Let k = 29 + -4. Suppose -13 - k*p + 5*p**2 - 38 + 1 + 70*p = 0. Calculate p.
-10, 1
Let d(j) be the first derivative of j**3/6 - 12*j**2 - 50*j - 1254. Factor d(g).
(g - 50)*(g + 2)/2
Let s be (57/9)/(5 + (-14)/3). Find r such that -7*r**5 + 2*r**4 - 3*r - s*r**4 + 10*r**3 + 7*r**4 + 4*r**2 + 6*r**4 = 0.
-1, 0, 3/7, 1
Suppose 18*n - 18/11*n**3 + 276/11*n**2 - 96/11 = 0. What is n?
-1, 1/3, 16
Let n(u) be the second derivative of 3*u**5/40 + 77*u**4/8 + 364*u**3 + 1035*u**2 - 9740*u. Let n(k) = 0. Calculate k.
-46, -30, -1
Factor -118*f**2 + 4261 + f**5 - 4261 - f**3 + 171*f**4 - 53*f**4.
f**2*(f - 1)*(f + 1)*(f + 118)
Let q(f) = 2*f**4 + 27*f**2 + 122*f + 63. Let a(w) = w**4 - 13*w**2 - 2*w. Let p(r) = 15*a(r) - 5*q(r). Factor p(j).
5*(j - 9)*(j + 1)**2*(j + 7)
Let w = 13314 - 13282. Let z(u) be the first derivative of 24/11*u - 30/11*u**3 + w - 6/11*u**4 - 36/11*u**2. Let z(l) = 0. Calculate l.
-2, 1/4
Suppose 379*k + 167*k + 27*k**3 - 72*k**2 - 24*k**3 - 162*k = 0. What is k?
0, 8, 16
Let h(l) be the first derivative of -l**5/5 - 2*l**4/3 + 22*l**3/3 + 24*l**2 - 92*l - 39. Let o(d) be the first derivative of h(d). Let o(w) = 0. What is w?
-4, -1, 3
Let v(b) be the third derivative of -b**5/30 - b**4/2 - 5*b**3/3 - 1486*b**2. Factor v(l).
-2*(l + 1)*(l + 5)
Let h(m) be the first derivative of -m**4/24 + 125*m**3/9 - 5875. What is d in h(d) = 0?
0, 250
Suppose -10*l - 130 = -90. Let z be ((-96)/(-420))/(((-24)/21)/l). Factor 4/5*i**2 - 2/5*i - z + 2/5*i**3.
2*(i - 1)*(i + 1)*(i + 2)/5
Let b(r) be the first derivative of -3/8*r**4 + 32 - 1/2*r**3 + 1/4*r**6 + 0*r + 3/10*r**5 + 0*r**2. Factor b(w).
3*w**2*(w - 1)*(w + 1)**2/2
Let x(i) be the first derivative of 7/12*i**3 - 2*i**2 + i - 24. Factor x(w).
(w - 2)*(7*w - 2)/4
Let c = 4129 + -4126. Let s(f) be the third derivative of 0*f**c + 12*f**2 + 0 + 1/420*f**7 + 0*f + 1/1344*f**8 - 1/120*f**5 - 1/480*f**6 + 0*f**4. Factor s(k).
k**2*(k - 1)*(k + 1)*(k + 2)/4
Factor 23*u - 20*u - 115*u + 172*u - 770 + u**2 + 7*u.
(u - 10)*(u + 77)
Suppose -10*o + 12*o = -3*h + 23, 4*h + 46 = 5*o. Suppose -o*f + 44 = 14. Factor 14/19*q**f + 4/19*q**4 + 0*q + 0 - 2/19*q**5 + 8/19*q**2.
-2*q**2*(q - 4)*(q + 1)**2/19
Let -2/3*l**4 + 188*l**3 - 566/3 + 568/3*l**2 - 188*l = 0. What is l?
-1, 1, 283
Let l(c) be the second derivative of c**5/30 + c**4/6 + c**2/2 + 19*c. Let k(b) be the first derivative of l(b). Find n such that k(n) = 0.
-2, 0
Let t be (9 - (-1441)/(-165))/(4*2/72). Let f be (-9)/(-9) + 2/(-5). Solve 12/5 + f*p**2 - t*p = 0.
2
Let f = -37817/5060 + 172/23. Let k(a) be the third derivative of 0 - 8/11*a**3 + f*a**6 - 1/55*a**5 - 11*a**2 + 0*a + 1/1155*a**7 - 7/33*a**4. Factor k(n).
