39*h**3/3 + 290521*h**2/2 - 156590819*h/3 + 6348. Solve l(u) = 0 for u.
539
Let w be (-1)/(14/4) - 414/(-126). Let l(r) = -r**3 - 2*r**2 - 5*r + 2. Let c be l(0). Let 2/5*u**c - 2/5*u**w - 2/5 + 2/5*u = 0. What is u?
-1, 1
Let s(a) be the second derivative of -5*a**4/12 - 65*a**3/2 - 425*a**2 + 1402*a. What is y in s(y) = 0?
-34, -5
Suppose 0 = 9*y + 308 - 362. Let k(n) be the second derivative of 1/6*n**y + 1/2*n**5 + 5/12*n**4 + 0*n**2 - 20*n + 0 + 0*n**3. Let k(d) = 0. What is d?
-1, 0
Let w(j) be the third derivative of j**5/15 - 53*j**4/3 + 416*j**3/3 + 2515*j**2. Factor w(c).
4*(c - 104)*(c - 2)
Let u(z) be the second derivative of z**5/30 - z**4/3 - 16*z**3/9 + 13*z + 3. Suppose u(w) = 0. Calculate w.
-2, 0, 8
Factor -1149128/9 - 1/9*d**3 - 571532/9*d + 1514/9*d**2.
-(d - 758)**2*(d + 2)/9
Let o be (2890/(-4335))/(1/(-3)). Solve 8/3 + 4/3*i - 1/3*i**3 + 1/3*i**4 - o*i**2 = 0 for i.
-2, -1, 2
Factor 53*h - 255 + 51*h - 475 - h**2 + 32*h + 3*h**2.
2*(h - 5)*(h + 73)
Let m = 3 + 11. Let z = m + -14. Factor z + 22*u**2 - 25*u**2 - 6*u - 3.
-3*(u + 1)**2
Let d(b) = -b**3 + 65*b**2 - 504*b + 3. Let s be d(9). Let i(o) be the first derivative of -34 + 392*o + 28*o**2 + 2/3*o**s. Factor i(m).
2*(m + 14)**2
Let j(f) = 5*f - 14. Suppose b - 2 = 0, -2*m - b + 4 = -4*b. Let a be j(m). Factor y**3 + 4 + 3*y - 16 - 3*y**2 + a.
(y - 1)**3
Let u(w) = 2*w**2 - 2*w + 2. Let j be u(1). Factor -5502*s**j + 5498*s**2 - 168 + 20*s + 72*s.
-4*(s - 21)*(s - 2)
Factor -5/2*b**4 - 10 + 15*b**3 - 65/2*b**2 + 30*b.
-5*(b - 2)**2*(b - 1)**2/2
Let z = -4 - -8. Suppose 6 + 6 = z*g. What is a in -6*a**g + 11*a**3 - 10*a**3 = 0?
0
Let b = -821 + 823. Solve -4810*y**2 + b*y**3 + y**3 + 4798*y**2 - 63*y = 0.
-3, 0, 7
Let b(m) = 8*m + 29. Let q(w) = 13*w + 30. Let f(u) = 5*b(u) - 6*q(u). Let n be f(-1). Suppose -13/8*h**3 - n*h**2 + 0 - 1/4*h**4 - 9/8*h = 0. What is h?
-3, -1/2, 0
Let g(q) be the first derivative of -2*q**3/45 + 1492*q**2/15 - 994*q/5 + 4882. Factor g(z).
-2*(z - 1491)*(z - 1)/15
Let s(u) be the third derivative of -u**5/120 - 493*u**4/24 - 243049*u**3/12 + 2*u**2 - 105*u. Factor s(v).
-(v + 493)**2/2
Let i(t) = -t + 7. Let l be i(0). Factor 8*s**3 - l*s**3 + 2*s**3 + 50*s**4 + 2*s**2 - 49*s**4.
s**2*(s + 1)*(s + 2)
Let l(d) = -d**3 + 2*d**2 + 2*d + 2. Let i be l(0). Suppose -28*y**2 - 2*y + 89*y**2 + 2*y**3 + 5*y - 34*y**2 - 34*y**i = 0. What is y?
0, 1/2, 3
Let f be (-176)/132 - (-52)/3. Let t be 6/f*(12/3 - -4). Factor 2/5*i - 2/5*i**t - 6/5*i**2 + 2/5*i**4 + 4/5.
2*(i - 2)*(i - 1)*(i + 1)**2/5
Let o = -1562 - -1562. Suppose 3*t = g - 24 + 20, 2*g - 4*t - 8 = o. Determine f so that 6/5*f**5 + 42/5*f**3 + 6/5*f - 27/5*f**g + 0 - 27/5*f**2 = 0.
