 120. Let w(y) be the first derivative of x(y). Factor w(j).
-j*(j - 1)**2*(j + 5)/2
Let b be (-3460)/173 + (6 - 9 - -28). Find p, given that -1/4*p**5 - 3/2*p**4 - 3/2*p**3 + 9/2 + 39/4*p + b*p**2 = 0.
-3, -1, 2
Let f(c) be the first derivative of -c**6/900 + 29*c**5/300 - 9*c**4/10 + 50*c**3 + 204. Let j(n) be the third derivative of f(n). Find w such that j(w) = 0.
2, 27
Let t(u) = -4*u + 27. Let a be t(-14). Suppose 15*w**2 - a + 6*w + 15*w + 3*w**3 + 92 = 0. What is w?
-3, -1
Let a(o) be the first derivative of 10*o - 37 + 25*o**3 - 85/2*o**2. Factor a(n).
5*(n - 1)*(15*n - 2)
Suppose -5*o - 14 = -3*n - 144, -175 = 4*n - 5*o. Let j = 29 - n. Factor 0*a + 8*a - a**2 - j + 58.
-(a - 4)**2
Suppose -2/7*l**2 - 36 - 50/7*l = 0. Calculate l.
-18, -7
Let q(h) be the first derivative of -4*h**3/3 - 314*h**2 + 632*h + 1296. Let q(v) = 0. Calculate v.
-158, 1
Suppose 1391 + 174*y - 27*y**2 - 362 - 48*y + 24*y**2 = 0. What is y?
-7, 49
Suppose 79*i = -44*i - 9*i + 396. Let l(b) be the second derivative of -10/3*b**3 + 0 + i*b + 1/4*b**5 + 0*b**2 + 0*b**4. Suppose l(m) = 0. Calculate m.
-2, 0, 2
Let 231*m + 930 - 742*m**2 + 127 - 745*m**2 + 1484*m**2 + 1553 = 0. Calculate m.
-10, 87
Factor -822296 - 218*s**3 + 6050*s - 2*s**4 - 2844*s**2 + 822296 - 2986*s**2.
-2*s*(s - 1)*(s + 55)**2
Suppose -25 + 2409 = -4*d - 2*z, 2*d = 4*z - 1192. Let q = d + 596. Factor 1/4*a**3 + q + 1/2*a + 3/4*a**2.
a*(a + 1)*(a + 2)/4
Let c be ((-3920)/120)/(5/(-75)). Determine h so that -c - 5/2*h**2 - 70*h = 0.
-14
Suppose -8*t + z + 5 = -9*t, 3*z = -6. Let f be -3 + (-2 - t) + 5. Factor 6*b**2 - 27 - 18*b - 10 + 61 - f*b**2.
3*(b - 4)*(b - 2)
Factor -5/4*h**3 + 67/4*h + 0 - 167/2*h**2.
-h*(h + 67)*(5*h - 1)/4
Let b(j) be the third derivative of -j**2 + 0*j - 43/6*j**4 - 12*j**3 + 1/3*j**5 - 75. Factor b(r).
4*(r - 9)*(5*r + 2)
Let s(r) = -200*r**3 + 36005*r**2 - 1591403*r - 25. Let v(f) = -25*f**3 + 4499*f**2 - 198925*f - 3. Let b(g) = -6*s(g) + 50*v(g). Solve b(a) = 0.
0, 446/5
Let o(x) be the second derivative of -x**5/20 + 5*x**4/3 + 31*x**3/2 + 36*x**2 - 1105*x. Factor o(m).
-(m - 24)*(m + 1)*(m + 3)
Let k = 817 + -815. Suppose -k*u + 119 = 109. Solve 0*h**2 + 0*h + 0 - 6/5*h**4 - 3/5*h**u - 3/5*h**3 = 0 for h.
-1, 0
Let y(w) be the third derivative of -w**5/20 - 35*w**4/8 - 147*w**3 - 2*w**2 + 28*w. Suppose y(f) = 0. Calculate f.
-21, -14
Let p(n) = 3*n**3 - 3*n**2 + 3*n + 3. Suppose 0 = 2*y - 5*l + 17, -19*y - 4*l = -22*y - 22. Let s(m) = -m**2 + m + 1. Let h(i) = y*s(i) + p(i). Factor h(o).
3*(o - 1)*(o + 1)**2
Let z be (6/4)/((90/(-48))/(-5)). Suppose m + 5*n = -6, m + 5*n - 50 = -z*m. Determine s so that -2*s + m*s + s**2 - 3*s**2 = 0.
0, 6
Suppose -24*t - 9 + 4 + 5 = 0. Let r(d) be the third derivative of 0*d - 7*d**2 + t - 1/330*d**5 + 0*d**3 + 1/132*d**4. What is z in r(z) = 0?