2*(n - 3)*(n + 2)**3/11
Let z(r) = -6*r**3 - 77*r**2 + 239*r - 131. Let u(y) = -114*y**3 - 1462*y**2 + 4538*y - 2490. Let n(k) = 6*u(k) - 116*z(k). Factor n(t).
4*(t - 2)*(t + 16)*(3*t - 2)
Let u(w) be the third derivative of -1/660*w**5 + 42*w**2 + 0*w + 0*w**4 + 0 + 1/1980*w**6 - 17/6*w**3. Let g(i) be the first derivative of u(i). Factor g(s).
2*s*(s - 1)/11
Suppose 2*k = -0*k + 7*k. Suppose k = 5*d + 4*a + 10, 3*a + 1 = 3*d + 4*a. Find p, given that -32*p**2 + 28*p**d + 3*p**3 - 4*p**3 = 0.
-4, 0
Let w(p) = -16*p - 98. Let i be w(-7). Factor -8 - 3*a - 2*a**4 - 30*a**2 - 17*a - i*a**3 - 6*a.
-2*(a + 1)**3*(a + 4)
Let -246*v**3 - 5*v**4 - 97*v**3 + 498*v**3 + 5*v**2 - 155*v = 0. Calculate v.
-1, 0, 1, 31
Suppose -5/2*v**5 - 325/4*v**3 - 55/2 + 235/4*v**4 + 335/4*v - 125/4*v**2 = 0. What is v?
-1, 1/2, 1, 22
Let g be (-420)/8*(-552)/80. Let l = -361 + g. Find f, given that -5*f + 5/2*f**3 + l*f**4 - 15/4*f**2 + 5 = 0.
-2, 1
Let g(p) = 28*p**2 + 63*p + 2. Let a = 313 - 316. Let y(b) = 28*b**2 + 62*b + 4. Let v(c) = a*y(c) + 2*g(c). Factor v(d).
-4*(d + 2)*(7*d + 1)
Let f(k) be the first derivative of k**6/48 - k**4/32 - 5468. Factor f(v).
v**3*(v - 1)*(v + 1)/8
Factor -41*q - 5272 + 2368*q - 118*q - 4*q**2 + 435*q.
-4*(q - 659)*(q - 2)
Suppose -15*x - 75 = -20*x. Factor 455*y**2 - x*y**3 + 41 - 585*y + 86 + 18.
-5*(y - 29)*(y - 1)*(3*y - 1)
Let s(k) = 1365*k + 4098. Let o be s(-3). Let w(t) be the first derivative of -16/5*t**2 + 4/15*t**o + 64/5*t + 28. Factor w(g).
4*(g - 4)**2/5
Let q be 117/(65/5) - 1. Let t(i) be the first derivative of -7 + 48*i**2 - q*i**3 - 128*i + 1/2*i**4. Find c, given that t(c) = 0.
4
Solve 43*x - 46*x + 483 - 519 + 51*x**2 - 12*x**3 = 0 for x.
-3/4, 1, 4
Let i(o) be the first derivative of o**4/6 + 8*o**3 + 144*o**2 + 48*o + 6. Let r(n) be the first derivative of i(n). Determine x, given that r(x) = 0.
-12
Let p(s) be the third derivative of -7*s + 5/42*s**4 - 1/15*s**5 - 5*s**2 - 2/21*s**3 + 1/70*s**6 + 0. Factor p(h).
4*(h - 1)**2*(3*h - 1)/7
Let c(i) be the first derivative of -i**4/4 - 4*i**3 + 30*i**2 - 114*i - 25. Let h(f) be the first derivative of c(f). What is n in h(n) = 0?
-10, 2
Let t(u) be the third derivative of u**6/240 - 149*u**5/40 + 22201*u**4/16 - 3307949*u**3/12 + 141*u**2. Find y such that t(y) = 0.
149
Let s(o) be the second derivative of o**7/210 - o**6/20 + 3*o**5/20 - o**4/6 - 39*o**2/2 + o. Let x(g) be the first derivative of s(g). Solve x(z) = 0 for z.
0, 1, 4
Let h(r) be the second derivative of 5/2*r**3 + r**2 - 1/240*r**6 + 5/8*r**4 - 23*r + 0 - 9/80*r**5. Let c(x) be the second derivative of h(x). Factor c(d).
-3*(d - 1)*(d + 10)/2
Let c(t) = 6*t**2 - 60*t. Let d be c(10). Suppose -6 = -3*b + 2*i + 11, b + 3*i + 9 = d. Factor 2/9*p**5 - 2/9 - 2/3*p + 2/3*p**4 - 4/9*p**2 + 4/9*p**b.
