hird derivative of 11*b**6/1620 - 13*b**5/540 + b**4/54 - 17*b**3 - 189*b**2. Let f(t) be the first derivative of d(t). Factor f(k).
2*(k - 1)*(11*k - 2)/9
Let w = 150211/676233 - -7/75137. Factor w*l**2 - 64/9 + 28/9*l.
2*(l - 2)*(l + 16)/9
Let j(d) be the second derivative of -3*d**3 + 0*d**2 - 4 + 0*d**4 + 1/10*d**5 - 5*d. Factor j(i).
2*i*(i - 3)*(i + 3)
Let h = 1561/3062 - 15/1531. Find l such that -h*l**2 + 4 + l = 0.
-2, 4
Let r(l) be the second derivative of -3*l**6/80 - 2*l**5/5 + 35*l**4/48 - l**3/2 + 69*l**2/2 + 169*l. Let f(j) be the first derivative of r(j). Factor f(z).
-(z + 6)*(3*z - 1)**2/2
Let t(c) be the third derivative of c**8/28 - 92*c**7/105 - 3*c**6 + 16*c**5/3 + 29*c**4/2 - 68*c**3/3 - 1887*c**2. Determine l so that t(l) = 0.
-2, -1, 1/3, 1, 17
Suppose -727 = o - 730. Suppose -8 = -3*v + j, -o*j + 6*j = v. Suppose -12/7*a**4 - 4/7*a + 6/7*a**2 + 0 + 10/7*a**v = 0. What is a?
-2/3, 0, 1/2, 1
Let x = 7143 + -7139. Let g(n) be the first derivative of n**3 - 3*n**2 + 23 + 0*n + 3/4*n**x. Factor g(p).
3*p*(p - 1)*(p + 2)
Solve 0 + 2/3*z**4 - 2/3*z**5 - 26/3*z**2 + 14/3*z**3 + 4*z = 0.
-3, 0, 1, 2
Let a(m) be the third derivative of m**2 - 2/3*m**3 + 0*m**4 - 41*m + 1/60*m**5 + 0. Determine k so that a(k) = 0.
-2, 2
Suppose -36*d + 31*d + 14*d = 0. Let x(t) be the second derivative of -4*t + 0*t**2 + 1/40*t**5 + d + 1/3*t**3 + 5/24*t**4. Factor x(b).
b*(b + 1)*(b + 4)/2
Solve 3/5*a**2 - 21/5*a - 3132/5 = 0.
-29, 36
Factor -25*v**5 + 30*v**5 - 463*v**2 + 1432*v - 381*v**2 + 16320 - 40*v**4 + 4408*v - 576*v**2 - 705*v**3.
5*(v - 17)*(v - 3)*(v + 4)**3
Let i(p) be the first derivative of -490*p**6/9 + 1099*p**5/3 - 1675*p**4/2 + 900*p**3 - 495*p**2 + 135*p - 152. Determine h so that i(h) = 0.
3/7, 3/4, 1, 3
Factor 0 + 0*k + 4/9*k**3 + 100/3*k**2.
4*k**2*(k + 75)/9
Let w be 2/104*70 - (-66)/429. What is s in 63/2 - 6*s - w*s**2 = 0?
-7, 3
Let x(z) = 4312*z + 8626. Let k be x(-2). Solve 0*v + 45/2*v**k - 5/2*v**3 - 270 = 0.
-3, 6
Let i be (-64)/40*(-5)/2. Let g be ((-8)/(-5))/(1*(-10)/(-25)). Suppose p**4 + 4*p**3 - 4*p**g + 4*p**4 + p**i = 0. Calculate p.
-2, 0
Let t(i) = -6*i**3 - 265*i**2 - 1519*i - 7. Let d(n) = -2*n**3 - 88*n**2 - 506*n - 2. Let z(m) = -7*d(m) + 2*t(m). What is b in z(b) = 0?
-36, -7, 0
Let k(a) be the second derivative of 243/20*a**5 + 1 + 279/4*a**4 + 18*a**2 - 37*a + 56*a**3. Let k(h) = 0. Calculate h.
-3, -2/9
Let x be (-10)/(-5)*-1 + 5. Suppose -3*l = u - 18, 16 = x*l + 1. Factor 10*d**3 + 50*d**2 - 11*d**2 - d + 8*d**3 + u*d**4 + 12 + 37*d.
3*(d + 1)**2*(d + 2)**2
Suppose 3*g + 4*f = 40, -7*f - 508 + 578 = 3*g. Factor g + 51/4*u**2 + 3/4*u**3 - 27/2*u.
3*u*(u - 1)*(u + 18)/4
Suppose -4*k = -19 + 7. Let r(z) = -11*z. Let m be r(0). Factor m*o**3 - 8*o + k*o**2 + 4*o**3 + o**2.