0, 1
Let f(c) be the second derivative of -c**7/14 + 9*c**6/5 - 57*c**5/4 + 63*c**4/2 - 6*c + 298. Find b, given that f(b) = 0.
0, 2, 7, 9
Let k(g) be the first derivative of 0*g**4 - 19/2*g**2 + 1/40*g**5 - 14 + 0*g + 0*g**3. Let y(i) be the second derivative of k(i). Factor y(o).
3*o**2/2
Let a(k) = 514*k - 15924. Let o be a(31). Let y(q) be the second derivative of -o*q - 2 + 0*q**2 - 1/3*q**4 + 10/3*q**3. Solve y(v) = 0.
0, 5
Suppose 9*b - 35 = 1. Let 5*t**3 + 9 + 5*t**3 - t**5 - 66*t**b - 9*t + 67*t**4 - 10*t**2 = 0. Calculate t.
-3, -1, 1, 3
Let a = -592 + 628. Factor -9*w**3 - 4*w**3 + a*w**4 - 4*w - 12*w**2 + 6*w**5 - 5*w**5 - 42*w**4 - 2*w**5.
-w*(w + 1)**2*(w + 2)**2
Suppose -5*y + 3*y = -s - 11, -3*y = s - 9. Let r be (s - 3)/((-9)/12*2). Determine b, given that b**4 + 2*b**3 + b**4 - b**2 - 5*b**4 + 2*b**r = 0.
0, 1
Let s(y) be the third derivative of y**7/3780 + y**6/120 - 3*y**4/8 + 11*y**2 + 1. Let m(i) be the second derivative of s(i). Factor m(n).
2*n*(n + 9)/3
Let y(b) = -b**2 - 2*b - 1. Let q(w) = 6*w**2 - 42*w - 264. Let i(a) = -q(a) - 9*y(a). Factor i(c).
3*(c + 7)*(c + 13)
Let g(s) be the third derivative of 0 - s**2 - 17/660*s**6 + 1/1155*s**7 + 0*s**3 + 61*s - 19/132*s**4 - 37/330*s**5. Find n such that g(n) = 0.
-1, 0, 19
Let b = 396 - 392. Determine l so that 24*l**2 + 80*l**3 + 45*l**b - 2*l**5 + 0*l**3 - 138*l**5 - 9*l**2 = 0.
-3/7, -1/4, 0, 1
Let h = -212709 + 1489017/7. What is n in 15*n**4 + 12/7*n**5 - 129/7*n - 9*n**3 - 339/7*n**2 + h = 0?
-9, -1, 1/4, 2
Let k = -99 + 105. Let g be (-21)/14 + (27/k - 1). Factor 9 - 1 - 4 + 8*r**2 - 7*r**g - 5*r.
(r - 4)*(r - 1)
Let m = 5189 - 5189. Let c(h) be the second derivative of 0*h**2 + 0*h**3 + m*h**5 - 26*h - 2/15*h**6 + 0 + 4/3*h**4. Factor c(j).
-4*j**2*(j - 2)*(j + 2)
Let a(j) = -2*j**2 + 7*j + 22. Let n(z) = 9*z**2 - 2*z - 35. Let d(f) = 5*f**2 - 17. Let y(v) = -5*d(v) + 3*n(v). Let h(l) = 6*a(l) + 7*y(l). Factor h(u).
2*(u - 2)*(u + 2)
Let x(r) be the third derivative of -105 + 0*r + 2197/18*r**3 - 1/360*r**6 + 13/60*r**5 - 169/24*r**4 + r**2. Factor x(k).
-(k - 13)**3/3
Suppose 6*r - 2*r - 3*t - 14 = 0, -4*t = 2*r + 4. Solve -484 - 57*m - 21*m - 4*m**r - 10*m = 0.
-11
Factor 2320/3*g - 64/3 - 21025/3*g**2.
-(145*g - 8)**2/3
Let q(f) = -4*f**3 - 3*f**2 - 24*f - 42. Let w be q(-2). Suppose -106 - w = -33*t. Solve -8/9*d + 0*d**2 + 2/3*d**3 - 2/9*d**t + 0 = 0.
-1, 0, 2
Let y(c) be the third derivative of -c**8/672 - 3*c**7/140 - 7*c**6/80 - 19*c**5/120 - c**4/8 - 12*c**2 - 13. Factor y(i).
-i*(i + 1)**3*(i + 6)/2
Let z be -14 + (6/24)/(4/(-16)). Let w be (-3)/z + -2*(-5)/(-50). Find l, given that 0 + 0*l**3 - 4/7*l**4 + 0*l**2 + 18/7*l**5 + w*l = 0.
