ppose -x*q**3 + 18/5*q + 0 + 3/5*q**2 = 0. Calculate q.
-2, 0, 3
Suppose -9*v = -14*v + 260. Factor 245*x + 170 - 13*x**3 + 17*x**3 - 133*x**2 - v*x**2 + 6*x**3.
5*(x - 17)*(x - 2)*(2*x + 1)
Let w = -1521 + 1521. Suppose w = 4*q - 386 + 338. Factor 3/2*f**4 + q*f**3 + 27*f + 0 + 63/2*f**2.
3*f*(f + 2)*(f + 3)**2/2
Let y(x) be the first derivative of 1/18*x**3 + 11/6*x**2 - 158 + 121/6*x. Factor y(z).
(z + 11)**2/6
Let h(x) be the first derivative of 1/22*x**4 - 8/33*x**3 - x**2 - 12/11*x + 55. Find p, given that h(p) = 0.
-1, 6
Suppose 2*f + 3 = -6*n + 43, 0 = 2*f - 10. Let m(p) be the first derivative of -3*p**2 + 8*p + 1/3*p**3 - n. Factor m(y).
(y - 4)*(y - 2)
Let 2/5*f**3 + 192192/5*f + 379456/5 + 1236/5*f**2 = 0. Calculate f.
-308, -2
Suppose -b = -4*u + 2, -7 = 4*b - 7*b - u. Let t be (-2)/6 + (-6364)/(-12). Factor 4 - 266*s**2 - 262*s**b - 6*s + t*s**2.
2*(s - 2)*(s - 1)
Let f be 27/24*(-952)/(-714). Factor 3/2 - 11/4*a + f*a**3 - 1/4*a**2.
(a - 1)*(2*a + 3)*(3*a - 2)/4
Let n(p) be the second derivative of -1/9*p**2 + 1/54*p**4 + 0 + 1/27*p**3 - 1/90*p**5 + 73*p. Factor n(v).
-2*(v - 1)**2*(v + 1)/9
Let c(g) be the third derivative of g**8/2520 - 2*g**7/75 - 181*g**6/900 - 71*g**5/225 + g**4 + 184*g**3/45 - 2663*g**2. Suppose c(l) = 0. Calculate l.
-2, -1, 1, 46
Solve -6/5*r - 12/5*r**3 + 0 - 3/5*r**4 - 3*r**2 = 0 for r.
-2, -1, 0
Factor 2/7*s**3 - 332750000/7 - 3300/7*s**2 + 1815000/7*s.
2*(s - 550)**3/7
Let 41/3*d**2 + 0 + 26*d = 0. What is d?
-78/41, 0
Let j(k) = -55*k**2 - 2180*k - 5. Let z(t) = 21*t**2 + 1091*t + 2. Let d(m) = 2*j(m) + 5*z(m). Suppose d(b) = 0. What is b?
0, 219
Suppose g - 255 = b, 56*b = g + 59*b - 267. Let x be (g/(-215))/((-21)/110). Suppose h**4 - x*h**3 + 96/7*h**2 - 80/7*h + 16/7 = 0. Calculate h.
2/7, 2
Let k(v) be the first derivative of -3*v**4/4 + 89*v**3 + 696*v**2 + 1692*v - 3224. Solve k(p) = 0 for p.
-3, -2, 94
Let q(r) be the second derivative of -2*r**7/35 + 178*r**6/75 - 357*r**5/25 + 57*r**4/5 + 40*r**3/3 + 1062*r. What is v in q(v) = 0?
-1/3, 0, 1, 4, 25
Let h(o) be the first derivative of -o**7/315 + o**5/30 + o**4/18 + 163*o**2/2 - 153. Let r(v) be the second derivative of h(v). Determine p so that r(p) = 0.
-1, 0, 2
Let r be ((-3)/(-24))/(36/1080). Let j(x) be the first derivative of -20/3*x**3 + 4*x**5 + 5/6*x**6 - 10*x**2 + r*x**4 + 0*x + 9. Factor j(h).
5*h*(h - 1)*(h + 1)*(h + 2)**2
Let a be ((-30)/(-65))/(2418/6448). Factor 28/13*p**2 - 14/13*p**3 - a*p + 2/13*p**4 + 0.
2*p*(p - 4)*(p - 2)*(p - 1)/13
Let x(f) be the second derivative of f**5/570 + 7*f**4/114 + 72*f**2 + 6*f - 5. Let w(n) be the first derivative of x(n). Solve w(q) = 0.
-14, 0
Let z(f) be the first derivative of -2*f**3/27 + 179*f**2/9 + 40*f - 2638. Solve z(h) = 0 for h.