0, 1/2, 1, 2
Let q be -1*9*75/(-1485). Let t(u) be the third derivative of 2*u**2 + 0*u - q*u**3 - 3/22*u**4 - 1/110*u**5 - 10. Solve t(p) = 0 for p.
-5, -1
Let b be (-3)/(8/((-16)/3)*56/156). Factor -45/7 - b*d - 6/7*d**2.
-3*(d + 5)*(2*d + 3)/7
Let g(m) be the second derivative of 0 + 54*m - 437/4*m**3 - 1587/2*m**2 - 3/40*m**5 + 11/2*m**4. Find d, given that g(d) = 0.
-2, 23
Find j, given that 4/5*j**4 - 36/5 + 24/5*j**3 + 32/5*j**2 - 24/5*j = 0.
-3, -1, 1
Let t(o) be the first derivative of o**6/360 - 7*o**5/12 - 71*o**4/24 + 2*o**3/3 + 13*o + 243. Let k(r) be the third derivative of t(r). Factor k(z).
(z - 71)*(z + 1)
Let w be (50/(-12))/((-93)/(5208/560)). Let m(q) be the second derivative of 21 + 1/48*q**4 + w*q**3 + 25/8*q**2 - 2*q. Find n, given that m(n) = 0.
-5
Let u(j) be the second derivative of -5*j**4/4 - 6655*j**3/3 - 4435*j**2/2 + 1071*j + 1. Factor u(t).
-5*(t + 887)*(3*t + 1)
Let q(a) be the first derivative of -59 - a**5 - 965/3*a**3 + 75/2*a**4 - 1200*a**2 - 1280*a. Factor q(k).
-5*(k - 16)**2*(k + 1)**2
Factor -1/7*b**2 + 8 + 1/7*b.
-(b - 8)*(b + 7)/7
Let a(b) = 10*b**2 + 180*b + 145. Let u(k) = 9*k**2 + 181*k + 152. Let q(h) = 4*a(h) - 5*u(h). Determine n, given that q(n) = 0.
-36, -1
Let s = -85 + 103. Let c be 5*(s/(-5) + 5). Factor c*n**2 - 2*n**2 - 10 - 73*n + 78*n.
5*(n - 1)*(n + 2)
Let p(z) = -2*z**2 + 6*z + 11. Let l be p(4). Factor -1224*q**4 + 12*q**2 + 1219*q**4 - 2*q**2 - 5*q**l.
-5*q**2*(q - 1)*(q + 2)
Find v, given that -72/5 + 14/5*v + 1/5*v**2 = 0.
-18, 4
Let g(t) = -t**3 - 541*t**2 - 1112*t - 572. Let w(a) = -a**3 - 271*a**2 - 557*a - 287. Let q(n) = 6*g(n) - 11*w(n). Let q(j) = 0. Calculate j.
-1, 55
Let b(v) be the second derivative of 147*v**5/20 - 12537*v**4/4 + 10719*v**3/2 - 6885*v**2/2 + 830*v - 3. Determine a so that b(a) = 0.
3/7, 255
Let r = 12849 - 12829. Let b(m) be the first derivative of -10*m + 10/3*m**3 - 5/2*m**2 + 5/4*m**4 + r. Factor b(p).
5*(p - 1)*(p + 1)*(p + 2)
Let s(x) = -x**2 - 32*x + 72. Let v be s(-34). Factor 30*c + 36*c**v - 9*c + 2*c**5 - 6*c**4 + c**5 + 72*c**3 + 66*c**2.
3*c*(c + 1)**3*(c + 7)
Solve -201*k**3 + 122*k**4 + 20*k**5 - 182*k**4 - 11*k**3 - 3*k**3 + 70*k**2 - 205*k**4 = 0 for k.
-1, 0, 1/4, 14
Factor -2*g**2 - 463*g - 331*g + 21*g - 1596 - 21*g + 4*g**2.
2*(g - 399)*(g + 2)
Let q(s) be the third derivative of 5*s**8/48 + 71*s**7/21 + 5*s**6/3 - 1501*s**2. What is k in q(k) = 0?
-20, -2/7, 0
Let j(p) = -7*p**4 - 3*p**3 - 155*p**2 + 205*p - 10. Let o(a) = -4*a**4 + 2*a**3 - 77*a**2 + 103*a - 6. Let g(s) = -3*j(s) + 5*o(s). Factor g(t).
t*(t - 1)*(t + 10)**2
Let n(y) be the first derivative of 70*y + 305/2*y**2 - 15*y**3 - 6. Factor n(o).
-5*(o - 7)*(9*o + 2)
Factor -10*i**2 + 40 + 547*i - i**3 - 268*i + 3*i**3 - 7*i**3 - 259*i.
