(y) - 3*v(y). Let p(a) = -8*a**2 - 18*a + 2. Let h(j) = p(j) + 6*t(j). Find u, given that h(u) = 0.
-1, -1/2
Let d(a) be the first derivative of a**7/21 - a**6/5 + 3*a**5/10 - a**4/6 - 2*a + 72. Let b(h) be the first derivative of d(h). Let b(q) = 0. What is q?
0, 1
Let m be (-6 - -14 - 5) + 26/2. Find j such that -134*j**2 - 4*j**4 + m*j**3 - 133*j**2 + 247*j**2 + 8*j = 0.
0, 1, 2
Let n(a) = 6*a**4 - 86*a**3 + 66*a**2 + 30*a - 8. Let s(t) = 4*t**4 - 3*t**3 + t**2 - 1. Let y(i) = -n(i) + 8*s(i). Factor y(r).
2*r*(r - 1)*(r + 3)*(13*r + 5)
Factor 138/5 + 16/5*f**2 - 94/5*f.
2*(f - 3)*(8*f - 23)/5
Let p = 657601 + -657597. Factor 55*a**3 - 1/4*a**p + 166375*a - 9150625/4 - 9075/2*a**2.
-(a - 55)**4/4
Let w(h) be the second derivative of 3*h**5/100 - 4*h**4/5 + 38*h**3/5 - 144*h**2/5 - 16*h + 57. Factor w(b).
3*(b - 8)*(b - 6)*(b - 2)/5
Suppose 1095 - 185*x + 371*x - 8*x**2 + 5*x**2 + 906*x = 0. Calculate x.
-1, 365
Let d(w) = 19*w**2 + 8. Let x be d(4). Suppose 0 = -306*r + x*r - 18. Factor -2/5*l - 4/15 + 2/15*l**r + 0*l**2.
2*(l - 2)*(l + 1)**2/15
Factor 29*u**2 - 109 - 28*u**2 + 952 + 1093 + 88*u.
(u + 44)**2
Let x be 2/((-12)/75)*(960/(-225) + 4). Let h(g) be the first derivative of 35/2*g**2 - 10*g + x*g**3 - 15 - 35/4*g**4. Suppose h(b) = 0. What is b?
-1, 2/7, 1
Let n(q) = 5*q**3 - 325*q**2 + 1610*q + 1895. Let x(z) = -3*z**3 + 163*z**2 - 799*z - 947. Let m(b) = 2*n(b) + 5*x(b). Solve m(f) = 0.
-1, 7, 27
Let f(r) = 5*r**2 + 4*r + 1. Let u be f(-1). Factor -8*k**u - 10*k**4 + 3*k**3 + 19*k**5 - 19*k**3 - 21*k**5.
-2*k**2*(k + 1)*(k + 2)**2
Suppose 4*h + 18 = 6, 4*h = -2*p. Determine j, given that -31*j**2 + p + 53*j**2 - 30*j**2 + 38*j + 4 = 0.
-1/4, 5
Let j(w) be the first derivative of 2*w**3/21 - 248*w**2/7 - 1586. Let j(h) = 0. Calculate h.
0, 248
Let u(z) be the second derivative of 3*z**6/2 + 303*z**5/20 + 31*z**4/2 - 12*z**3 - 5158*z. Let u(d) = 0. Calculate d.
-6, -1, 0, 4/15
Let o(p) be the third derivative of p**5/360 - 73*p**4/16 - 329*p**3/18 + 2*p**2 - 242*p. Factor o(j).
(j - 658)*(j + 1)/6
Let k(g) be the third derivative of -g**6/600 + 33*g**5/100 - 563*g**4/120 + 31*g**3/2 + 22*g**2 + 76*g. Factor k(b).
-(b - 93)*(b - 5)*(b - 1)/5
Let p(t) be the second derivative of t**5/180 + t**4/8 + 4*t**3/9 - 55*t**2 + 4*t - 15. Let i(d) be the first derivative of p(d). Let i(h) = 0. What is h?
-8, -1
Let c(n) be the first derivative of -2*n**3/51 - 666*n**2/17 - 221778*n/17 + 299. Solve c(x) = 0 for x.
-333
Let u(c) be the first derivative of -5*c**3/3 + 535*c**2/2 + 1650*c + 1787. Suppose u(k) = 0. What is k?
-3, 110
Factor -8*d + 12*d - 4*d + 235*d**3 - 3*d**4 - 240*d**2 + 8*d**4.
5*d**2*(d - 1)*(d + 48)
Let y(t) be the third derivative of -t**8/168 - 4*t**7/21 + 91*t**6/60 - 59*t**5/15 + 4*t**4 + 153*t**2. Find m, given that y(m) = 0.