-1, 180
Let s(k) be the first derivative of k**6/80 - k**5/8 + k**4/2 - k**3 - 18*k**2 + 50. Let q(a) be the second derivative of s(a). Factor q(d).
3*(d - 2)**2*(d - 1)/2
Solve 2*u**4 + 346*u**2 + 152*u + 72 + 0*u**4 + 301*u**2 - 541*u**2 + 28*u**3 = 0.
-9, -2, -1
Let c(j) be the second derivative of 7*j**5/20 + j**4/48 - j**3/12 - 3*j + 11. Factor c(a).
a*(4*a - 1)*(7*a + 2)/4
Solve 0 - 13*c**5 - 21*c**3 + c - 5/2*c**2 - 61/2*c**4 = 0.
-1, -1/2, 0, 2/13
What is d in -522*d**2 + 36 + 258*d**2 + 265*d**2 + 20*d + 64 = 0?
-10
Suppose 2*w = 3*s + 2, 0 = -4*w - 9*s + 10*s + 14. Find d such that 367*d**4 + 30*d**2 - 186*d**4 - 199*d**w + 3*d**5 + 9*d**3 = 0.
-1, 0, 2, 5
Let z(k) be the first derivative of -5*k**3/3 - 14620*k**2 - 42748880*k - 6907. Suppose z(v) = 0. Calculate v.
-2924
Factor -746*n**2 + 6294*n**3 - 749*n + 6337*n**3 - 12630*n**3 + 1494.
(n - 747)*(n - 1)*(n + 2)
Let g = -144/7 + 583/28. Suppose 0 = -6*y + 11*y - 10. Factor 1/4 - 1/2*f + g*f**y.
(f - 1)**2/4
Let c(k) be the first derivative of -k**4/2 + 10*k**3 + 34*k**2 + 5891. Factor c(d).
-2*d*(d - 17)*(d + 2)
Suppose -2*i - 5*y = -7*i + 10, 0 = i + 3*y + 14. Let l be 8/48 + i/(-20). Factor 2/3*h - 2/15*h**3 + l + 2/5*h**2 - 2/15*h**4.
-2*(h - 2)*(h + 1)**3/15
Let r = 464 + -462. Factor 28*a**r + 754 - 32*a + 753 - 4*a**3 - 1571.
-4*(a - 4)**2*(a + 1)
Let a = -419 - -421. Suppose 3*v - y - 2 = -6, a*y - 8 = 4*v. Factor 4/5*g**3 - 8/5*g**2 + v*g + 0.
4*g**2*(g - 2)/5
Let t = 130 + -134. Let q = -2 - t. Factor -5*w**3 + 4*w**3 - 44*w**2 - 4*w**3 - 4*w + 36*w**q - w**4.
-w*(w + 1)*(w + 2)**2
Suppose -x - 25 = 3*r, 2*x - 92 = 4*r - 42. Let d be (-6)/r - (-9)/(-15). Suppose 4/17*i**4 + 2/17*i**5 + 0*i**2 + 0 + d*i + 2/17*i**3 = 0. Calculate i.
-1, 0
Solve -395*s + 4597 - 5415 + 137*s + s**2 - 149*s = 0 for s.
-2, 409
Let s(x) = 52*x**3 + 4384*x**2 - 1201216*x + 1196840. Let g(y) = 38*y**3 + 4383*y**2 - 1201215*y + 1196839. Let r(t) = 4*g(t) - 3*s(t). Factor r(p).
-4*(p - 547)**2*(p - 1)
Let u(k) be the second derivative of -k**6/35 - 3*k**5/70 + 18*k**4/7 + 16*k**3/7 - 960*k**2/7 - 461*k. Determine d so that u(d) = 0.
-5, -4, 4
Let o be 266/(-7847) + (-185141)/(-5192). Solve -507/8 - 2049/4*l**2 + 741/2*l + 168*l**3 + o*l**4 + 3/2*l**5 = 0 for l.
-13, 1/4, 1
What is y in 15*y + 32 - 1/2*y**2 = 0?
-2, 32
Determine s so that 15*s**3 + 144 + 2571*s**2 - 100*s + s**4 - 5124*s**2 + 2493*s**2 = 0.
-18, -2, 1, 4
Factor -33568*i + 4*i**3 + 94872*i - 1155*i**2 - 2925*i - 181*i**2 + 53177*i.
4*i*(i - 167)**2
Let k(v) be the first derivative of -1/2*v**4 + 0*v - 49*v**2 + 127 + 28/3*v**3. Let k(z) = 0. What is z?
