t j(s) be the first derivative of s**6/39 - 96*s**5/65 + 35*s**4/2 - 8673. Determine a so that j(a) = 0.
0, 13, 35
Suppose 2*s = b + 18, -3*s + s + 3*b + 6 = 0. Let d(t) be the first derivative of 5/11*t**2 - s - 2/33*t**3 - 12/11*t. Let d(r) = 0. What is r?
2, 3
Let t(w) be the third derivative of -1/24*w**4 + 0*w + 1/60*w**6 + 0*w**3 + 0 + 0*w**7 + 38*w**2 + 0*w**5 - 1/336*w**8. Determine n so that t(n) = 0.
-1, 0, 1
Let x(k) be the third derivative of k**5/20 - 2551*k**4/8 - 2*k**2 - 14*k + 33. What is h in x(h) = 0?
0, 2551
Let y(r) be the second derivative of r**5/5 + 343*r**4 + 235298*r**3 + 80707214*r**2 + 3*r - 29. Factor y(s).
4*(s + 343)**3
Factor -2/11*z**3 - 4014/11*z**2 - 2012018/11 - 2016030/11*z.
-2*(z + 1)*(z + 1003)**2/11
Let v(k) be the first derivative of 2*k**3/21 + 538*k**2/7 + 144722*k/7 - 577. Factor v(f).
2*(f + 269)**2/7
Let d(h) = -4*h**2 + h - 6. Let m(t) = -15*t**2 + 7*t - 14. Let k(w) = 22*d(w) - 6*m(w). Solve k(a) = 0.
-2, 12
Let r(q) be the second derivative of -q**5/240 + 31*q**4/96 - 13*q**2/2 - q + 13. Let d(z) be the first derivative of r(z). Factor d(s).
-s*(s - 31)/4
Let a be ((-12)/(-45))/(14512/13605). Let a*q + 0 + 3/4*q**2 = 0. Calculate q.
-1/3, 0
Let x be 202/14 - 324/180*(-25)/105. Find j such that -128/7 - x*j**2 - 2/7*j**4 - 24/7*j**3 - 192/7*j = 0.
-4, -2
Factor 2610*n - 22707/2 - 150*n**2.
-3*(10*n - 87)**2/2
Let l(z) = 5*z**2 - 8830*z + 19518718. Let f(h) = -12*h**2 + 17657*h - 39037433. Let j(g) = -2*f(g) - 5*l(g). Factor j(k).
-(k - 4418)**2
Let x = -1191699 - -5958549/5. Factor 0 + 2/5*u**2 - x*u.
2*u*(u - 27)/5
Let k = -54 + 52. Let o be (14/4)/(k/(-12)). Determine p, given that -12*p - 23 + 3 - p**2 - o + 5 = 0.
-6
Let m be 12/(-10)*(-30)/18. Factor c**4 - 34 + c**4 + 24*c**m - 14 - 5*c**4.
-3*(c - 2)**2*(c + 2)**2
Let n(t) = -20*t**4 + 20*t**3 + 4*t**2 - 20*t - 32. Let y(w) = -13*w**4 + 13*w**3 + 3*w**2 - 13*w - 20. Let z(b) = 5*n(b) - 8*y(b). Factor z(h).
4*h*(h - 1)**2*(h + 1)
Let r(n) = -19*n**2 + 155*n - 18. Let w be r(8). Let f(c) be the first derivative of 3/2*c**2 - w*c + 3*c**3 - 17 - 3/5*c**5 - 3/4*c**4. Factor f(l).
-3*(l - 1)**2*(l + 1)*(l + 2)
Factor -2368/7*b - 16/7 - 12348*b**3 - 12684*b**2.
-4*(b + 1)*(147*b + 2)**2/7
Let k(u) = 17968505*u**3 - 1306825*u**2 + 31695*u - 256. Let t(x) = 17968504*x**3 - 1306820*x**2 + 31692*x - 256. Let f(c) = -4*k(c) + 5*t(c). Factor f(p).
4*(165*p - 4)**3
Factor -72*b - 3/5*b**3 - 129/5*b**2 + 0.
-3*b*(b + 3)*(b + 40)/5
Let m(p) be the first derivative of -p**3/9 + 697*p**2/3 - 485809*p/3 - 1763. Suppose m(l) = 0. Calculate l.
697
Let r be 3/(-25)*343490/(-2103). Factor -2/5*z**3 - r - 14*z + 26/5*z**2.