2*(p - 1)*(p + 1)**4/9
Suppose 43*h - 8 = 39*h. Determine v so that 6*v**2 - 19*v**h - 13*v - 3*v**4 + v + 4*v**4 = 0.
-3, -1, 0, 4
Let o = -615 - -681. Solve -o*l**2 + 95 + 19*l**2 + 32*l**2 + 280*l = 0 for l.
-1/3, 19
Let m be (-3)/(-8) + (53802/784)/(-183). Let 32/3*i**2 + 0*i - 44/3*i**3 + 10/3*i**4 + 2/3*i**5 + m = 0. What is i?
-8, 0, 1, 2
Let w be (12/10*-1)/((-20)/(-50)). Let q be 2*-3*w/(-24)*-1. Factor -3/2 + q*h**2 - 3/4*h.
3*(h - 2)*(h + 1)/4
Let m(q) be the first derivative of q**4/2 + 784*q**3/3 - q**2 - 784*q - 2083. Suppose m(r) = 0. What is r?
-392, -1, 1
Let s be (1/(-16))/((-341)/20460)*32/72. Determine b so that 0 + 1/3*b**2 - s*b = 0.
0, 5
Let y(u) be the second derivative of u**10/6048 - u**8/448 - u**7/252 + 29*u**4/4 - 56*u. Let n(z) be the third derivative of y(z). Solve n(q) = 0 for q.
-1, 0, 2
Suppose -128*k + 71 = -24*k - 137. Factor 24/11 + 2/11*d**k + 14/11*d.
2*(d + 3)*(d + 4)/11
Let a(s) be the first derivative of -s**3/12 + 7*s**2/2 - 40*s - 1570. Factor a(t).
-(t - 20)*(t - 8)/4
Let y(n) = -23*n**2 - 306*n + 278. Let p(o) = 39*o**2 + 603*o - 557. Let t(c) = -6*p(c) - 10*y(c). Solve t(f) = 0 for f.
-281/2, 1
Factor 1150*s + 5/4*s**2 - 2305.
5*(s - 2)*(s + 922)/4
Let i(u) be the second derivative of u**7/126 + u**6/15 + u**5/12 - 4*u**4/9 - 2*u**3/3 + 8*u**2/3 - 1114*u. What is p in i(p) = 0?
-4, -2, 1
Suppose 3*j - 1 = 131. Factor 39*v**3 + 38*v**3 - 76*v**3 - 7*v**2 - 40*v - j.
(v - 11)*(v + 2)**2
Suppose -3430/3*n**2 + 2/3 + 973/3*n = 0. What is n?
-1/490, 2/7
Let y(a) be the first derivative of -8/5*a + 12/25*a**5 - 19/10*a**4 - 13 + 4/5*a**2 + 26/15*a**3. Suppose y(j) = 0. What is j?
-1/2, 2/3, 1, 2
Let a(u) be the third derivative of 0*u - 1/510*u**5 - 2/51*u**4 + 0*u**3 - 59*u**2 + 0. Factor a(w).
-2*w*(w + 8)/17
Let r(p) be the second derivative of p**4/6 + 577*p**3/7 + 494*p**2/7 + 249*p + 2. Factor r(f).
2*(f + 247)*(7*f + 2)/7
Let t = 65/51 + -16/17. What is o in -1/3*o + 0 + 1/3*o**4 + 1/3*o**3 - t*o**2 = 0?
-1, 0, 1
Factor -49/5*q**3 + 763/5*q**2 + 12 - 424/5*q.
-(q - 15)*(7*q - 2)**2/5
Let i(k) be the first derivative of 23*k**3/3 - 108*k**2 - 2416*k - 62. Let l(v) = 62*v**2 - 649*v - 7249. Let b(d) = 11*i(d) - 4*l(d). Factor b(p).
5*(p + 22)**2
Suppose -158 = 5*q + 24*f, -46*q = -49*q + 5*f + 41. Solve -14/11 + 58/11*j - 50/11*j**q + 6/11*j**3 = 0 for j.
1/3, 1, 7
Suppose -2*w - 5*u = 22, -12*w = -11*w + 2*u + 8. Let l(x) be the second derivative of 2*x**2 - x + 0 + 1/2*x**3 + 1/24*x**w. Suppose l(j) = 0. What is j?
-4, -2
Let x(y) be the second derivative of 0 + 0*y**2 - 64/45*y**3 - 101*y - 1/150*y**5 - 8/45*y**4. Factor x(r).
-2*r*(r + 8)**2/15
Let f(v) be the second derivative of -v**5/4 + 40*v**4/3 - 50*v**3 - 5096*v. Factor f(j).