b + 4)
Factor -327265120*s - 626971072 - 2/7*s**5 - 57200*s**3 - 1460/7*s**4 - 7003360*s**2.
-2*(s + 2)*(s + 182)**4/7
Let w(k) be the second derivative of -k**4/36 - 161*k**3/9 - 2457*k. Suppose w(o) = 0. What is o?
-322, 0
Let c(b) be the third derivative of -b**8/20160 - b**7/1008 + b**6/120 + 7*b**5/30 + 6*b**2 - 2. Let p(s) be the third derivative of c(s). Factor p(o).
-(o - 1)*(o + 6)
Let n(s) be the second derivative of 33 + 1/114*s**4 + 7/19*s**2 + 8/57*s**3 - 4*s. Factor n(v).
2*(v + 1)*(v + 7)/19
Let m(g) be the first derivative of 0*g + 199 + 1/12*g**4 + 0*g**2 - 7/9*g**3. Solve m(x) = 0.
0, 7
Let r(p) be the third derivative of -p**6/24 + 17*p**5/6 - 55*p**4/6 - 12100*p**3/3 - 1441*p**2. Find q, given that r(q) = 0.
-10, 22
Let j(c) be the third derivative of -28/3*c**3 + 0*c + 0 + 60*c**2 - 1/15*c**5 + 3/2*c**4. Find r, given that j(r) = 0.
2, 7
Factor -14*j**2 + 17/2*j - 4*j**4 + 1/2*j**5 + 11*j**3 - 2.
(j - 4)*(j - 1)**4/2
Let g(l) be the third derivative of -l**6/540 - l**5/270 + 25*l**4/108 + 25*l**3/27 + 728*l**2. Factor g(r).
-2*(r - 5)*(r + 1)*(r + 5)/9
Suppose -1730*v - 2253 = -2481*v. Suppose 1/2*r**2 - 65/2*r - 225/2 + 1/2*r**v = 0. Calculate r.
-5, 9
Let n be 225/189 - 168/196. Let r(z) be the first derivative of -n*z**3 - 36*z - 3 + 6*z**2. Suppose r(g) = 0. What is g?
6
Let z = 20 - 12. Suppose 0 = 6*m - 5*m - 5. Factor -10*v - z*v + m*v**2 + 8*v.
5*v*(v - 2)
Let b be 1 + (3 - 12*-1). Factor 32 + 4*d - 13*d**2 - 23*d**2 - b*d**2 - 4*d**3 + 20*d**2.
-4*(d - 1)*(d + 1)*(d + 8)
Factor -45592*g - 2*g**2 + g**2 + 45784*g + 4*g**2 + 3072.
3*(g + 32)**2
Let r(k) be the first derivative of 1/6*k**6 + 6/5*k**5 + 0*k + 10/3*k**3 + 3*k**4 + 3/2*k**2 - 70. Suppose r(z) = 0. What is z?
-3, -1, 0
Let a be (-77)/70 - 2/(-20). Let r be (19/95)/(2 + a). Factor 0*b**2 - r + 1/10*b**3 - 3/10*b.
(b - 2)*(b + 1)**2/10
Let m = -7/7864 + 15805/86504. Let -m*s**2 + 34/11 + 32/11*s = 0. Calculate s.
-1, 17
Let a(w) be the first derivative of 125*w**6/6 - 105*w**5 - 115*w**4/2 + 1100*w**3/3 + 420*w**2 + 160*w - 35. Let a(n) = 0. What is n?
-1, -2/5, 2, 4
Determine t so that -417316*t + 269586136/3 + 646*t**2 - 1/3*t**3 = 0.
646
Let j(b) = b**2 - 4*b + 3. Let h be j(3). Let f = 2291 + -2287. Factor 15*i - 31*i + 12*i**3 + h*i - 4*i**f.
-4*i*(i - 2)**2*(i + 1)
Let h = 1529 + -1520. Let o be -5 - -11 - (h + (0 - 7)). Factor 0 - 17/4*k**3 + 5*k**2 + k**o - k.
k*(k - 2)**2*(4*k - 1)/4
Let b(x) = -x**2 + 28*x - 49. Let z be b(2). Let s(g) be the first derivative of 0*g**2 + 10 + 0*g + 1/3*g**6 - 1/3*g**z - 1/2*g**4 + 1/5*g**5. Factor s(w).
w**2*(w - 1)*(w + 1)*(2*w + 1)
Let q(k) = 1747*k + 26205. Let a be q(-15). Factor a - 16/7*h + 2/7*h**2.
2*h*(h - 8)/7
Let v be (4/(-8))/(3/(-12)). Suppose 105 = -v*m + 37*m. Factor -2/15*b**2 + 0*b - 4/15*b**m - 2/15*b**4 + 0.
-2*b**2*(b + 1)**2/15
Let i(o) be the second derivative of o**6/300 + o**5/150 - o**4/30 + 60*o**2 - o - 25. Let v(q) be the first derivative of i(q). Solve v(k) = 0.
