 - 9. Let p be u(a). Determine h so that h**4 - 4*h**4 - h**2 + 4*h**4 - 4*h**3 + h**5 + 3*h**p = 0.
-1, 0, 1
Let d(x) be the first derivative of x**8/112 + x**7/14 + 9*x**6/40 + 7*x**5/20 + x**4/4 - 9*x**2/2 + 13. Let g(s) be the second derivative of d(s). Factor g(n).
3*n*(n + 1)**3*(n + 2)
Let x be 0 + 14 - (24 - 29)*-2. Factor -768/5*n + 4/5*n**x + 576/5 + 352/5*n**2 - 64/5*n**3.
4*(n - 6)**2*(n - 2)**2/5
Let g(h) = -8*h**3 - 34*h**2 - 32*h - 6. Let f(i) = i**3 + 3*i**2 + i - 1. Let p(l) = 6*f(l) + g(l). Factor p(k).
-2*(k + 1)**2*(k + 6)
Let x(t) be the second derivative of t**9/5040 + 3*t**8/2240 + t**7/280 + t**6/240 - 3*t**4/2 - 18*t. Let g(d) be the third derivative of x(d). Factor g(u).
3*u*(u + 1)**3
Let h(n) = -n**3 + 185*n**2 - 204*n + 3683. Let s be h(184). Factor -69/8*y - 15/4*y**2 + 3/8*y**s - 9/2.
3*(y - 12)*(y + 1)**2/8
Let h be (-100)/(-21) - (-25 + 4275/175). Factor 4/3*m**2 + 4 + h*m.
4*(m + 1)*(m + 3)/3
Let n(f) be the second derivative of f**5/120 + 7*f**4/144 - f**3/6 + 25*f**2/2 - 5*f. Let q(b) be the first derivative of n(b). Factor q(z).
(z + 3)*(3*z - 2)/6
Suppose -13*o - 187 + 408 - 195 = 0. Factor -2/5*v - 7/5*v**o + 0.
-v*(7*v + 2)/5
Let a(w) be the third derivative of -1/150*w**6 + 0 + 0*w - 16/15*w**3 + 35*w**2 + 2/75*w**5 + 2/15*w**4. Solve a(i) = 0.
-2, 2
Let i be (-5)/7 + 8/(-28). Let b be 15/(-180) - i/3. Factor 1/4*c - 1/4 + 1/4*c**2 - b*c**3.
-(c - 1)**2*(c + 1)/4
Let l(m) be the first derivative of 0*m + 4/3*m**3 + 0*m**2 - 18. Let l(y) = 0. Calculate y.
0
Let f(y) = -5 + y**3 - 5*y**3 + 3*y**2 + 8*y**3 + 5*y**3. Let m(k) = -10*k**3 - 2*k**2 + 6. Let d(c) = -6*f(c) - 5*m(c). Factor d(b).
-4*b**2*(b + 2)
Let y(s) = -3*s - 7. Let q be y(-3). Suppose 0 = -q*z + g - 1, 0 = 4*z + 2*g - 18. Determine d so that -6/7*d - 4/7 + 10/7*d**z = 0.
-2/5, 1
Let f be (-40)/(-3) + (-2)/(-3). Let s be (-2)/(-5)*25/5. Determine j, given that 6 - f*j + 3*j**4 - 7*j - 19*j**3 + 27*j**s + 4*j**3 = 0.
1, 2
Let h(j) be the third derivative of j**8/448 - j**6/32 + j**4/8 + 7*j**2 - 1. Find a such that h(a) = 0.
-2, -1, 0, 1, 2
Suppose 3*n - 8 + 5 = 0. Let f = -1/3 + n. Solve -2/3*r**5 + 0*r - 2/3*r**4 + 2/3*r**2 + 0 + f*r**3 = 0.
-1, 0, 1
Let v(x) be the third derivative of 2*x**7/105 - 19*x**6/30 + 31*x**5/5 + 9*x**4/2 - 324*x**3 - 2*x**2 - 970*x. Determine a, given that v(a) = 0.
-2, 3, 9
Factor -35 - 24 - 39 + 81*i + 33*i - 3*i**2 - 13.
-3*(i - 37)*(i - 1)
Suppose 5 = -73*z + 68*z. Let h(d) = -d**2 - d - 1. Let r = 0 - 6. Let p(v) = 10*v**2 + 22*v + 22. Let t(c) = r*h(c) + z*p(c). Factor t(q).
-4*(q + 2)**2
Let m(k) = 16*k + 11. Let s be m(-3). Let a = s - -40. Determine i so that 0 - 1/3*i**a - 1/3*i - 2/3*i**2 = 0.
-1, 0
Let f(z) be the first derivative of -2*z**3/15 + 8*z**2/5 - 6*z - 26. Factor f(x).
-2*(x - 5)*(x - 3)/5
What is h in -248*h**2 - 5*h**4 - 247*h**2 - 100*h**3 + 500 + 0 + 100*h = 0?
-10, -1, 1
Let r be (-2)/(22/(-9))*(-39)/(1209/(-62)). Factor -18/11*h + 2/11*h**3 + 2/11*h**2 - r.
2*(h - 3)*(h + 1)*(h + 3)/11
Let t = 32889 - 230203/7. Let 4/7*r**5 - 32/7 + 16/7*r + 40/7*r**2 - 8/7*r**4 - t*r**3 = 0. What is r?
-2, -1, 1, 2
Let l(c) be the second derivative of c**10/136080 + c**9/34020 + c**8/30240 + 3*c**4/4 - 3*c. Let o(n) be the third derivative of l(n). What is h in o(h) = 0?
-1, 0
Let c(h) be the first derivative of 4/19*h - 22/57*h**3 - 20 + 9/19*h**2. Factor c(g).
-2*(g - 1)*(11*g + 2)/19
Suppose 2*y - 29 = -13 - 10. Factor 0 + 3/5*i**2 - 2/5*i + 0*i**y - 1/5*i**4.
-i*(i - 1)**2*(i + 2)/5
Factor -17/8*s - 1/4*s**2 - 13/4.
-(s + 2)*(2*s + 13)/8
Let c(j) be the first derivative of j**7/210 - j**6/60 - j**5/60 + j**4/12 - 5*j**2/2 + 4. Let s(q) be the second derivative of c(q). Factor s(v).
v*(v - 2)*(v - 1)*(v + 1)
Suppose -5*z + z - 158 = -i, 138 = i + z. Suppose 15 = 147*a - i*a. Solve -2/7*c**a + 0 + 0*c - 4/7*c**2 = 0 for c.
-2, 0
Let v = -21362 + 21364. Find z, given that 15/4*z**3 - 5/2*z + 0 - 5/4*z**v = 0.
-2/3, 0, 1
Factor -2/3 + 2/3*c**2