 + 54)**2/3
Let b(h) = 2*h**2 - 40*h - 133. Let i be b(23). Let w(q) be the second derivative of -1/4*q**4 + 27/10*q**2 - 3/100*q**i + 16*q + 0 - 3/10*q**3. Solve w(m) = 0.
-3, 1
Let h(i) = -i**2 + 25*i - 61. Let f be h(22). Suppose -b - u = -7, f*b + 21*u = 25*u + 8. Factor 1/5*x**b - 4/5*x + 0 + 3/5*x**3 + 0*x**2.
x*(x - 1)*(x + 2)**2/5
Let b(s) be the third derivative of -s**5/420 - 271*s**4/21 - 587528*s**3/21 - 813*s**2 + 1. Factor b(y).
-(y + 1084)**2/7
Let x(k) be the first derivative of -3*k**4/4 + 569*k**3 + 855*k**2 + 5152. Factor x(d).
-3*d*(d - 570)*(d + 1)
Let d(r) be the first derivative of -r**3/3 + r**2 + 35*r + 2965. Factor d(p).
-(p - 7)*(p + 5)
Let b(a) be the second derivative of -a**7/112 + 11*a**6/80 - 111*a**5/160 + 29*a**4/32 + 19*a**3/8 - 15*a**2/2 - 874*a. Find u such that b(u) = 0.
-1, 1, 2, 4, 5
Solve 181/4*c**2 - 87/4*c**3 - 93/4*c + 9/4*c**4 + 7/2 = 0 for c.
1/3, 2, 7
Factor -630*n**3 - 4*n + 1277*n**3 + 140 - 140*n**2 - 643*n**3.
4*(n - 35)*(n - 1)*(n + 1)
Suppose j + 52 = 4*i, 0 = 3*i - 5*j + 23 - 79. Find b, given that -14*b - i*b**2 + 12 + 9*b**2 + 5*b**2 = 0.
1, 6
Let d(n) be the first derivative of 5*n**3/3 - 2205*n**2 + 4405*n - 2250. What is u in d(u) = 0?
1, 881
Let t(b) be the second derivative of b**6/50 + 9*b**5/50 - b**4/5 - 12*b**3/5 + 4*b - 15. What is j in t(j) = 0?
-6, -2, 0, 2
Let q(f) be the third derivative of f**7/42 - 7*f**6/24 - 7*f**5 + 60*f**4 - 11311*f**2. What is m in q(m) = 0?
-8, 0, 3, 12
Let b(c) be the first derivative of -7*c**4 - 5048*c**3/3 - 720*c**2 - 9089. What is a in b(a) = 0?
-180, -2/7, 0
Let i(l) be the second derivative of l**7/42 + l**6/5 - l**5/20 - 17*l**4/6 - 2*l**3 + 20*l**2 + 8*l - 38. Determine p, given that i(p) = 0.
-5, -2, 1, 2
Let n be (-4)/(-11)*67352956/35464. Factor -n + 266/13*j**2 - 670*j - 2/13*j**3.
-2*(j - 67)**2*(j + 1)/13
Let i = 56608 + -169822/3. Suppose 0 + 13/3*x**3 + i*x + 5*x**2 = 0. What is x?
-1, -2/13, 0
Let x(i) be the first derivative of -68*i + 31 + 4/3*i**3 + 32*i**2. Factor x(t).
4*(t - 1)*(t + 17)
Factor 70*w**2 - 39 - 15*w**3 - 5*w**4 - 3*w**3 - 46*w**3 + 4*w**3 + 60*w - 26.
-5*(w - 1)**2*(w + 1)*(w + 13)
Let t(q) be the first derivative of -q**6/24 - 289*q**5/20 - 20735*q**4/16 + 21025*q**3/12 + 2536. Factor t(z).
-z**2*(z - 1)*(z + 145)**2/4
Let r(k) be the first derivative of -1/30*k**5 + 15*k + 0*k**2 + 0*k**3 - 15 + 1/18*k**4. Let a(l) be the first derivative of r(l). Suppose a(m) = 0. What is m?
0, 1
Let k be (-30)/(6120/442) - 64/(-24). Let h be 2/20 - 6/(-15). Factor k*a**3 - h*a**4 + 1 - 5/2*a + 3/2*a**2.
-(a - 1)**3*(a + 2)/2
Let w(m) be the first derivative of -1/16*m**4 + 5/12*m**3 + 0*m + 3/4*m**2 - 23. Suppose w(u) = 0. What is u?
-1, 0, 6
Let m(x) be the third derivative of -x**8/9240 - x**7/770 + 8*x**5/165 + 3*x**3/2 + 2*x**2 + 7. Let g(h) be the first derivative of m(h). Solve g(j) = 0.