-24, 0, 1, 2
Factor 306*u + 444*u + 332 - 4*u**2 - 4*u**2 + 3*u**2 + 423.
-5*(u - 151)*(u + 1)
Factor -785*b - 902322*b**2 + 2310 - 902317*b**2 + 1804644*b**2.
5*(b - 154)*(b - 3)
Let t(x) = -32*x**3 - 7*x**2 + 6*x - 18. Let y be t(12). Let q be y/(-20)*(-1)/(-6). Suppose -q + 15*p**3 - 225/2*p**2 + 375*p - 3/4*p**4 = 0. Calculate p.
5
Let n(c) = -12*c + 268. Let l be n(23). Let h be l/6*3/(-2). Factor -2/3 + 2/3*d**h + 0*d.
2*(d - 1)*(d + 1)/3
Let n be 0 - (-1 - (-106)/2). Let w = -50 - n. Factor 45*b + 4*b**w + 6 + 94 - 5*b.
4*(b + 5)**2
Let u be ((-100)/(-80))/((-1)/(-4)). Suppose 8*f - f**u + 13*f + 0*f**2 + 6*f**3 - 23*f - 3*f**3 + f**4 - f**2 = 0. Calculate f.
-1, 0, 1, 2
Let x(a) = 7*a - 23. Let j be x(-19). Let l be (-28)/(-49) - (j/70)/1. Determine m, given that l*m**3 - 8/5*m**4 - 14/5*m - 4/5 + 12/5*m**2 = 0.
-1, -1/4, 1, 2
Let w(a) be the first derivative of 4/5*a**2 - 4/5*a**3 + 16/5*a - 1/2*a**4 + 66 - 2/25*a**5. Solve w(x) = 0 for x.
-2, 1
Let i be 4 + 148/(-52) - 4/26. Let n be (-4*1/14)/(i/(-1)). Factor -16/7*a - 2 - n*a**2.
-2*(a + 1)*(a + 7)/7
Let z(u) = 3*u**3 + 9*u**2 - 15*u + 9. Let m(h) be the first derivative of h**3/3 + 2. Let v(w) = -6*m(w) + z(w). Factor v(d).
3*(d - 1)**2*(d + 3)
Suppose 0 = -3*n - 2*r + 10, -28*n + 3 = -26*n + 5*r. Let h(z) be the second derivative of -121/15*z**2 - 1/90*z**n - 22/45*z**3 + 4*z + 0. Factor h(v).
-2*(v + 11)**2/15
Let o(f) = 2*f**4 - 40*f**3 - 150*f**2 - 180*f - 52. Let h(i) = i**4 + i**3 + i**2 + i + 5. Let l(z) = 4*h(z) - o(z). Factor l(j).
2*(j + 1)**2*(j + 2)*(j + 18)
Let v(n) = -342*n**2 + 378*n - 6. Let p(b) = -684*b**2 + 770*b - 11. Let u(l) = 2*p(l) - 5*v(l). Factor u(r).
2*(r - 1)*(171*r - 4)
Let l(a) = -3*a**2 + 16*a - 64. Let v(c) = 7*c**2 - 32*c + 128. Let k be 6*((-9)/3 - -4). Suppose 120 = 323*t - 315*t. Let i(o) = k*v(o) + t*l(o). Factor i(p).
-3*(p - 8)**2
Let o(p) be the third derivative of -11*p**6/480 + 7*p**5/30 - p**4/2 + 1103*p**2. Solve o(n) = 0 for n.
0, 12/11, 4
Suppose 3*p + 14 = -5*b, -8 + 10 = 4*b - 2*p. Let y(z) = -z - 1. Let h be y(b). Solve 1/3*v**2 + h + 0*v = 0 for v.
0
Let v = 36305/275332 - -2/4049. Let c = 73/476 + v. Find g such that c*g**5 + 2/7 - 4/7*g**3 - 4/7*g**2 + 2/7*g**4 + 2/7*g = 0.
-1, 1
Let q(w) = w**3 - w**2 + 5*w. Let n(y) = -51*y**3 + 127*y**2 - 71*y. Let c(t) = n(t) + 3*q(t). Solve c(o) = 0 for o.
0, 7/12, 2
Factor f**4 + 8*f + 7*f**3 - 41*f + 18*f + 2*f**2 + 5*f**2.
f*(f - 1)*(f + 3)*(f + 5)
Let s(y) = 4*y**2 + 4*y + 15. Let z(t) = -11*t**2 - 7*t - 48. Let j(m) = 8*s(m) + 3*z(m). Factor j(o).
-(o - 8)*(o - 3)
Let s = 22596/395 - 2244/79. Factor s*v**2 + 8*v**4 + 136/5*v**3 + 4/5*v**5 - 108/5*v - 216/5.