0, 2/9
Let r(y) be the first derivative of -y**3/2 - 1896*y**2 - 2396544*y + 1348. Factor r(w).
-3*(w + 1264)**2/2
Let d(t) be the third derivative of 0*t - 1/36*t**4 + 1/180*t**6 + 66*t**2 + 0 - 1/18*t**5 + 5/9*t**3. Solve d(v) = 0 for v.
-1, 1, 5
Let c(h) = 5*h**2 - 149*h - 31. Let j be c(30). Let g be ((-10)/(-6) + j)*(-153)/(-34). Factor -2*i**2 - 18/7 - 30/7*i - 2/7*i**g.
-2*(i + 1)*(i + 3)**2/7
Let g be (-153)/162*699/(-3961). What is m in -4/3 - 3/2*m - g*m**2 = 0?
-8, -1
Let i(a) be the third derivative of -a**6/600 + 38*a**5/75 - 5*a**4/2 + 83*a**2 - a + 23. Factor i(z).
-z*(z - 150)*(z - 2)/5
Let z(m) be the first derivative of -m**6/27 + 8*m**5/45 - 2*m**4/9 - 4*m**3/27 + 5*m**2/9 - 4*m/9 + 95. Solve z(d) = 0.
-1, 1, 2
Let f(r) be the first derivative of 1/3*r**3 + 107 - 4/3*r + 1/12*r**4 + 0*r**2. Factor f(y).
(y - 1)*(y + 2)**2/3
Factor -38*y**2 - 57*y**2 - 16*y**2 + 3*y**5 - 45*y**4 - y**3 - 116*y**3 - 36*y - 6*y**5.
-3*y*(y + 1)**3*(y + 12)
Suppose f = 3*z + 15, -10*f + 5*f + z = -5. Let g(v) be the first derivative of 2/3*v**3 - 2/5*v**5 - 34 - 1/6*v**6 - 3/2*v**2 + v**4 + f*v. Factor g(k).
-k*(k - 1)**2*(k + 1)*(k + 3)
Suppose 2*t + 0*f + f - 697 = 0, -1738 = -5*t - 4*f. Suppose -t = -5*h - 9*h. Suppose -18*a**3 + 53*a**3 - 90*a**2 - 13 + h*a + 43 = 0. What is a?
-3/7, 1, 2
Let h = 2192 - 1356. Factor -425 - 100*f + 10*f**3 + 803 - 80*f**2 + 786 - 15*f**3 + h.
-5*(f - 4)*(f + 10)**2
Suppose 2*l - 38 = -3*w, -l - 36 = -475*w + 471*w. Factor -2*h - l - 1/4*h**2.
-(h + 4)**2/4
Let f be ((-4941)/1830)/((-28)/30). Let b(w) be the third derivative of 0 + f*w**4 - 243/7*w**3 - 7*w**2 + 1/420*w**6 - 9/70*w**5 + 0*w. Factor b(t).
2*(t - 9)**3/7
Let s(p) be the second derivative of 2*p**3 - 15/2*p**2 + 85*p + 1/4*p**4 + 0. Factor s(q).
3*(q - 1)*(q + 5)
Let p = -2/10825 + 147222/10825. Factor 128/5*o + 312/5*o**2 - 512/5 + 4/5*o**4 + p*o**3.
4*(o - 1)*(o + 2)*(o + 8)**2/5
Let q(f) be the second derivative of -1/36*f**4 + 0 + 0*f**2 + 128*f + 7/18*f**3. Factor q(z).
-z*(z - 7)/3
Let q(r) be the second derivative of -7*r**6/150 - 2*r**5/25 + 13*r**4/60 + r**3/15 + 4*r - 43. Factor q(h).
-h*(h - 1)*(h + 2)*(7*h + 1)/5
Let o be (-20)/(-14) + 83/(13944/96). Factor 0 + 5/3*m**o - 35/3*m.
5*m*(m - 7)/3
Let t(k) = -k**2 + 3*k + 11. Let y(p) = -2*p**2 + 2471*p + 4947. Let g(i) = -3*t(i) - y(i). Factor g(w).
5*(w - 498)*(w + 2)
Let l(p) be the third derivative of -p**5/120 + 583*p**4/24 + 389*p**3/4 + 4553*p**2. Factor l(v).
-(v - 1167)*(v + 1)/2
Suppose -2*j = -5*n + 16, -17836*j - 10 = -17833*j - 4*n. Let 0*h - 9/2*h**4 - 6 + 3/2*h**3 + 21/2*h**j - 3/2*h**5 = 0. What is h?
-2, -1, 1
Let c(z) = -z**2 - 17*z + 41. Let y be c(-19). Suppose 166*u - 341*u = -166*u -