-4, 0, 2
Let t(y) be the third derivative of y**6/270 - 9*y**5/10 + 610*y**4/9 + 3721*y**3/27 + 4445*y**2. Determine u so that t(u) = 0.
-1/2, 61
Suppose -29*n - 30 = -31*n. Factor -5*h**3 - 243*h**4 + 5*h + 3 + 248*h**4 + 3 - n*h**2 + 4.
5*(h - 2)*(h - 1)*(h + 1)**2
Let f(j) be the second derivative of -57/40*j**5 - 65/4*j**3 + j - 97 - 33/2*j**2 + 1/20*j**6 - 63/8*j**4. Determine h, given that f(h) = 0.
-1, 22
Factor 1/4*r**2 + 329/4 - 165/2*r.
(r - 329)*(r - 1)/4
Suppose 3 = -s + 3*b, 2*s = -890*b + 892*b - 2. Let 6/11*i**2 + 2/11*i**5 - 2/11*i**3 + 0*i - 6/11*i**4 + s = 0. Calculate i.
-1, 0, 1, 3
Let u(p) be the third derivative of 0 - 8/3*p**4 + 128/3*p**3 + 1/15*p**5 - 68*p**2 + 0*p. Factor u(y).
4*(y - 8)**2
Let s(d) be the second derivative of -d**5/100 - 77*d**4/20 - 4329*d**3/10 + 41067*d**2/10 + 1678*d. Suppose s(k) = 0. What is k?
-117, 3
Suppose -5*u + 5*n + 40 = 20, 4*u + n = 16. Find k, given that -6*k**3 + 269*k**2 - 130*k**2 - 3*k**u - 9 - 127*k**2 + 6*k = 0.
-3, -1, 1
Let p(k) = 7*k**2 + 77*k + 6. Let a be (-1 + -2)/(40 + -41). Let b(n) = -n**2 + n - 2. Let t(r) = a*b(r) + p(r). Solve t(j) = 0.
-20, 0
Let -f**2 - 484 + 0*f**2 - 2920*f + 2876*f = 0. Calculate f.
-22
Suppose -38*c = -24*c + 1960. Let u be (-16)/6 + c + 143. Solve 1/3*f**2 - 1/6*f**5 + 1/6*f + 0*f**3 - u*f**4 + 0 = 0 for f.
-1, 0, 1
Let f be 4*(-82)/(-144) + 30/135. Let d(x) be the first derivative of -f*x**4 + 0*x**2 + 0*x - 16 + 1/5*x**5 + 25/3*x**3. Factor d(p).
p**2*(p - 5)**2
Let n = 516 - 511. Let w(s) be the first derivative of -9/4*s**4 + 0*s**2 + 25 + 0*s**n + 0*s - 2*s**3 + 1/2*s**6. Factor w(r).
3*r**2*(r - 2)*(r + 1)**2
Let b(f) be the second derivative of f**5/105 + f**4/6 - 26*f**2 - 49*f. Let i(d) be the first derivative of b(d). Suppose i(o) = 0. What is o?
-7, 0
Let f(m) = -5*m**3 + m**2. Let u(t) = -8*t**5 - 14*t**4 - t**3 + t**2. Let x(r) = 2*f(r) - 2*u(r). Factor x(p).
4*p**3*(p + 2)*(4*p - 1)
Determine n, given that -499*n + 4609*n - 3890 - 1377*n**2 + 3*n**3 + 1154 = 0.
1, 2, 456
Suppose 0 = 1426*d - 1434*d + 24. Suppose 4*h - 10 = 2*s, 5*h - d = h - 5*s. Factor 0*n + 99*n**4 + 0 + 81/2*n**5 + 4*n**h + 38*n**3.
n**2*(n + 2)*(9*n + 2)**2/2
Let c(z) = 17*z**2 + 70 - 28*z**2 - 6*z + 2*z**3 + 19*z + 27*z**2 - 3*z**3. Let p be c(17). Factor 0 - 1/3*m - 1/6*m**p.
-m*(m + 2)/6
Let o be (-2 - -13 - (-2 - -11)) + 0 + 539/33. Factor 2/3 - o*n**2 + 1/3*n.
-(5*n - 1)*(11*n + 2)/3
Let u be 50528/192*(-8)/1218. Let z = 10/203 - u. Find o such that 110/9*o**4 - 4/3*o**3 + 50/9*o**5 - 56/9*o**2 + z*o + 0 = 0.
-2, -1, 0, 2/5
Solve 8*w**4 + 8 - 17017*w**2 + 228*w**3 + 6 - 14 + 16841*w**2 + 16*w - 76*w**5 = 0.