-5*(i - 2)*(i + 2)**2
Let l(i) be the third derivative of 0*i + 0 - 1/2*i**3 + 170*i**2 + 5/72*i**4 + 1/45*i**5. Factor l(x).
(x - 1)*(4*x + 9)/3
Factor 3/7*q**2 - 404/7 - 173*q.
(q - 404)*(3*q + 1)/7
Let d(b) be the third derivative of b**7/210 - 353*b**6/120 - 297*b**5/10 - 715*b**4/6 - 716*b**3/3 - 3452*b**2. Factor d(k).
(k - 358)*(k + 1)*(k + 2)**2
Let x be (-4)/14 - (-60)/14. Let c(m) = 6000*m. Let v be c(0). Factor 2/13 + 2/13*g**x - 4/13*g**2 + 0*g**3 + v*g.
2*(g - 1)**2*(g + 1)**2/13
Let u = -97544 - -97546. Factor -8/3*n + 1/3*n**u + 0.
n*(n - 8)/3
Let y be (-405)/(-2)*(36 + (-9152)/260). Factor y*z + 90*z**2 + 2/3*z**4 + 0 + 14*z**3.
2*z*(z + 3)*(z + 9)**2/3
Let n(q) be the second derivative of q**4/32 - 11*q**3/2 - 53*q + 5. Let n(l) = 0. What is l?
0, 88
Let u be -6 + (294/(-6))/(-7). Let r be ((-28)/(-49) - u)/((-27)/42). Determine j so that -14/3*j + 2 - r*j**3 + 10/3*j**2 = 0.
1, 3
Let -136*j**4 + 39*j**4 - 120 + 5*j**5 + 240*j**3 + 122*j**4 + 65*j**4 + 40*j**4 - 245*j - 10*j**2 = 0. Calculate j.
-24, -1, 1
Let l(n) be the second derivative of -n**6/135 - 2*n**5/45 - 2*n**4/27 + 44*n - 6. Factor l(z).
-2*z**2*(z + 2)**2/9
Let s = 169943 - 169940. Solve 106/11*p**2 + 1456/11*p + 2/11*p**s + 1352/11 = 0 for p.
-26, -1
Let l = -3 + 8. Let c(h) = 0*h**3 - 233*h**2 - 4*h**3 + 3*h**3 + 2*h**3 + 234*h**2. Let x(q) = 6*q**3 + 6*q**2 - 2*q. Let n(k) = l*c(k) - x(k). Factor n(d).
-d*(d - 1)*(d + 2)
Suppose 0 = -5*c, -c = 3*a - 6*c - 9. Determine t, given that 189*t**2 + 4 + 16*t + 77*t**2 - 141*t**3 + 130*t**a + 211*t**3 + 54*t = 0.
-1, -1/4, -2/25
Let g = 36486 - 36484. Let v(t) be the first derivative of -6*t + 8*t**g + 2/5*t**5 - 4*t**3 + 0*t**4 + 44. Factor v(r).
2*(r - 1)**3*(r + 3)
Let v(b) be the first derivative of 1/4*b**2 + 9*b - 21 + 1/9*b**3 + 1/72*b**4. Let m(s) be the first derivative of v(s). What is r in m(r) = 0?
-3, -1
Let q(a) = -a**3 - 9*a**2 - a + 8. Let j be q(-9). Suppose 0 = 18*r - j - 55. Factor 0*w + 0 + 4/5*w**3 + 6/5*w**2 - 2/5*w**r.
-2*w**2*(w - 3)*(w + 1)/5
Let t be 16/(20/(-5)) + 6/1. Solve -r**4 - 193*r**t - 2*r**4 - 12*r**3 + 2*r**4 + 157*r**2 = 0 for r.
-6, 0
Let b be 1400/(-468) + (-11 - -5). Let z = -114/13 - b. Factor -z*n**2 + 8/9 - 2/3*n.
-2*(n - 1)*(n + 4)/9
Let o(w) be the first derivative of w**6/24 - 6*w**5/5 + 25*w**4/8 + 100*w**3 + 1125*w**2/8 - 2142. Find d such that o(d) = 0.
-5, -1, 0, 15
Let i(a) be the second derivative of a**5/40 - 2*a**4/3 + 77*a**3/12 - 49*a**2/2 - 1634*a. Factor i(o).
(o - 7)**2*(o - 2)/2
Let -4/5*v**2 - 219024/5 + 1872/5*v = 0. What is v?
234
Let m be 1/(18/8 - 2). Let i(s) = 4*s**3 + 40*s**2 + 4. Let c be i(-10). Factor 12*o**5 - 13*o**4 + m*o**2 + 2*o**4 + c*o**3 - 9*o**4.
4*o**2*(o - 1)**2*(3*o + 1)
Let y(w) be the second deri