 44
Let d(x) be the second derivative of x**4/6 - 70*x**3/3 + 1225*x**2 - 11*x. Determine q, given that d(q) = 0.
35
Let z(p) be the first derivative of -2*p**7/21 + p**6/15 + p**5/3 - p**4/3 - 173*p**2/2 - 189. Let c(j) be the second derivative of z(j). Factor c(b).
-4*b*(b - 1)*(b + 1)*(5*b - 2)
Let b = -290966/5 + 58194. Factor -b*d**2 + 2/5*d**3 + 0 + 2/5*d.
2*d*(d - 1)**2/5
Let z(i) = -i**3 + 34*i**2 - 3*i + 105. Let d be z(34). Find h, given that 3*h**4 + 13*h + 33*h**2 - 21*h**d - 25*h - 3*h = 0.
0, 1, 5
Solve 0 + 3868/5*t + 2/5*t**2 = 0 for t.
-1934, 0
Let l(k) = 14*k**2 - 1608*k - 161604. Let b(d) = -3*d**2 + 402*d + 40401. Let j(q) = -18*b(q) - 4*l(q). Factor j(y).
-2*(y + 201)**2
Let v = -87 + 90. Let t = v + 25. Factor 3*u**2 - u**2 + 12 - 7*u**2 + t*u.
-(u - 6)*(5*u + 2)
Let w(d) be the first derivative of d**6/1620 + 17*d**5/540 - 19*d**4/54 + 14*d**3 - d**2 + 142. Let k(q) be the third derivative of w(q). Factor k(g).
2*(g - 2)*(g + 19)/9
Let j be (-10)/(-20) + (-10)/((-140)/189). Let m(n) be the first derivative of j*n**2 - 16/3*n**3 + 13 + 8*n. Factor m(z).
-4*(z - 2)*(4*z + 1)
Let w(t) = -2*t**2 - 13*t - 55. Let s(z) be the second derivative of z**4/12 + 11*z**3/6 + 28*z**2 + 4*z + 3. Let f(q) = 5*s(q) + 4*w(q). Solve f(k) = 0 for k.
-4, 5
Let n(j) = -2*j**3 + 11*j**2 + 24*j - 142. Let q be n(5). What is r in 0*r**2 + 6*r + 0 - 3/2*r**q = 0?
-2, 0, 2
Suppose 2*k - 3*s = -0*k - 66, -s = -k - 31. Let h = 85 + k. Find p, given that 5*p**2 - 1 + 59*p**5 - h*p**5 + p - 2*p**3 - p**4 - 3*p**2 = 0.
-1, 1
Factor 840 + 1338*n + 131*n**2 - 118*n**2 + 4*n**3 - 2*n**3 - 11*n**3 + 98*n**2.
-3*(n - 20)*(n + 7)*(3*n + 2)
Factor -10012*s - 13*s**4 + 28*s**4 + 1551*s**2 - 2*s**4 - 114*s**3 - 10*s**4 + 18252 + 1120*s.
3*(s - 13)**2*(s - 6)**2
Let s(h) be the third derivative of 41*h**2 + 0 + 11/60*h**5 + 1/15*h**6 - 13/24*h**4 + 0*h - h**3. Factor s(c).
(c - 1)*(c + 2)*(8*c + 3)
Determine x, given that -2078/7*x**2 - 5216/7*x + 4/7*x**3 - 2088/7 = 0.
-2, -1/2, 522
Let k(u) be the first derivative of u**6/42 + 24*u**5/35 - 13*u**4/14 - 8*u**3/7 + 25*u**2/14 + 4. Determine m, given that k(m) = 0.
-25, -1, 0, 1
Let x be ((-46)/(-4))/((-4646)/(-808)). Suppose -2/7*f**3 + 0 - 4/7*f - 6/7*f**x = 0. Calculate f.
-2, -1, 0
Let c(r) = -r**2 - r - 2. Let k(b) = 2*b**3 + 248*b**2 - 926*b + 988. Let s(y) = -36*c(y) - 2*k(y). Solve s(m) = 0 for m.
-119, 2
Let n(r) be the second derivative of 1/5*r**5 + 44*r - r**2 - 1/6*r**4 - 5/6*r**3 + 2/15*r**6 + 0 + 1/42*r**7. Find i such that n(i) = 0.
-2, -1, 1
Let -128 - 4/7*b**3 - 1796/7*b - 904/7*b**2 = 0. Calculate b.
-224, -1
Let d = 1422781 - 2845551/2. Determine n, given that -25/2 + 35/2*n + 1/2*n**3 - d*n**2 = 0.
1, 5
Let i = 265 + -263. Solve -71*k**2 - 4*k - 16*k**i + 10 - 5*k - 18*k**2 - 86*k = 0.