-2*(z - 7)**2*(z + 1)/5
Suppose -3*g + k = -292, -5*g + 200 + 296 = -4*k. Find z, given that -572*z**3 - g - 22*z**4 - 663*z**4 + 824*z**2 + 180*z**5 - 323*z**4 + 112*z = 0.
-1, -2/5, 1/3, 2/3, 6
Let q be (-39)/(-12) - (759 - 757). Factor 3/2*n + 1/4*n**2 + q.
(n + 1)*(n + 5)/4
Suppose -4607 = 26*s - 4659. Let a(c) be the second derivative of 4/3*c**3 + 2*c + 0 + 0*c**s + 1/3*c**4. Solve a(j) = 0 for j.
-2, 0
Let d(b) be the first derivative of -10*b - 4/9*b**4 - 3 + 0*b**2 - 1/30*b**5 - 16/9*b**3. Let s(j) be the first derivative of d(j). Let s(f) = 0. What is f?
-4, 0
Suppose 3*h + 234 - 247 = -o, -h + 11 = 2*o. Let g(z) be the first derivative of -9/10*z**2 - 4/5*z**h - 3/20*z**4 + 0*z + 19. Find p such that g(p) = 0.
-3, -1, 0
Let i(b) be the first derivative of -14/3*b + 1/15*b**5 - 5/2*b**2 - 183 + 13/9*b**3 + 5/4*b**4. Let i(q) = 0. Calculate q.
-14, -1, 1
Let z(u) be the second derivative of -u**8/2940 - u**7/210 - u**6/105 - 3*u**3/2 - u - 16. Let v(o) be the second derivative of z(o). Factor v(p).
-4*p**2*(p + 1)*(p + 6)/7
Let c(x) be the first derivative of x**3/7 - 69*x**2/14 + 18*x + 560. Factor c(p).
3*(p - 21)*(p - 2)/7
Let k(q) be the first derivative of -3*q**5/25 + 21*q**4/4 + q**3/5 - 21*q**2/2 + 4936. Find f, given that k(f) = 0.
-1, 0, 1, 35
Determine k so that -168*k + 11 + 81*k**2 + 9 + 11 + 15 - 10 + 63*k**3 - 12*k**4 = 0.
-2, 1/4, 1, 6
Suppose 8 = 2*r, 4*s - 51 = 3*r + 17. Suppose 4*h - 3*t = 31, -5*h + 4*t = 2*t - 30. Let -13*i + i + 28*i**2 + s*i**3 + 4*i**2 - h*i = 0. What is i?
-2, 0, 2/5
Let g(x) be the first derivative of -5*x**4/12 + 5*x**3/3 + 12*x + 41. Let n(o) be the first derivative of g(o). Suppose n(q) = 0. Calculate q.
0, 2
Let a(w) be the first derivative of w**4/24 + 37*w**3/9 + 71*w**2/4 - 953. Factor a(u).
u*(u + 3)*(u + 71)/6
Let o(n) be the third derivative of 0*n + 5*n**2 - 1/7*n**4 + 0 + 1/15*n**5 - 2/21*n**3. Factor o(k).
4*(k - 1)*(7*k + 1)/7
Suppose 3*a - 3 = 2*a. Determine o so that 17*o**3 - 320*o + 16*o**3 - 36*o**4 - 19*o**4 + 147*o**a + 5*o**5 - 80*o**2 = 0.
-1, 0, 4
Let w = 589 - 583. Let f be 38/w - 6 - -1. Solve -4/3*b**2 + 8 + f*b = 0.
-2, 3
Suppose -3*g + g + 46 = -5*p, 5*p + 5*g + 60 = 0. Let b be (-21)/p*45/54. Determine n, given that -1 + 5/4*n**4 - 1/4*n**5 - 1/4*n**2 - b*n**3 + 2*n = 0.
-1, 1, 2
Factor 0 + 25/7*h**2 - 2/7*h.
h*(25*h - 2)/7
Let p(a) be the third derivative of a**8/1008 + 4*a**7/63 + 3*a**6/5 + 104*a**5/45 + 34*a**4/9 + 73*a**2 + 7*a - 5. Solve p(d) = 0 for d.
-34, -2, 0
Let -118662*m**5 + 4*m**2 + 4*m**2 + 13*m**4 + 118667*m**5 - 26*m**3 = 0. Calculate m.
-4, 0, 2/5, 1
Let t = -3137/190 - -1616/95. Factor -1/2*o**2 + 5*o**3 + 0 - 5*o + t*o**4.
o*(o - 1)*(o + 1)*(o + 10)/2
Let n = -133008 + 133008. Solve 4/3*o**3 + 2*o**4 - 2/3*o**5 + n - 8*o**2 + 16/3*o = 0 for o.
