256951/42. Let f(p) be the third derivative of -1/28*p**4 + 0*p - 12*p**2 + 0 - 1/420*p**5 - k*p**3. Determine z, given that f(z) = 0.
-5, -1
Suppose 1860*o = 1774*o. Let n(x) be the second derivative of -x**3 + 0 + o*x**2 + x + 1/12*x**4 + 1/20*x**5. Suppose n(a) = 0. Calculate a.
-3, 0, 2
Suppose 4*c - o = -5*o - 16, 4*c = -o - 19. Let w be c + 7 - 0/2. What is i in 2/17*i + 0 + 0*i**w - 32/17*i**3 = 0?
-1/4, 0, 1/4
Let b(u) = u**2 + u - 1. Suppose 36 = 400*v - 398*v. Let c(g) = 10*g**2 + 6*g - 7. Let q(z) = v*b(z) - 2*c(z). Factor q(l).
-2*(l - 2)*(l - 1)
Find c such that 0*c**2 + 0*c + 5/3*c**3 + 5/6*c**4 + 0 = 0.
-2, 0
Determine m so that 1/8*m**2 - 111/8*m - 171/4 = 0.
-3, 114
Let h(y) be the third derivative of -y**6/420 - 23*y**5/210 + 7*y**4/12 - 25*y**3/21 + 620*y**2 + 1. Factor h(b).
-2*(b - 1)**2*(b + 25)/7
Let l(y) be the first derivative of -1/5*y + 2/15*y**3 + 0*y**2 - 39 - 1/25*y**5 + 0*y**4. Let l(i) = 0. What is i?
-1, 1
Let j(r) be the first derivative of r**5/180 - 7*r**4/72 + 5*r**3/9 + 81*r**2 + 51. Let c(z) be the second derivative of j(z). Factor c(a).
(a - 5)*(a - 2)/3
Let n(r) be the third derivative of -r**8/1344 + 13*r**7/140 - 723*r**6/160 + 207*r**5/2 - 1026*r**4 + 5184*r**3 + 709*r**2. Let n(i) = 0. What is i?
3, 24
Factor -292/5*i - 4/5*i**3 - 296/5*i**2 + 0.
-4*i*(i + 1)*(i + 73)/5
Let h(j) be the first derivative of 0*j + 1/27*j**4 + 1/9*j**3 - 17/2*j**2 - 18 + 1/270*j**5. Let x(o) be the second derivative of h(o). Factor x(v).
2*(v + 1)*(v + 3)/9
Factor -34961 + 28*k**3 - 552*k**2 + 32785 + 0*k**4 + 2048*k + 4*k**4.
4*(k - 4)**2*(k - 2)*(k + 17)
Suppose a = 3*k - 5, 5*k = 3*a + 27 - 24. Let -3*y**2 + 5*y**4 - 2*y**2 + 332*y**k - 322*y**3 - 10*y = 0. What is y?
-2, -1, 0, 1
Let n be (207/6)/((-12)/16). Let f = n - -49. Factor 2*g**2 - g**2 + 14*g**3 - 9*g**f.
g**2*(5*g + 1)
Let z be ((-100)/144 - ((-1800)/(-160))/(-45))*27/(-42). Factor -z*c**2 - 6/7*c - 4/7.
-2*(c + 1)*(c + 2)/7
Let r(z) = -2*z**3 - 11*z**2 + 5*z + 16. Let b be r(-6). Factor 378 + 88*k + 84 + b + 4*k**2.
4*(k + 11)**2
Let i(t) = 189*t**2 - 103*t - 64. Let l(h) be the second derivative of 19*h**4/6 - 7*h**3/2 - 13*h**2/2 + 10*h + 1. Let x(f) = -2*i(f) + 11*l(f). Factor x(q).
5*(q - 1)*(8*q + 3)
Let i(y) be the first derivative of -2*y**2 - 207 + 0*y + 22/3*y**3 - 2*y**4 - 2*y**5. Determine x so that i(x) = 0.
-2, 0, 1/5, 1
Let o = 3413/108 + -752/27. Let i(d) be the first derivative of -20*d + o*d**4 - 15/2*d**2 - d**5 + 37 + 25/3*d**3. Let i(b) = 0. Calculate b.
-1, 1, 4
Let p = -1/1535 + 1538/4605. Let j(a) be the first derivative of -a**2 + p*a**3 + a - 11. Factor j(b).
(b - 1)**2
Let y = 270225 + -270223. Find i, given that 27/2*i**y - 12 - 51*i = 0.
-2/9, 4
Find r such that -56792*r**2 + 6*r + 56697*r**2 + 95*r**4 + 120*r**5 - 315*r**5 + 185*r**3 + 4*r = 0.
