first derivative of -16/3*h - 5*h**3 + 32/3*h**2 - 27/8*h**4 - 41. Factor z(a).
-(a + 2)*(9*a - 4)**2/6
Let c be 89265/3630 - 20/(-22) - 21. Factor 0 + c*y + 19/2*y**2 + y**3.
y*(y + 9)*(2*y + 1)/2
Suppose 7963 = 29*c + 1728. Factor 0*u**2 + c - 30*u - 2*u**3 - 197 + 8*u**2 + 6*u**2.
-2*(u - 3)**2*(u - 1)
Let k(y) = y**3 + y**2 + y + 76. Let u be k(0). Determine t, given that 10*t**2 + 14*t**2 - 8 + u*t + 16*t**2 = 0.
-2, 1/10
Suppose 75 = -23*f + 167. Let i(o) be the third derivative of 22*o**2 + 5/6*o**f + 1/12*o**6 - 7/12*o**5 + 0*o + 0 + 10/3*o**3. Factor i(b).
5*(b - 2)**2*(2*b + 1)
Suppose 5*k - 12 = 2*k. Let l(a) = -2*a + 14. Let p be l(k). Find w such that 22*w - p - 3*w**3 + 15*w - 28*w = 0.
-2, 1
Let u(r) be the first derivative of 5*r**3/3 + 85*r**2/2 - 90*r + 487. Solve u(j) = 0 for j.
-18, 1
Let t(v) = 702*v**3 - 1407*v**2 + 687*v - 24. Let m(h) = -701*h**3 + 1406*h**2 - 691*h + 22. Let g(c) = 7*m(c) + 6*t(c). Find q such that g(q) = 0.
2/139, 1
Factor 639/7*o + 150/7*o**2 - 3/7*o**3 + 486/7.
-3*(o - 54)*(o + 1)*(o + 3)/7
Let a(n) be the second derivative of -n**8/13440 - n**7/1680 - n**6/576 - n**5/480 - 10*n**3/3 + 64*n. Let f(g) be the second derivative of a(g). Factor f(v).
-v*(v + 1)**2*(v + 2)/8
Let 32 + 550/3*f**2 + 496/3*f - 242/3*f**3 = 0. Calculate f.
-4/11, 3
Suppose 0 = -2*p - 4*a - 36, 13 = 3*p - 2*a - 13. Determine v so that -3/4*v + 1/4 - v**p = 0.
-1, 1/4
Let 102*w**4 + 552*w**3 + 6*w**5 - 224*w**4 + 188*w**4 + 108*w + 435*w**2 + 165*w**4 = 0. What is w?
-36, -1, -1/2, 0
Determine p, given that -36/7 + 24/7*p**5 + 18/7*p**2 + 178/7*p**4 + 158/7*p - 342/7*p**3 = 0.
-9, -2/3, 1/4, 1
Factor 1192*t - 2832*t + 1238*t - 1560 - 3*t**2.
-3*(t + 4)*(t + 130)
Let z(j) be the second derivative of -j**4/54 - 7*j**3/27 + 20*j**2/3 - 2*j + 3. Factor z(w).
-2*(w - 5)*(w + 12)/9
Let f be 954/108 + -9 - 2/(-6). Let y(b) be the second derivative of -17*b - f*b**4 + 5/3*b**3 + 6*b**2 + 0. What is m in y(m) = 0?
-1, 6
Let a(o) = 2*o**4 + 46*o**3 - 262*o**2 + 338*o - 12. Let j(q) = -3*q**4 - 45*q**3 + 266*q**2 - 337*q + 15. Let c(h) = 5*a(h) + 4*j(h). Factor c(y).
-2*y*(y - 19)*(y - 3)**2
Let n(o) = -3*o**3 + 83*o**2 - 85*o - 10. Let v(r) = 2*r**3 - 42*r**2 + 43*r + 6. Let y(g) = 3*n(g) + 5*v(g). Let y(a) = 0. What is a?
-40, 0, 1
Factor -21315*j + 369*j**4 - 7203 + 89*j**4 - 173*j**4 - 6330*j**3 - 20730*j**2 - 3*j**5.
-3*(j - 49)**2*(j + 1)**3
Let y(r) be the third derivative of r**5/30 - 46*r**4/3 - 185*r**3/3 + 24*r**2 + 3*r. Factor y(m).
2*(m - 185)*(m + 1)
Suppose -6*z = -2*z. Suppose 3*y - 2*y - 18 = z. Let 5*i**2 - 16 + 30*i - i**2 - y*i = 0. What is i?
-4, 1
Let o(i) be the second derivative of i**5/15 - 10*i**4/3 + 38*i**3/3 - 77*i**2 - 75*i. Let a(t) be the first derivative of o(t). What is v in a(v) = 0?