-1, 2/21
Let d(i) be the second derivative of -i**6/120 - 3*i**5/10 - 23*i**4/48 - 4*i - 55. Factor d(y).
-y**2*(y + 1)*(y + 23)/4
Let m(i) = -136*i**2 + 433*i - 71. Let p be m(3). Factor -8/5*u**3 + 0 + 0*u + 4/5*u**2 + 4/5*u**p.
4*u**2*(u - 1)**2/5
Let r be ((-7)/(-15))/(267/126 - (-30)/140). Find t, given that -3/5*t**3 + 0 + 2/5*t - r*t**2 + 1/5*t**5 + 1/5*t**4 = 0.
-2, -1, 0, 1
Factor -1/3*z**2 + 499/3*z - 166.
-(z - 498)*(z - 1)/3
Suppose 5*m + 4*w + 18 = 0, 2*m = 4*m - 4*w - 4. Let g(s) = 3*s**2 + 4*s. Let p be g(m). Suppose -5*f**2 + 2*f**4 + 3*f**p + 7*f**4 - 7*f**4 = 0. Calculate f.
-1, 0, 1
Let v(m) be the third derivative of 0*m**3 + 3*m**2 - 5*m + 0 + 11/540*m**6 + 1/45*m**5 + 0*m**4 + 2/315*m**7 + 1/1512*m**8. Suppose v(d) = 0. What is d?
-3, -2, -1, 0
Suppose -3*j = -398 + 392. Suppose -3*k - 20 = -5*o, 4*o = k - j*k + 16. Factor -1/2*f**2 + 1/2*f**4 + k + 0*f + 0*f**3.
f**2*(f - 1)*(f + 1)/2
Let i(j) be the first derivative of 4*j**3/3 - 1760*j**2 - 7056*j - 6393. Find c, given that i(c) = 0.
-2, 882
Suppose f - 2*z + 1025 = 0, 4*z = 4 - 12. Let n = f + 1032. Factor 0 - 7/5*r**4 + 0*r + 16/5*r**2 - 1/5*r**5 - 8/5*r**n.
-r**2*(r - 1)*(r + 4)**2/5
Let a(h) be the second derivative of 2 - 72*h + 57*h**3 + 1/4*h**4 + 9747/2*h**2. Factor a(s).
3*(s + 57)**2
Suppose -5579 + 15*h**4 - 5*h**5 - 375*h**2 + 125*h**3 + 11163 - 5584 = 0. Calculate h.
-5, 0, 3, 5
Let x(o) be the first derivative of -o**4/2 + 34*o**3/3 - 80*o**2 + 200*o + 6450. Solve x(f) = 0.
2, 5, 10
Factor 0*g - 550/3*g**3 + 0 - 1/3*g**4 - 75625/3*g**2.
-g**2*(g + 275)**2/3
Let z(l) = -35*l**2 + 60*l + 95. Let y(x) = 3*x**2 - 5*x - 8. Suppose 24*a - 2 = 23*a. Let v(h) = a*z(h) + 25*y(h). Factor v(i).
5*(i - 2)*(i + 1)
Suppose -705*m - 432 = -693*m. Let l be 1/((-3*(-30)/m)/(-5)). Factor -5/7 - 3/7*n**l + 1/7*n**3 - 9/7*n.
(n - 5)*(n + 1)**2/7
Let g(q) be the second derivative of -q**5/20 - 7*q**4/12 + q**3/6 + 7*q**2/2 - 788*q. Factor g(j).
-(j - 1)*(j + 1)*(j + 7)
Let z(s) = -3*s**2 - 1. Let h(m) = -3*m**3 + 72*m**2 - 759*m + 2174. Let r(v) = h(v) - 4*z(v). Factor r(b).
-3*(b - 11)**2*(b - 6)
Let l be -2 - (-13)/(-7) - (2273 + -2282). Determine i so that 3/7*i**5 + 33/7*i + 6/7*i**4 - 6*i**2 - 36/7*i**3 + l = 0.
-4, -1, 1, 3
Let k(r) = -5*r**5 + 85*r**3 + 50*r**2 - 70*r - 65. Let o(y) = -7*y**5 + 128*y**3 + 74*y**2 - 105*y - 98. Let q(f) = -8*k(f) + 5*o(f). Solve q(l) = 0.
-2, -1, 1, 3
Suppose 119 - 11 = 6*u. Let h(j) = -39*j**2 - 1092*j - 14196. Let k(w) = -11*w**2 - 312*w - 4056. Let l(r) = u*k(r) - 5*h(r). Solve l(s) = 0 for s.
-26
Let v(b) = b**2 + b. Let f(c) = -4*c**2 - 10*c + 4. Let q(g) = -f(g) - 5*v(g). Let n be q(3). Let -4*k**3 + 41*k + k**3 - 137*k - 30*k**n - 96 = 0. Calculate k.