-1, 0, 2/13, 1/3, 1
Let n be 15/39 - (-5)/(-15). Let o(f) be the second derivative of -6*f + 0 - n*f**3 + 3/13*f**2 - 1/78*f**4. What is p in o(p) = 0?
-3, 1
Let u(y) = 23*y**2 - 88*y + 20. Let g(s) = s**2 + s - 2. Let m(j) = -j**3 - 35*j**2 - 34*j + 1. Let a be m(-34). Let q(o) = a*u(o) - 2*g(o). Factor q(t).
3*(t - 4)*(7*t - 2)
Suppose -129 - 53 = -150*j + 59*j. Let r(l) be the first derivative of 0*l**3 + 0*l - 2/7*l**j + 1/7*l**4 - 23. Factor r(q).
4*q*(q - 1)*(q + 1)/7
Let x be ((-64)/(-8) + -7)/(1*25/625). Determine f so that -10/3*f - 5/3*f**2 + x = 0.
-5, 3
Suppose -142 = -5*j - 112. Factor 6*i - 15*i**3 + j*i + 7*i**3 - i**3 + 3*i**2.
-3*i*(i + 1)*(3*i - 4)
Determine i so that 2/15*i**2 - 22 - 104/15*i = 0.
-3, 55
Determine r, given that 70795720069*r + 28400*r**3 + 13743582043132 - 13529960069*r + 6585762756868 + 60492000*r**2 + 5*r**4 = 0.
-1420
Let j be (-9)/15*(-345)/483. Let k(w) be the first derivative of 1/21*w**3 + 14 + 1/7*w**2 - j*w. Factor k(r).
(r - 1)*(r + 3)/7
Let p(s) be the third derivative of 0 + 5/336*s**8 - 1/12*s**6 + 0*s**5 + 0*s**7 + 0*s**3 + 5/24*s**4 - 9*s**2 - 8*s. Let p(v) = 0. Calculate v.
-1, 0, 1
Let g(b) be the second derivative of b**7/21 - 2*b**6/15 - 7*b**5/2 + 12*b**4 - 12*b**3 + 197*b - 1. Determine r so that g(r) = 0.
-6, 0, 1, 6
Let z(w) be the first derivative of w**3/9 - 487*w**2/6 + 162*w - 2931. Factor z(f).
(f - 486)*(f - 1)/3
Let c(d) be the third derivative of -d**7/210 + 191*d**6/480 + 287*d**5/80 + 593*d**4/48 + 65*d**3/3 - 337*d**2 + 2. Suppose c(q) = 0. What is q?
-2, -5/4, -1, 52
Let s = -606 + 605. Let i be (2/(-3))/s*63/14. Let 15/8*a**4 - 3*a - 39/4*a**2 + 0 - 39/8*a**i = 0. What is a?
-1, -2/5, 0, 4
Let y(r) be the first derivative of 2/11*r**2 + 0*r**4 + 0*r - 71 - 2/55*r**5 + 2/11*r**3. Solve y(d) = 0.
-1, 0, 2
Let g(b) = b**3 - 183*b**2 - 538*b - 465. Let f(i) = -2*i**3 + 220*i**2 + 538*i + 464. Let y(t) = 3*f(t) + 4*g(t). Factor y(p).
-2*(p + 1)*(p + 9)*(p + 26)
Let f = -352 + 358. Let g(m) = m**4 + 8*m**3 - 11*m**2. Let j(z) = -2*z**4 - 15*z**3 + 21*z**2 + z. Let i(a) = f*j(a) + 11*g(a). Factor i(w).
-w*(w - 2)*(w + 1)*(w + 3)
Let m be (-14)/(-21)*(-4)/((-8)/6). Let s be (-2 - 5/m)/(60/(-40)). Factor 0 - 2/13*x**2 + 2/13*x**4 - 2/13*x**s + 0*x + 2/13*x**5.
2*x**2*(x - 1)*(x + 1)**2/13
Let c(h) be the second derivative of -h**6/280 + 3*h**5/70 + h**4/56 - 3*h**3/7 - 10*h**2 + 7*h - 3. Let b(f) be the first derivative of c(f). Factor b(m).
-3*(m - 6)*(m - 1)*(m + 1)/7
Let w(m) be the second derivative of m**4/6 - 3404*m**3/3 + 2896804*m**2 - 87*m - 3. Factor w(q).
2*(q - 1702)**2
Let d(o) be the third derivative of o**6/180 - o**5/12 - 28*o**3/3 + 2*o**2 + 16. Let r(s) be the first derivative of d(s). Suppose r(c) = 0. Calculate c.