1, 19
Let r be (-3 - 21)*4/60*-5 - 6. Factor 3/10*v - 1 + 1/10*v**r.
(v - 2)*(v + 5)/10
Let q(u) be the second derivative of -u**5/20 - 23*u**4/12 + 35*u**3/2 - 81*u**2/2 + 306*u + 3. Factor q(d).
-(d - 3)*(d - 1)*(d + 27)
Let f**3 - 781/3*f**2 + 0 + 260/3*f = 0. Calculate f.
0, 1/3, 260
Factor -84*a**2 - a**4 + 51*a**3 + 49*a**3 - 21*a**2 + 6*a**4.
5*a**2*(a - 1)*(a + 21)
Let b(r) = 7*r**2 - 44*r. Let d(z) = -8*z**2 - 5 + 29*z + 15*z + 5. Let t(y) = 4*b(y) + 3*d(y). Factor t(u).
4*u*(u - 11)
Let s(l) = l**2 + 243*l + 1716. Let a(z) = -3*z + 3. Let n(d) = 26*a(d) + 2*s(d). Factor n(o).
2*(o + 9)*(o + 195)
Let x be (253/(-22) - -11)*-10. Let m(s) be the first derivative of 0*s**3 + 5 + 0*s - 2*s**4 - 2/3*s**6 - 12/5*s**x + 0*s**2. What is i in m(i) = 0?
-2, -1, 0
Let s(p) be the third derivative of -1/24*p**6 + 0*p - 7/12*p**5 + 0 - 111*p**2 + 0*p**3 - 5/4*p**4. Factor s(q).
-5*q*(q + 1)*(q + 6)
Let c(p) be the first derivative of -p**5/15 + 5*p**4/3 - 37*p**3/9 + 3*p**2 - 2572. Factor c(q).
-q*(q - 18)*(q - 1)**2/3
Let a(b) be the third derivative of -b**5/210 - b**4/12 - 2*b**3/7 - 2*b**2 + 260*b. Factor a(o).
-2*(o + 1)*(o + 6)/7
Let r(z) = -42*z**2 + 95*z - 15. Let w(b) = 2*b**2. Let m = -80 - -86. Let x(i) = m*w(i) + r(i). Factor x(h).
-5*(h - 3)*(6*h - 1)
Let l(n) be the first derivative of n**6/360 - 19*n**5/120 - 7*n**4/4 + 251*n**3/3 + 155. Let r(s) be the third derivative of l(s). What is f in r(f) = 0?
-2, 21
Let f(a) be the first derivative of -525/8*a**2 - 243/16*a**4 - 87 + 45*a**3 + 81/40*a**5 + 375/8*a. Solve f(m) = 0 for m.
1, 5/3
Let w(t) be the third derivative of -t**5/15 - 5*t**4/2 + 3*t**2 - 2. Factor w(y).
-4*y*(y + 15)
Let k(n) be the second derivative of n**8/112 - n**6/40 - 85*n**2/2 + 14*n - 2. Let c(v) be the first derivative of k(v). Factor c(b).
3*b**3*(b - 1)*(b + 1)
Let w(h) = 18*h**4 - 531*h**3 + 27*h**2 + 591*h - 15. Let a(t) = -5*t**4 + 132*t**3 - 7*t**2 - 148*t + 4. Let c(r) = 15*a(r) + 4*w(r). Factor c(b).
-3*b*(b - 1)*(b + 1)*(b + 48)
Let o(c) = c**2 + 32*c - 228. Let s be o(6). Let j(i) be the second derivative of 1/3*i**4 + 0*i**3 - 1/10*i**5 - 1/15*i**6 - 8*i + 0 + s*i**2. Factor j(x).
-2*x**2*(x - 1)*(x + 2)
Let a(y) be the second derivative of 2*y**6/15 + 7*y**5/5 + 16*y**4/3 + 8*y**3 + 436*y. What is l in a(l) = 0?
-3, -2, 0
Let j(q) = 12*q**5 + 46*q**4 + 205*q**3 - 336*q**2 - 803*q. Let n(v) = 5*v**5 + 20*v**4 + 88*v**3 - 144*v**2 - 344*v. Let k(h) = -8*j(h) + 19*n(h). Factor k(z).
-z*(z - 14)*(z - 2)*(z + 2)**2
Let u(c) be the third derivative of c**6/140 - 9*c**5/70 - 11*c**4/14 + 4192*c**2. Let u(d) = 0. Calculate d.
-2, 0, 11
Let n = 333 + -211. Suppose 4*s = -106 + n. Determine h, given that 1/2 + 15/4*h + 6*h**2 - s*h**3 = 0.