4*o*(o - 1)*(o + 2)
Let h(l) be the first derivative of 2/7*l**2 - 2/21*l**3 + 0*l - 1/14*l**4 - 13. Factor h(g).
-2*g*(g - 1)*(g + 2)/7
Let x(a) = -2*a. Let c be -2*(-6 - -4) + -7. Let i be x(c). Solve 4*k + 0*k**3 + i*k**2 - 3*k**5 - 6*k**4 - k**5 - 2*k**3 + 2*k**5 = 0.
-2, -1, 0, 1
Let n(h) be the second derivative of h**5/5 - 106*h**4/3 - 904*h**3/3 + 2640*h**2 - 2882*h. Factor n(w).
4*(w - 110)*(w - 2)*(w + 6)
Let m(j) = -j - 29. Let l(b) = -b - 28. Let d(o) = -4*l(o) + 3*m(o). Let x be d(-6). Factor 4*t + 2*t - 6*t**3 + 3 + x*t**4 - 12*t**2 - 10*t**4.
3*(t - 1)**2*(t + 1)*(3*t + 1)
Factor -74*x**3 + 24618*x**2 + 103960*x + 41197 + 64603 - 220*x**3 + 2*x**4 - 158*x**3.
2*(x - 115)**2*(x + 2)**2
Let t(l) be the third derivative of -32 + 0*l**3 - 1/220*l**5 - 5*l**2 + 1/132*l**4 + 1/1320*l**6 + 0*l. Find w, given that t(w) = 0.
0, 1, 2
Let k = 11763 - 247022/21. Let j(n) be the second derivative of 35*n + k*n**4 + 0 + 2/7*n**3 + 4/7*n**2. Factor j(m).
4*(m + 1)*(m + 2)/7
Let x(q) = 278*q + 281. Let d be x(-1). Let c(f) be the first derivative of 0*f + 1/3*f**3 + d + 1/2*f**2. Factor c(h).
h*(h + 1)
Suppose 1824*w - 38998 - w**2 - 55545 + 146431 + 5*w**2 + 156048 = 0. Calculate w.
-228
Let c = 39 + 236. Solve -c*t - 63 - 4*t**2 - 4*t**2 - 4*t**2 + 20*t = 0 for t.
-21, -1/4
Let u(k) = -k**3 + 1. Let v(d) = -10*d**2 + 9*d + 19. Let f(p) = 3*u(p) - v(p). Let i(a) = a**3 - a**2 - a - 2. Let l(h) = -f(h) - 2*i(h). Factor l(s).
(s - 5)*(s - 4)*(s + 1)
Let s(w) = -w**3 + 4*w**2 + 2*w - 4. Let v be s(4). Suppose -5*k = y - 15, 4*y + 2*k - 30 = 2*y. Factor -1769*x - y*x**2 + 1769*x - 12*x**3 + 3*x**v.
3*x**2*(x - 5)*(x + 1)
Factor -2*p**5 - 1/5*p**4 + 9/5*p**3 + 0*p + 0*p**2 + 0.
-p**3*(p + 1)*(10*p - 9)/5
Let q(m) = 4*m**2 - 1066*m - 1065. Let r be q(-1). Suppose 0*w + 4*w - 16 = 0. Factor -1/8*d**3 + 1/8*d**2 + 0 + 1/8*d**r - 1/8*d**w + 0*d.
d**2*(d - 1)**2*(d + 1)/8
Let k(l) be the third derivative of l**8/84 - 13*l**6/30 + 16*l**5/15 + 2*l**4 - 32*l**3/3 - 24*l**2 - 7. Find o, given that k(o) = 0.
-4, -1, 1, 2
Let v = 3414 - 682799/200. Let c(h) be the third derivative of 0*h + 0*h**3 + v*h**6 - 1/30*h**4 + 0*h**5 - 22*h**2 + 0 - 1/1050*h**7. Factor c(f).
-f*(f - 2)**2*(f + 1)/5
Let f(y) be the third derivative of -y**6/540 + 41*y**5/90 - 1681*y**4/36 - 21*y**3 - 2*y**2 - 3. Let o(l) be the first derivative of f(l). Factor o(i).
-2*(i - 41)**2/3
Factor -27/7*w**3 + 0 - 1/7*w**4 + 120/7*w + 94/7*w**2.
-w*(w - 4)*(w + 1)*(w + 30)/7
Solve -90 + 60*i**3 + 21974*i**4 - 204*i**2 - 294 - 624*i - 21953*i**4 - 3*i**5 = 0 for i.
-2, -1, 4, 8
Determine n so that -9/4*n**2 + 3/4*n**4 + 75/4*n - 27/4*n**3 + 27/2 = 0.