-2, 0, 1, 2
Let k(v) be the third derivative of 1/210*v**7 + 13/60*v**5 + 0 - 1/20*v**6 - v + 2/3*v**3 - 1/2*v**4 + 138*v**2. Find j, given that k(j) = 0.
1, 2
Let z(u) = 55*u**2 - 110*u + 55. Let f(k) = -24218*k**2 + 10*k - 1 + 24213*k**2 + 6 - 10. Let d = -22 - -67. Let c(l) = d*f(l) + 4*z(l). Factor c(w).
-5*(w - 1)**2
Suppose -1012/5*q + 1/5*q**2 + 256036/5 = 0. Calculate q.
506
Let s(a) be the third derivative of a**6/720 + a**5/72 - a**4/24 + 605*a**2. What is g in s(g) = 0?
-6, 0, 1
Let k(n) = -67*n - 2139. Let i be k(-32). Let j(a) be the first derivative of 0*a + 3/4*a**3 - 29 + 15/16*a**4 + 0*a**2 + 3/20*a**i - 1/8*a**6. Factor j(o).
-3*o**2*(o - 3)*(o + 1)**2/4
Suppose -94998 + 95582 = 292*p. Let -5/4*x**p + 7/4 - 17/2*x = 0. Calculate x.
-7, 1/5
Let a(p) be the third derivative of -p**8/1344 - p**7/420 + p**6/160 + p**5/60 - p**4/24 - 7*p**2 - 182. Factor a(t).
-t*(t - 1)**2*(t + 2)**2/4
What is o in -7035*o + 6172*o**3 + 3676*o**2 + 1232 + 879*o - 4908*o**4 - 7*o**5 - 9*o**5 = 0?
-308, -1, 1/4, 1
Suppose -32*j = 2*j + 29*j - 126. Let w(g) be the first derivative of 2/9*g**3 - 2/9*g**6 + 0*g + 0*g**j + 7/12*g**4 + 4/15*g**5 + 15. What is m in w(m) = 0?
-1/2, 0, 2
Suppose -11*a + 306 = -222. Suppose 2*f - 10 = -3*f. Let 223 - a*b + 6*b**f + 4*b**2 - 79 - 6*b**2 = 0. Calculate b.
6
Let u(m) be the first derivative of m**6/4 + 51*m**5/5 - 105*m**4/8 - 2819. Determine a, given that u(a) = 0.
-35, 0, 1
Factor 38*j**2 - 57*j - 25*j - 1696 + 1708 + 132*j**3.
2*(j + 1)*(6*j - 1)*(11*j - 6)
Let k(d) be the second derivative of d**6/30 - 7*d**5/20 - 23*d**4/12 + 13*d**3/2 + 27*d**2 - 1205*d. Find u such that k(u) = 0.
-3, -1, 2, 9
Let f = -33455/14 + 13504/7. Let t = -460 - f. Factor -t + z**2 + 1/2*z.
(z + 1)*(2*z - 1)/2
Let r = -6165 + 6165. Let x be (-1)/(-2)*(-2 - -6). Find c such that -2/3*c**x + 0 + r*c + 1/3*c**3 = 0.
0, 2
Let p(h) be the third derivative of 2*h**7/105 + 7*h**6/15 + 4*h**5 + 52*h**4/3 + 128*h**3/3 - 59*h**2 - 2*h. Suppose p(k) = 0. What is k?
-8, -2
Let s(f) be the first derivative of -f**4/12 + 88*f**3/9 - 170*f**2/3 + 112*f - 1160. Factor s(u).
-(u - 84)*(u - 2)**2/3
Let b be 15/18*210/525. Let h(f) be the first derivative of 0*f - 30 + 1/2*f**2 - b*f**3. What is w in h(w) = 0?
0, 1
Factor 0 + 22/7*v + 1/7*v**2.
v*(v + 22)/7
Let n(l) be the third derivative of -l**6/180 - 3*l**5/10 - 181*l**3/6 - 2*l**2 + l. Let q(b) be the first derivative of n(b). Determine k so that q(k) = 0.
-18, 0
Factor 20*u**2 - 146*u - 2/3*u**3 + 380/3.
-2*(u - 19)*(u - 10)*(u - 1)/3
Let p(w) be the first derivative of -3*w**7/280 - w**6/40 + w**5/20 - 27*w**2/2 - w - 111. Let i(m) be the second derivative of p(m). Let i(k) = 0. What is k?
-2, 0, 2/3
Let u = 5167/53592 + -3/2552. Let r(j) be the 