-1/4, 2
Let g(h) = -5*h**5 - 181*h**4 - 438*h**3 + 1415*h**2 - 803*h - 6. Let a(u) = 2*u**4 + u**3 + u + 2. Let d(w) = -3*a(w) - g(w). Determine c so that d(c) = 0.
-32, -5, 0, 1
Let c be 3*2/42 + (-7462)/(-1274). Let w(t) be the first derivative of 12*t**3 + 14*t**2 + 8*t + 4/5*t**5 - c + 5*t**4. Suppose w(f) = 0. Calculate f.
-2, -1
Let m(y) be the third derivative of 5*y**8/336 - 4*y**7/7 - 19*y**6/3 + 33*y**5/2 + 755*y**4/24 - 145*y**3 - 2018*y**2. Find h, given that m(h) = 0.
-6, -1, 1, 29
Let p(a) = 220*a. Let r be p(1). Solve 206 + r*n - 40*n + 42*n - 4313 - n**2 - 2*n**2 = 0 for n.
37
Solve -1744*r - 5*r**3 - 24398 - 440*r**2 - 3296*r - 6382 + 165*r**2 = 0 for r.
-19, -18
Determine j, given that 8/7*j**4 + 126*j**3 + 220/7*j**2 + 0 + 0*j = 0.
-110, -1/4, 0
Suppose 19*m + 17 - 73 - 1 = 0. Let r(w) be the first derivative of -1/3*w**2 + 2/9*w**m - 23 - 4/3*w. Factor r(k).
2*(k - 2)*(k + 1)/3
Let z(h) = -20*h**3 - 880*h**2 - 5*h - 5. Let v(a) = -9*a**3 - 440*a**2 - 2*a - 2. Let f(s) = 5*v(s) - 2*z(s). Suppose f(k) = 0. Calculate k.
-88, 0
Let y(o) be the second derivative of -o**6/6 + o**5 - 25*o**4/12 + 5*o**3/3 - 596*o + 1. Let y(f) = 0. What is f?
0, 1, 2
Let v(l) be the third derivative of l**5/12 + 35*l**4/24 + 274*l**2 + 2. Factor v(r).
5*r*(r + 7)
Let r(k) be the second derivative of -k**8/2688 + k**6/320 + k**5/240 - 6*k**2 + 3*k - 9. Let q(m) be the first derivative of r(m). Factor q(d).
-d**2*(d - 2)*(d + 1)**2/8
Let s(p) = 9*p + 108. Let o be s(-7). Let 2*n**4 - 20*n**2 - 33*n**4 - 4*n**4 + 10*n**5 + 0*n**4 - 5*n**2 + o*n**3 + 5*n = 0. Calculate n.
0, 1/2, 1
Let z(s) = 35*s**2 - 4464*s - 4888521. Let h(f) = 99*f**2 - 13385*f - 14665563. Let k(o) = -6*h(o) + 17*z(o). Factor k(l).
(l + 2211)**2
Determine i so that -55/3*i**2 - 15*i**3 + 15*i + 50/3 + 5/3*i**4 = 0.
-1, 1, 10
Let i = 2/2941 - -2617/476442. Let s = 109/162 - i. Let -k**4 + 0 - 3*k**2 - 10/3*k**3 - s*k = 0. Calculate k.
-2, -1, -1/3, 0
Let u be ((-30366)/140)/(-9) + 1/(-10). Suppose -3*g + 3 = -2*z - 10, -3*g = -z - 11. Solve -g*k**4 - 36*k**2 - 27*k + 27*k - u*k**3 - k**4 = 0 for k.
-3, 0
Let o = 2 + 0. Let x = -344544 - -2411809/7. Factor -1/7 - 1/7*d + 1/7*d**o + x*d**3.
(d - 1)*(d + 1)**2/7
Suppose 72*v + 81*v - 299 - 7 = 0. Let k(d) be the third derivative of 0*d - 9/2*d**3 + 3/4*d**4 + 0 - 23*d**v - 1/20*d**5. Suppose k(w) = 0. What is w?
3
Factor -126*x**2 - 55*x - 3*x + 20*x - 54*x + 130*x**2 + 520.
4*(x - 13)*(x - 10)
Determine w so that -228 + 132*w**2 - 72 + 397*w**3 + 15*w - 433*w**3 = 0.
-4/3, 5/2
Let -28*n**2 + 46068*n - 6799 - 7939 + 4532 + 247 - 3201 = 0. Calculate n.
2/7, 1645
Let y(o) be the third derivative of o**5/60 + 35*o**4/24 - 16*o**2 - 29. Factor 