-4, -2
Factor 2*y**2 - 330*y + 44 + 149*y + 155*y.
2*(y - 11)*(y - 2)
Let i(s) = 4*s + 4. Let p be i(0). Solve -4*m**5 + 4*m**2 + 4*m**3 - 3*m**4 - p*m**4 + 3*m**4 = 0 for m.
-1, 0, 1
Factor -153*k**3 - 4*k**4 + 106*k + 86*k - 455*k + 116*k - 297*k**2 + k**4.
-3*k*(k + 1)**2*(k + 49)
Let -250/3 - 2/9*u**3 - 350/9*u - 50/9*u**2 = 0. Calculate u.
-15, -5
Let v(u) be the third derivative of 1/270*u**5 + 0 + 1/108*u**4 + 0*u - 5*u**2 - 2/9*u**3. Factor v(a).
2*(a - 2)*(a + 3)/9
Let q(t) be the second derivative of -t**6/30 + 5*t**5/4 - 23*t**4/12 - 25*t**3/6 + 12*t**2 + 723*t - 2. Factor q(y).
-(y - 24)*(y - 1)**2*(y + 1)
Suppose -39 - 2 = -v. Let m = -39 + v. Factor -3*r**m + 0 + 4*r**2 + 0.
r**2
Let y(s) be the third derivative of -7/15*s**6 + 201*s**2 + 0 + 2/105*s**7 + 49/15*s**5 + 0*s**3 - 6*s**4 + 0*s. Factor y(c).
4*c*(c - 9)*(c - 4)*(c - 1)
Let u(h) = 4227*h - 185985. Let k be u(44). Factor -310/11*a + 150/11 + 106/11*a**2 - 10/11*a**k.
-2*(a - 5)**2*(5*a - 3)/11
Suppose -4*p - 24 = 20. Let o(k) = k**2 + 10*k + 8. Let a be o(p). Suppose -5*d**3 - a*d**2 + 4*d**2 + 5*d**2 - 5*d = 0. What is d?
-1, 0
Factor -159*f**3 - 2*f**4 - 157*f**3 + 7*f**4 - 173*f**3 - 160*f**2 + 509*f**3.
5*f**2*(f - 4)*(f + 8)
Let l(p) = -20*p**3 + 25*p**2 + 7*p - 24. Let z(u) = 230*u - 113*u - 17*u**2 - 122*u + 7 + 14*u**3 + 9. Let v(x) = -5*l(x) - 7*z(x). Find a such that v(a) = 0.
-1, 2
Let h be 4*1 - (-7 - -55)/(-8). Find l, given that h*l**2 + 9*l**3 + 31*l**4 - 4*l**2 - 28*l**4 = 0.
-2, -1, 0
Let n(o) = 8*o**3 + 507*o**2 - 534*o - 1057. Let b(w) = -15*w**3 - 1020*w**2 + 1070*w + 2115. Let m(l) = 3*b(l) + 5*n(l). Suppose m(k) = 0. What is k?
-106, -1, 2
Let t(r) be the third derivative of -1/120*r**5 - 65*r**2 - 1/12*r**4 + 0 + 0*r + 0*r**3. Factor t(c).
-c*(c + 4)/2
Let f(g) be the third derivative of g**6/480 - 167*g**5/80 - 335*g**4/32 - 503*g**3/24 + 30*g**2 + 2*g - 2. Find k, given that f(k) = 0.
-1, 503
Let b be (-360)/(-48)*(-10)/(-15). Let a(g) be the first derivative of 22 + 100*g**2 + 215*g**4 + 77*g**b + 16*g + 760/3*g**3 + 121/12*g**6. Factor a(n).
(n + 2)**3*(11*n + 2)**2/2
Let b = -793188 + 3965941/5. Factor 0*a + 0 - 6/5*a**3 - b*a**4 - 8/5*a**2.
-a**2*(a + 2)*(a + 4)/5
Let b(p) be the second derivative of -p - 1/50*p**6 - 3/100*p**5 + 1/10*p**3 + 0*p**2 - 14 + 1/20*p**4. Find r such that b(r) = 0.
-1, 0, 1
Factor -685/3*h**2 + 5/6 + 455/2*h.
-5*(h - 1)*(274*h + 1)/6
Let h(r) = 2*r**2 - 26*r - 56. Let s be h(15). Let z(t) = -150*t + 2890. Let k(w) = w**2 + 149*w - 2891. Let y(u) = s*k(u) + 6*z(u). Factor y(a).
4*(a - 38)**2
Let k = 1048/249 - 133206/30295. Let o = -4/73 - k. Factor -o*h**2 + 0 + 0*h.
-2*h**2/15
Let v(w) be the first derivative of -w*