-2, 0, 2/19, 1
Let p(j) be the second derivative of -2601/2*j**2 + 44*j + 1 - 1/12*j**4 + 17*j**3. Find b such that p(b) = 0.
51
Let g be 5/(-8) - (-3960)/704. Let j(z) be the second derivative of 0 + 0*z**2 + 5/84*z**4 + 2/21*z**3 + 1/140*z**g - 28*z. Let j(t) = 0. What is t?
-4, -1, 0
Let n be ((49 - 0/(-4)) + 5)*-1. Let t be ((-267)/n - (11 - 6))*-16. Solve 2/3 - t*a + 2/9*a**2 = 0.
1, 3
Let l(j) be the second derivative of -1/189*j**7 + 0*j**3 + 0 + 25/54*j**4 - 1/6*j**5 - 139*j + 0*j**2 - 1/15*j**6. Solve l(k) = 0.
-5, 0, 1
Let l be 15/(-2)*(28 + -50). Let n be (-11)/(l/(-18)) - (0 + 1). Solve -1/5*s**4 + 0*s**2 + 0 - n*s**3 + 0*s = 0 for s.
-1, 0
Suppose 4*r = -3*v + 264, -r + 5*v + 36 = -7. Factor 24*u**2 - r*u**2 + 17*u**2 + 18*u**2 - 64 - 32*u.
-4*(u + 4)**2
Suppose 2 = 13*g - 24. Suppose -19*z**2 + 128*z - 38*z - 405 + 14*z**g = 0. Calculate z.
9
Let r(w) = -w**4 + 17*w**3 - 67*w**2 - 229*w. Let n(l) = -3*l**4 + 36*l**3 - 132*l**2 - 459*l. Let k(b) = 4*n(b) - 9*r(b). Factor k(a).
-3*a*(a - 5)*(a + 3)*(a + 5)
Let w = -3573 - -3577. Let y(r) be the first derivative of -r**2 + 7 + 14/9*r**3 + 1/2*r**w - 2/3*r**5 - 4/3*r. Suppose y(i) = 0. Calculate i.
-1, -2/5, 1
Let g be ((-112)/49)/(-9 + 7). Let z be -12*((-56)/(-140) + (-47)/105). Factor -z - g*h - 4/7*h**2.
-4*(h + 1)**2/7
Let s(x) be the second derivative of x**6/70 - 9*x**5/20 - 157*x**4/28 - 135*x**3/14 + 3434*x. Factor s(m).
3*m*(m - 27)*(m + 1)*(m + 5)/7
Let o(c) be the first derivative of 1/3*c**2 - 2/3*c + 40 - 1/24*c**4 + 1/18*c**3. Let o(w) = 0. What is w?
-2, 1, 2
Let c be 210/135*(-24)/(-14)*(-47 - -51). What is m in 6*m + 1/3*m**2 + c = 0?
-16, -2
Let o(h) be the second derivative of -1/240*h**5 - 1/96*h**4 + 8*h + 0 + 0*h**3 - 2*h**2. Let d(v) be the first derivative of o(v). Factor d(p).
-p*(p + 1)/4
Let l = 361 - 341. Suppose -153 + 113 = -l*p. Factor -1/3*s**3 - p*s**2 - 3*s + 0.
-s*(s + 3)**2/3
Let f be 1*-7*4/(-12). Let b be ((-760)/(-15))/19 + 36/(-54). What is k in -11/3*k - 13/3*k**4 + f*k**3 + 4/3*k**5 + 2/3 + 11/3*k**b = 0?
-1, 1/4, 1, 2
Let l(d) = -d**2 - 21*d + 62. Let c be l(-23). Factor 2*z**3 + 6*z**2 - 2*z - 26 + 4 + c.
2*(z - 1)*(z + 1)*(z + 3)
Let b(n) be the second derivative of -n**7/18900 - n**6/1800 + n**5/225 - 31*n**4/6 - 60*n. Let x(t) be the third derivative of b(t). Solve x(a) = 0 for a.
-4, 1
Suppose o - 3*h - 8 = -9, -o = -h - 3. Suppose -13*m + 11*m = f, 0 = -4*f - o*m + 3. Factor 4/3*s**f - 16/3 - 2/3*s**3 + 8/3*s.
-2*(s - 2)**2*(s + 2)/3
Suppose 5*w - 2*p = p - 15, -4*p - 15 = 5*w. Let r be 3 - w/(12/8). Factor 4*x**2 + r*x**2 - 15*x**3 - 20 + 18*x**2 + 20*x - 2*x**2.
-5*(x - 2)*(x + 1)*(3*x - 2)
Let -46/3*w**2 - 1/3*w**3 - 120 - 83*w