+ 2223. Let p = 229/6 + k. Solve 0 - 1/4*w**2 + p*w = 0 for w.
0, 6
Let j = 1216823/60240 + 5/12048. Find z such that 4/5 - 19/5*z**5 + j*z**2 + 11*z**3 - 21/5*z**4 + 48/5*z = 0.
-1, -2/19, 2
Suppose -5*d = 7 - 17. Suppose -4*v + 8*v = -4, 4*l - d*v = 18. Find t, given that -10*t + l*t + 2*t**2 + 0*t = 0.
0, 3
Let j(b) be the first derivative of 11/7*b**2 - 36/7*b - 2/21*b**3 - 177. Factor j(y).
-2*(y - 9)*(y - 2)/7
Let u(m) be the first derivative of -1/72*m**4 - 1/3*m**3 - 3*m**2 - 11 + 6*m. Let x(n) be the first derivative of u(n). Factor x(w).
-(w + 6)**2/6
Factor 228488/3*i - 77228944/9 + 2/9*i**3 - 676/3*i**2.
2*(i - 338)**3/9
Find v such that -536*v - 294797 + 916*v + 1104*v + 19515 - 2*v**2 = 0.
371
Let h(o) be the first derivative of -o**6/39 - 6*o**5/65 + 5*o**4/26 + 10*o**3/13 - 4*o**2/13 - 24*o/13 - 961. Determine u so that h(u) = 0.
-3, -2, -1, 1, 2
Suppose -58*d - 95 + 315 = -12. Factor 0 - 2/11*u**2 + 0*u + 2/11*u**3 - 2/11*u**5 + 2/11*u**d.
-2*u**2*(u - 1)**2*(u + 1)/11
Let g(h) = -h**2 - 40*h + 37. Let m be g(14). Let q = -5749/8 - m. Let 3/8 - 3/8*n**2 - q*n + 3/8*n**3 = 0. What is n?
-1, 1
Let q(x) = -2*x**3 + 33*x**2 + 20*x + 25. Let z be q(15). What is a in 2344*a**2 - 221 + 727 + 4*a**5 + 2132*a + z*a**3 + 116*a**4 + 170 = 0?
-13, -1
Let s(u) be the third derivative of 98/3*u**3 + 347*u**2 + 22/15*u**5 + 2/105*u**7 + 0*u + 0 - 14*u**4 + 2/5*u**6. Let s(n) = 0. Calculate n.
-7, 1
Let j(f) = 27*f**2 - 852*f - 1740. Let r(k) = -33*k**2 + 849*k + 1740. Let x(h) = 5*j(h) + 4*r(h). What is d in x(d) = 0?
-2, 290
Let o(t) be the second derivative of -t**4/60 - 28*t**3 + 841*t**2/10 - 12303*t. What is b in o(b) = 0?
-841, 1
Let g be 1 + (15/(-2))/(7174/844). Find m, given that 0 + 0*m + 0*m**2 - g*m**3 - 2/17*m**4 = 0.
-1, 0
Let r(j) be the second derivative of 5*j**4/12 + 25*j**3/6 - 315*j**2 + 169*j + 21. Find m such that r(m) = 0.
-14, 9
Let f(h) be the second derivative of 1/144*h**5 + 1/2160*h**6 + 1/36*h**4 - 3*h + 0*h**2 + 2*h**3 + 0. Let a(s) be the second derivative of f(s). Factor a(d).
(d + 1)*(d + 4)/6
Let i(z) be the second derivative of -z**7/4200 + 13*z**5/600 + z**4/10 - 7*z**3/6 - z**2 + 2*z + 50. Let p(l) be the second derivative of i(l). Factor p(h).
-(h - 4)*(h + 1)*(h + 3)/5
Let r(t) be the second derivative of t**4/12 - 53*t**3/24 - 21*t**2/4 - 45*t. Find w, given that r(w) = 0.
-3/4, 14
Suppose -5*x - 50 = -245. Suppose -3*f + 213 = -3*d, -f - 5*d = -38 - x. Factor f*n - 35*n + 8*n**5 - 10*n**3 - 32*n - 3*n**5.
5*n*(n - 1)**2*(n + 1)**2
Let l(m) be the first derivative of 8 - 2/3*m**3 + m**2 + 4*m. Factor l(v).
-2*(v - 2)*(v + 1)
Factor 7/3*h**2 + 0 - 2/3*h - 1/3*h**5 - 3*h**3 + 5/3*h**4.
-h*(h - 2)*(h - 1)**3/3
Let t(k) be the third derivative of 0*k**5 - 23/35*k**7 + 0*k - 529/40*k**6 - 1/112*k**8 - 48*k**2 + 0*k**4 + 0*k**3 - 2. Factor t(f).