0, 5
Let b = 318 - -440. Let h = 1517/2 - b. Factor 3/2*j + 1/2 + h*j**3 + 3/2*j**2.
(j + 1)**3/2
Let x(c) be the third derivative of c**6/540 + c**5/18 + 23*c**3/2 + 90*c**2. Let s(f) be the first derivative of x(f). Find u such that s(u) = 0.
-10, 0
Let d be 1 - (4/2)/(-2). Suppose -3*f = -0 - 9. Find y such that 2*y**f - 8 - 4*y + 3*y - 7*y + d*y**2 = 0.
-2, -1, 2
Let k = 2/1503185 + 58624211/3006370. Solve -3/2*u**5 + 18 + 12*u - 9/2*u**3 + 15/2*u**4 - k*u**2 = 0 for u.
-1, 2, 3
Factor 2/7*h**2 - 1336*h + 1561784.
2*(h - 2338)**2/7
Let u(h) be the first derivative of h**8/2940 - 3*h**7/490 - 2*h**3 - 2*h**2 + 21. Let a(x) be the third derivative of u(x). Factor a(p).
4*p**3*(p - 9)/7
Let j(t) = 4*t**2 + 62*t + 87. Suppose -35*c - 70*c - 1470 = 0. Let s be j(c). Factor -13/3*h + 16/3*h**2 - 2 + h**s.
(h - 1)*(h + 6)*(3*h + 1)/3
Find k such that 3/4*k**5 - 2625/4*k**2 + 45/4*k**4 + 15/4*k**3 - 4116 - 6615/2*k = 0.
-7, -2, 8
Let p(c) be the second derivative of c**5/120 - 13*c**4/72 + 55*c**3/36 - 25*c**2/4 + 532*c. Factor p(y).
(y - 5)**2*(y - 3)/6
Suppose -98*g + 6 = -95*g. Let r be g/3*(9 - 17/2). Determine p, given that -r*p**3 + 3 + 17/3*p + 7/3*p**2 = 0.
-1, 9
Let y be (6 + -3)*((-1840)/12 - 8). Let w be (-5)/(-4) - y/(-528). Factor 2/3*t - w*t**2 + 1.
-(t - 3)*(t + 1)/3
Let j(g) = -g**3 - 28*g**2 + 60*g - 5. Let z be j(-30). Let o(c) = -5*c**2 - 29*c - 15. Let q be o(z). Factor -1/2*n**2 - 25/2 + q*n.
-(n - 5)**2/2
Let m be (-117)/(-27) - (-427)/(-183). Factor 0 - 16/3*u + 22/3*u**m - 7/3*u**3.
-u*(u - 2)*(7*u - 8)/3
Let f be 22 - (3612/(-210) - -38). Factor f*t - 2/5*t**2 + 4.
-2*(t - 5)*(t + 2)/5
Suppose -42*q = 35*q + 79*q - 468. Factor 0*o + 16/3*o**4 + 0 + 2/3*o**5 + 0*o**2 + 32/3*o**q.
2*o**3*(o + 4)**2/3
Suppose -21*q + 99 = 12*q. Suppose 0 = -5*f + 5*m - 5, 10*f - m = 12*f - 7. Factor -l**f + 0 - 1/2*l**q - 1/2*l.
-l*(l + 1)**2/2
Factor 20*k - 100*k + 5*k**2 + 29580 - 31260.
5*(k - 28)*(k + 12)
Let b(p) = -2*p**2 + p + 24. Let j(t) = -18*t**2 + 400*t + 586. Let l(g) = -8*b(g) + j(g). Solve l(a) = 0 for a.
-1, 197
Suppose 3*n + 2*z - 23 - 11 = 0, 0 = -2*n - z + 23. Suppose d - 7*d = -n. Find q such that 4*q**2 - 125 - 6*q**2 - 50*q - 3*q**d + 0*q**2 = 0.
-5
Factor -371/2*r**2 + 369/2*r**3 - 1/2*r**5 + 62*r + 0 - 121/2*r**4.
-r*(r - 1)**3*(r + 124)/2
Suppose -62*w + 245 - 121 = 0. Determine t, given that -1/2*t**w + 0*t - 1/4*t**3 + 0 + 1/4*t**4 = 0.
-1, 0, 2
Factor 208/19 - 2/19*g**2 - 206/19*g.
-2*(g - 1)*(g + 104)/19
Determine w, given that -6304/3 + 2/3*w**3 + 3184/3*w - 410/3*w**2 = 0.
4, 197
Let m(i) be the first derivative of -3*i**7/560 + 119*i**6/240 + i**5/2 + 14*i*