4*(v - 1)*(v + 2)*(v + 3)**3/5
Suppose 673*f + 673*f = 1367*f - 63. Let l(n) be the second derivative of 4*n**2 + 5/6*n**4 - 4*n**f + 6*n + 0. Let l(o) = 0. What is o?
2/5, 2
Factor 44/3*y**2 - 40/9*y**3 - 2/9*y**4 - 136/9*y + 46/9.
-2*(y - 1)**3*(y + 23)/9
Let f(c) = -198*c**5 - 408*c**4 - 12*c**3 - 6*c + 3. Let o(d) = 199*d**5 + 408*d**4 + 12*d**3 + 4*d - 2. Let r(u) = -2*f(u) - 3*o(u). Solve r(w) = 0.
-2, -2/67, 0
Let n(w) be the first derivative of -1/3*w**5 + 20/3*w**4 - 230/9*w**3 - 135*w - 120*w**2 + 77. Factor n(y).
-5*(y - 9)**2*(y + 1)**2/3
Let k = -4951109/3 - -1650371. What is n in 0*n + 76/9*n**4 + 0 + k*n**2 + 2*n**5 + 70/9*n**3 = 0?
-3, -1, -2/9, 0
Suppose -173*w = -420*w. Let d(y) be the first derivative of 0*y**4 - 2/35*y**5 + 2/7*y**3 - 4 + w*y - 2/7*y**2. Solve d(k) = 0 for k.
-2, 0, 1
Let k be (616/40 - 10)*20/6. Let x be (-48)/(-27) - ((-94)/k - -5). Factor -r**x - 1/2*r - 1/2*r**3 + 0.
-r*(r + 1)**2/2
Let y be (-4 - -5)/((-4)/(-14 - 2)). What is i in 176*i**3 + 2*i**4 + 2*i**4 - 4 - 3*i**y - 8*i - 3*i**2 - 174*i**3 = 0?
-2, -1, 2
Let v(u) = -1. Let m(o) = -3*o**3 - 10*o**2 - 9*o + 4. Suppose 0 = -5*y + p - 13 - 16, -7 = 2*y - 5*p. Let z(t) = y*v(t) - m(t). Suppose z(l) = 0. What is l?
-2, -1, -1/3
Let -50 + 2*u**4 + 18013*u**2 - 8987*u**2 - 8998*u**2 + 195*u + 2*u**4 - 33*u**3 = 0. Calculate u.
-2, 1/4, 5
Let a(m) be the first derivative of -25/3*m**3 - 5/6*m**6 + 20*m + 25/4*m**4 + m**5 - 10*m**2 + 104. Determine o, given that a(o) = 0.
-2, -1, 1, 2
Let p(z) = 20*z**3 + 545*z**2 - 1130*z. Let n(b) = 23*b**3 + 543*b**2 - 1130*b. Let x(k) = 5*n(k) - 6*p(k). Solve x(c) = 0.
-113, 0, 2
Suppose 6*q - 22 = -10. Factor z**q + 33 - 14 - 6 + 7 - 9*z.
(z - 5)*(z - 4)
Let y(g) be the third derivative of -5*g**8/672 - 15*g**7/28 + 49*g**6/48 + 137*g**5/24 - 5*g**4 - 115*g**3/3 - 11*g**2 - 38*g + 3. Let y(q) = 0. Calculate q.
-46, -1, 1, 2
Suppose -392*g + 357*g - 17 = -26 - 61. Suppose 58/7*w**2 + 8/7 + g*w**3 + 64/7*w = 0. Calculate w.
-2, -1/7
Suppose 2*j - 2 = 2. Let i(z) = -z**3 + 6*z**2 - z - 8. Let t be i(4). Solve 5*p**j - 5 - 1 + 14 + t*p + 12 = 0 for p.
-2
Factor 2/9*w**4 - 16/9*w**2 + 32 - 16/9*w**3 + 64/3*w.
2*(w - 6)**2*(w + 2)**2/9
Let r(s) be the second derivative of s**7/1120 + s**6/80 + s**5/32 - 2*s**3/3 + 11*s**2/2 - s + 5. Let n(u) be the second derivative of r(u). Factor n(v).
3*v*(v + 1)*(v + 5)/4
Let f = -530624 + 530624. Factor 3/2*j**5 + 54*j**2 + f*j + 60*j**3 + 39/2*j**4 + 0.
3*j**2*(j + 2)**2*(j + 9)/2
Let x(a) = -9*a**3 + a**2 + 4. Let z be x(-3). Suppose -z = q - 9*q. Suppose 20*w - q*w**2 - 25*w**2 + 59*w**2 + 50 = 0. Calculate w.
-5
Let m(j) be the second derivative of -j**6/30 - 133*j**5/5 - 17953*j**4/3 - 46816*j**3 - 139392*j**2 - 3399*j. F