-1, 2, 9
Let p(r) = r**3 - 3*r - r**2 - 2 + 3 + 4*r. Suppose 35*k + 20*k = -165. Let c(t) = -2*t**3 + 9*t**2 - 21*t + 15. Let d(w) = k*c(w) - 3*p(w). Solve d(b) = 0.
2, 4
Let c(y) be the third derivative of -5*y**8/336 + 23*y**7/14 - 449*y**6/8 + 5303*y**5/12 - 520*y**4 - 7680*y**3 - 264*y**2. Solve c(x) = 0 for x.
-1, 3, 32
Determine w so that -161240*w - 26912 - 3*w**3 + 2783/2*w**2 = 0.
-1/6, 232
Let -832/7 - 38/7*w**3 - 2/7*w**4 + 348/7*w**2 - 64*w = 0. What is w?
-26, -1, 4
Let y = -421/3 + 1697/12. Let w(s) be the second derivative of 0 + 9*s - 1/2*s**2 - y*s**4 - 3/10*s**5 - 4/3*s**3. Determine b, given that w(b) = 0.
-1, -1/6
Let s(l) = -3*l**2 + 179 + l - 179. Let x(f) = 19*f**2 - 19*f + 32. Let g(d) = 14*s(d) + 2*x(d). Determine h, given that g(h) = 0.
-8, 2
Find u such that -1/3*u**5 + 71/3*u**3 + 0*u**4 - 268/3*u - 42*u**2 + 168 = 0.
-9, -2, 2, 7
Let k = 57908/9 + -6434. Let b(n) be the first derivative of -k*n**3 + 0*n + 1/6*n**4 - 7 + 0*n**2. Let b(w) = 0. Calculate w.
0, 1
Suppose -55 - 4*f**5 - 212*f**2 + 84*f**3 - 3*f + 199 + 50*f**4 - 77*f + 18*f**4 = 0. What is f?
-2, -1, 1, 18
Let q(o) = -32*o**2 + 160*o. Let k be q(5). Let i(x) be the first derivative of k*x - 2/9*x**3 + 0*x**2 - 17. Determine z, given that i(z) = 0.
0
Suppose 0*k = -6*k. Suppose 3*y = j - 5, -3*y + 37 = 2*j - k. Suppose -j*i + i**3 + 17 - 5*i**3 - 18*i - 1 + 20*i**2 = 0. Calculate i.
1, 2
Suppose 155 = -6*h + 239. Suppose -h = 50*c - 57*c. Suppose 9/2 + 0*z - 1/2*z**c = 0. Calculate z.
-3, 3
Let o be 3*2/9*27/189. Let k(s) be the first derivative of -2/63*s**3 + 0*s**2 + o*s + 16. Let k(q) = 0. Calculate q.
-1, 1
Let i = 12 - -16. Solve i*p**2 - 1 - 8*p**2 + p**3 - 11*p**2 + 15*p + 8 = 0.
-7, -1
Let k be 6 + ((-5)/10 + 0)*6. Factor 6*m**k - m**4 - 23*m + 10*m - 2*m**4 + 3*m**3 + m.
-3*m*(m - 2)**2*(m + 1)
Let y(i) be the second derivative of -5*i**4/18 - 56*i**3/9 + 16*i**2 + 3916*i. Find j, given that y(j) = 0.
-12, 4/5
Suppose 342792 - 178*f**2 - 184*f**2 - 185*f**2 + 734*f**2 - 185*f**2 - 1656*f = 0. What is f?
414
Let z(l) be the third derivative of l**9/60480 - l**8/6720 + 3*l**4/8 + 85*l**2. Let j(h) be the second derivative of z(h). Let j(x) = 0. Calculate x.
0, 4
Let z(v) = 2*v - 1. Let w(k) = k**2 - 9*k + 7. Let a(o) = w(o) + 5*z(o). Let c(j) = 4*j**2 - j - 22. Let f(i) = -a(i) - c(i). Factor f(x).
-5*(x - 2)*(x + 2)
Let o = 13032007/10 + -1301984. Factor o + 69/10*r**2 + 1/10*r**3 + 1587/10*r.
(r + 23)**3/10
Let g = -676 + 678. Suppose -564*v**g - 85*v - 280*v - 390*v**3 - 239 + 149 - 7*v**5 + 4*v**2 - 110*v**4 + 2*v**5 = 0. Calculate v.
-18, -1
Let d(k) be the third derivative of k**9/15120 + k**8/1680 + k**7/630 - 9*k**5/20 - k**4/12 - k**2 - 4. Let s(x) be the third derivative of d(x). Factor s(g).
4*g*(g + 1)*(g + 2)
Factor 1/