-3*f**3*(f + 23)**2
Suppose 3 - 9 = 2*u. Let f be (-1 + (-8)/(-12))*u*6. Factor 6*w**2 - f - 3*w**2 + 53*w - 105*w + 49*w.
3*(w - 2)*(w + 1)
Let z(y) be the second derivative of 0*y**2 + 0*y**3 - 2 - 24*y - 1/15*y**7 - 26/75*y**6 + 0*y**4 + 4/25*y**5. Solve z(b) = 0 for b.
-4, 0, 2/7
Let f(c) = -c**2 - 6*c + 2. Let x be f(-6). Suppose 0 = -x*i - i + 12. Factor 8*r**4 - r**3 - 13*r**i + 0*r**3 - 4*r**3.
-5*r**3*(r + 1)
Let c = 70/45561 - -663185426/318927. Let b = c + -2076. Determine n, given that -120/7*n**2 - b + 4*n**3 + 116/7*n = 0.
2/7, 1, 3
Let n(c) = 23*c + c - 5 - 25*c**2 + 6*c + 15*c**3. Let p(k) = 7*k**3 - 13*k**2 + 15*k - 3. Let x(z) = 2*n(z) - 5*p(z). Suppose x(y) = 0. What is y?
1
Let j(x) be the second derivative of 0 + 0*x**2 + 1/80*x**5 - 41*x + 0*x**3 + 1/24*x**4. Factor j(h).
h**2*(h + 2)/4
Let m be (1 - (-3)/2) + 435/(-174). Let y(q) be the first derivative of -17 + 2*q**2 - 4/5*q**5 + 4/3*q**3 - q**4 + m*q. Factor y(v).
-4*v*(v - 1)*(v + 1)**2
Let t = -163 - -487. Factor -60*i**3 + 330*i**4 - 2*i**2 - 3*i**2 + t*i**4 + 60*i - 649*i**4.
5*i*(i - 12)*(i - 1)*(i + 1)
Suppose 5*c - 1 + 11 = 0. Let p be (-544)/34*c/8. Determine g so that -108*g**3 + 24 + 21*g**4 - 28*g - 21 + 7*g**p + 90*g**2 - g**4 = 0.
1/3, 3
Let s(x) be the first derivative of 3*x**5/25 + 21*x**4/20 - 3*x**3/5 - 69*x**2/10 - 42*x/5 - 360. What is b in s(b) = 0?
-7, -1, 2
Let r(i) be the second derivative of i**5/12 + 55*i**4/4 + 1815*i**3/2 + 53*i**2/2 + 2*i - 41. Let u(q) be the first derivative of r(q). Factor u(y).
5*(y + 33)**2
Let m(w) = -4*w**2 + 141*w - 31. Let v be m(35). Let h(r) be the second derivative of 0 - 7/24*r**3 + 5/48*r**v + 3/8*r**2 - 1/80*r**5 - r. Factor h(y).
-(y - 3)*(y - 1)**2/4
Let l(z) be the third derivative of 2*z**7/105 - 83*z**6/60 + 2651*z**5/80 - 11039*z**4/48 + 17689*z**3/24 + 859*z**2. Find g, given that l(g) = 0.
7/4, 19
Let r(p) be the third derivative of 0 - 17/56*p**4 + 0*p + 13*p**2 + 0*p**3 + 1/140*p**5. Determine v so that r(v) = 0.
0, 17
Let o(n) = 19*n**2 - 57*n. Let t be o(3). Let l(y) be the first derivative of 22 + 0*y**2 + 0*y**3 + 1/20*y**5 - 1/24*y**6 + 1/8*y**4 + t*y. Factor l(k).
-k**3*(k - 2)*(k + 1)/4
Let s(g) = g**2 + 7*g + 13. Let c be -4 + 4/(-3 + 1). Let u be s(c). What is n in -u + 2*n - 3 + 9 - n**2 = 0?
1
Let 464/7*c**2 - 1240*c + 42400/7 - 2/7*c**3 = 0. What is c?
10, 212
What is n in -3/5*n**2 + 459/5 - 456/5*n = 0?
-153, 1
Let t(j) be the first derivative of -j**3/15 - 743*j**2/10 - 1482*j/5 - 1514. Determine g, given that t(g) = 0.
-741, -2
Let z = 41335 + -371759/9. Determine h so that 64/9*h - z + 28/9*h**2 + 2/9*h**3 = 0.
-8, 2
Let j(d) = 16*d**2 + 523*d - 13517. Let q(n) = 23*n**2 + 524*n - 13516. Let c be -1 - 15/(120/16). Let w(a) = c*q(a) + 4*j(a). Factor w(b).