0, 7
Let c(p) be the first derivative of -1/10*p**5 - 2/3*p**2 + 5/9*p**3 + 2/9*p**4 - 18*p - 1. Let r(m) be the first derivative of c(m). Factor r(u).
-2*(u - 2)*(u + 1)*(3*u - 1)/3
Suppose 93*q + 3941 = 100*q. Let r = -560 + q. Factor 6*b**5 - 3*b**4 - 15/2*b**r + 3*b + 3/4 + 3/4*b**2.
3*(b - 1)**2*(2*b + 1)**3/4
Let s be (0 - (-126)/28)*5. Let t(f) be the second derivative of 0 + 1/6*f**6 - 6*f + 20*f**3 + s*f**2 + 2*f**5 + 55/6*f**4. What is k in t(k) = 0?
-3, -1
Let p(b) be the first derivative of b**6 + 33*b**5/5 - 69*b**4/4 - 11*b**3 + 63*b**2/2 + 2479. Solve p(g) = 0.
-7, -1, 0, 1, 3/2
Let q be -4 + ((-6)/(-15))/((-7)/(-2345)). Let p = q - 389/3. Factor 4/3 - p*r**3 + 5/3*r**2 - 8/3*r.
-(r - 2)**2*(r - 1)/3
Factor -9870*s + 936/11*s**2 - 220900/11 - 2/11*s**3.
-2*(s - 235)**2*(s + 2)/11
Suppose 4*u - 17 = 43. Let a = u - 7. Factor -a + 16 - x - 4*x - x + x**2.
(x - 4)*(x - 2)
Let c(g) be the third derivative of -g**8/784 - g**7/245 + 3*g**6/40 - 11*g**5/70 - 5*g**4/14 + 12*g**3/7 - 776*g**2. Suppose c(t) = 0. Calculate t.
-6, -1, 1, 2
Let z(n) be the second derivative of 0 + 145/12*n**4 + 11/4*n**5 - 1/6*n**6 - 5/42*n**7 + 65/3*n**3 + 20*n**2 - 112*n. Factor z(t).
-5*(t - 4)*(t + 1)**3*(t + 2)
Let j(x) be the first derivative of 20 + 0*x**2 - x**3 - 1/4*x**4 + x. Let l(i) be the first derivative of j(i). Determine u so that l(u) = 0.
-2, 0
Factor 5/2*b**4 - 900*b**3 + 0 + 0*b + 0*b**2.
5*b**3*(b - 360)/2
Let j(m) = -15*m**3 + 460*m**2 + 935*m + 480. Let z(v) = -7*v**3 + 230*v**2 + 469*v + 240. Let b(i) = -2*j(i) + 5*z(i). What is l in b(l) = 0?
-1, 48
Let k(p) be the second derivative of -1/4*p**4 + 0 + 9*p**2 - 18*p - 1/2*p**3. Let k(g) = 0. Calculate g.
-3, 2
Let s(i) be the second derivative of i**5/30 + i**4/2 - 10*i**3 + 7*i + 117. Let s(m) = 0. What is m?
-15, 0, 6
Let s(w) be the second derivative of w**6/900 - 7*w**4/180 + 2*w**3/15 + 4*w**2 - 48*w + 1. Let g(k) be the first derivative of s(k). Factor g(b).
2*(b - 2)*(b - 1)*(b + 3)/15
Let u(r) be the second derivative of -r**7/21 + 106*r**6/15 - 4057*r**5/10 + 32944*r**4/3 - 404480*r**3/3 + 819200*r**2 + 279*r - 10. Solve u(d) = 0 for d.
5, 32
Let k = -2/1158135 - -16085423/124306490. Let f = k - -6/161. Solve -1/6 - f*t**2 + 1/3*t = 0 for t.
1
Suppose 3 = -3*r + 9. Suppose 4*f - 14 = -2*l, r*f = 4*f + 4*l - 16. Factor 5*d**2 - 5*d + 9 + 3*d**3 + f*d**3 - 9 - 5*d**4.
-5*d*(d - 1)**2*(d + 1)
Let o(i) = -i**4 - 34*i**3 - 169*i**2 + 15*i. Let v(x) = 4*x**3 - x. Let u(y) = 2*o(y) + 30*v(y). Factor u(z).
-2*z**2*(z - 13)**2
Let x(a) be the second derivative of -3*a**7/350 + a**6/25 - a**5/25 - 51*a**2/2 + 39*a. Let t(j) be the first derivative of x(j). Find m, given that t(m) = 0.
0, 2/3, 2
Suppose 0 = 4*l + 2*l + 4*l. Let z(n) be the first derivative of -1/6*n**2 - 5 + l*n - 1/12*n**4 - 2/9*n**3. Suppose z(c) = 0. Calculate c.
-