-5*(b - 52)**2
Factor 0 + 76/7*q**4 + 4/7*q**5 + 28*q**2 + 204/7*q**3 + 64/7*q.
4*q*(q + 1)**3*(q + 16)/7
Let j(t) be the third derivative of -1/540*t**6 - 169/36*t**4 + 13/90*t**5 + 2197/27*t**3 + 0*t - 13*t**2 - 2. Factor j(c).
-2*(c - 13)**3/9
Let l(z) be the third derivative of -2 + 0*z - 88*z**2 - 1/80*z**5 + 1/24*z**4 - 1/480*z**6 + 0*z**3. Factor l(j).
-j*(j - 1)*(j + 4)/4
Let n be 14*(-10)/8*(-12)/10. Determine x, given that -11*x - 48*x**3 + 0*x**5 + 48 + 59*x - n*x**4 - 327*x**2 - 3*x**5 + 303*x**2 = 0.
-2, 1
Suppose -34 + 25 = -9*g. Let i(p) = -2*p**3 + 2*p**2 + 2*p. Let v(d) = 33*d**3 + 67*d**2 - 8*d. Let h(x) = g*v(x) - i(x). Factor h(u).
5*u*(u + 2)*(7*u - 1)
Let r(s) be the third derivative of s**5/360 + 67*s**4/9 + 71824*s**3/9 - 3648*s**2. Solve r(c) = 0 for c.
-536
Suppose 0 = -10*q + q. Suppose q = -o - 3*l - l - 13, 3*l + 15 = o. Let 9*b**2 + 3*b**5 - 10*b**4 + 0*b + b**4 + 3*b**3 - 9*b + o*b = 0. What is b?
-1, 0, 1, 2
Let m(d) be the third derivative of d**8/84 + 2*d**7/35 + d**6/10 + d**5/15 + 200*d**2 + 8. Factor m(f).
4*f**2*(f + 1)**3
Let p(n) be the second derivative of 30*n**2 + 0*n**6 - 7/2*n**5 + 65/6*n**3 - 5*n**4 - 1 - n + 5/42*n**7. Determine o, given that p(o) = 0.
-3, -1, 1, 4
Let g be (-480)/(-180)*(-1 - 22/(-4)). Suppose 8 = 4*f - g, 0 = 2*m - f - 3. Factor 0*a**4 - 117*a**2 - 16*a**3 + 4*a**m + 129*a**2.
4*a**2*(a - 3)*(a - 1)
Find x such that 18/5 - 1278/5*x + 30246/5*x**2 - 715822/15*x**3 = 0.
3/71
Let w(b) = -12*b**4 + 16*b**3 - 3*b**2 - b. Let r(p) = p**3 + p**4 - 7*p**4 + 22*p**4 - 17*p**4. Let s(h) = 35*r(h) - 5*w(h). Determine l, given that s(l) = 0.
-1/5, 0, 1
Let w(k) = k**5 - 6*k**4 - k**3 - k**2 - 1. Let j(u) = -8*u**5 - 12*u**4 - 14*u**3 - 3*u**2 + 1. Let b(i) = 3*j(i) + 3*w(i). Factor b(f).
-3*f**2*(f + 1)**2*(7*f + 4)
Let d(q) be the third derivative of 0*q - 13/5*q**5 + 21*q**2 - 4 + 3/70*q**7 + 7/2*q**4 + 0*q**3 + 13/40*q**6. Let d(y) = 0. What is y?
-7, 0, 2/3, 2
Let c = -22 - -157/7. Suppose -j - 3*h = -18, 35*j - 39*j = -2*h + 12. Factor -c*p**2 + 3/7*p**3 + j - 6/7*p.
3*p*(p - 2)*(p + 1)/7
Let i(o) = -o + 6. Let w(n) = -10*n + 279. Let t(x) = 2*i(x) + w(x). Let v be t(24). Factor -1/9*f**v + 1/3*f + 0*f**2 - 2/9.
-(f - 1)**2*(f + 2)/9
Factor -222264 - 2/7*r**2 - 504*r.
-2*(r + 882)**2/7
Solve 149187/8 + 3/8*p**2 + 669/4*p = 0 for p.
-223
Let i(p) be the third derivative of -p**7/1050 + 7*p**6/200 - 27*p**5/50 + 9*p**4/2 - 108*p**3/5 + 2*p**2 + 4*p - 22. Determine l, given that i(l) = 0.
3, 6
Let s(z) = -7*z**4 - z**3 - 4*z**2 + 6*z + 6. Let u(r) = 13*r**4 + 2*r**3 + 7*r**2 - 11*r - 11. Let b =