-2, 0, 1
Suppose q = 2*c + 8, q - 22 = 1779*c - 1784*c. Factor 5/3*a**3 + 0 - 4/3*a + 8/3*a**c.
a*(a + 2)*(5*a - 2)/3
Suppose 2/15*j**3 + 266/5 + 794/15*j**2 - 1594/15*j = 0. What is j?
-399, 1
Suppose -21*j = -23*j + 46. Determine a, given that 14*a - 3*a**3 - j*a + 7*a + 5*a**3 = 0.
-1, 0, 1
Suppose 377 = -0*d + 29*d. Let w be (-8)/(-18) + d/(-39). Solve -2/9*l + 1/9 + w*l**2 = 0 for l.
1
Suppose 0 = -2*h - 3 - 5. Let u be 2*(-3 + (-18)/h). What is v in -u - 10*v**4 - 9*v**4 + 28*v**4 + 6*v**2 - 12*v**4 = 0?
-1, 1
Factor 3/7*l**3 + 18/7*l**2 - 57/7*l - 36.
3*(l - 4)*(l + 3)*(l + 7)/7
Let l(h) be the first derivative of 2*h**5/5 - 46*h**4 + 60*h**3 + 92*h**2 - 182*h - 1364. Factor l(r).
2*(r - 91)*(r - 1)**2*(r + 1)
Suppose 71*y - 96 + 96 = 8*y. What is u in -1/2*u + y - 5/6*u**4 + 19/6*u**3 - 7/6*u**2 - 2/3*u**5 = 0?
-3, -1/4, 0, 1
Suppose -4*c - 97 + 129 = 0. Let h(z) be the first derivative of -4/5*z**5 - 14 - 4*z**4 - c*z**2 - 4*z - 8*z**3. Find r such that h(r) = 0.
-1
Suppose -19088 + 9552 + 226*v + 9992 - v**2 = 0. Calculate v.
-2, 228
Let s = -1472 - -1474. Let m(i) be the second derivative of 1/12*i**3 + 0*i**5 + 1/30*i**6 + 3*i - 1/84*i**7 + 0*i**s + 0 - 1/12*i**4. Factor m(r).
-r*(r - 1)**3*(r + 1)/2
Factor 36*y**4 - 83*y**4 + 67*y**3 + 735*y - 13*y**3 + 42*y**4 + 111*y**3 - 290 - 605*y**2.
-5*(y - 29)*(y - 2)*(y - 1)**2
Solve 3 - 1/4*d**5 + 5/4*d**3 + 3/4*d**4 - d - 15/4*d**2 = 0 for d.
-2, -1, 1, 2, 3
Let c(l) = l**2 + 15*l + 39. Let y be c(-12). Determine d so that 5*d**2 - 20*d + 4*d**y + 12*d**2 - 24 - 9*d**2 = 0.
-3, -1, 2
Suppose 226*j = 19*j. Let p(a) be the third derivative of 1/4*a**4 + 0*a**3 - 1/20*a**5 + 0 + j*a - 12*a**2. Determine z, given that p(z) = 0.
0, 2
Let i(t) be the third derivative of t**6/210 - 29*t**5/105 + 179*t**4/42 + 418*t**3/21 - 471*t**2. Solve i(d) = 0.
-1, 11, 19
Let g be 1450/(-696)*(-216)/60. Factor g*k**2 - 5/2*k**4 - 10 + 5*k**3 - 10*k.
-5*(k - 2)**2*(k + 1)**2/2
Let z(j) be the second derivative of 2/5*j**5 + 0*j**2 + 0 + 1/6*j**6 + 1/3*j**4 + 1/42*j**7 - 231*j + 0*j**3. Factor z(f).
f**2*(f + 1)*(f + 2)**2
Let c(b) = -b + 1918 - 5*b - 1917 + 5*b. Let r(h) = -2000*h**2 + 605*h - 50. Let g(y) = -5*c(y) - r(y). Factor g(a).
5*(20*a - 3)**2
Let w(t) be the second derivative of -t**7/42 - t**6/3 - 8*t**5/5 - 19*t**4/6 - 5*t**3/2 + 1161*t. Factor w(f).
-f*(f + 1)**2*(f + 3)*(f + 5)
Let p be 1836/(-13770) + 32/15. Suppose 147/2*s**3 - 1029/8*s**4 + 63/8*s**p - 27/4*s + 0 = 0. What is s?
-2/7, 0, 3/7
Let k(o) = -o**2 - 439*o + 2673. Let d be k(6). Factor 2/3*t**d + 6*t + 0 - 4*t**2.
2*t*(t - 3)**2/3
Let q(m) be the first derivative of -4*m**3/3 - 604*m**2 - 91204*m - 419. Find l, given that q(l) = 0.
-151
Let l(k) be the first derivative of -k**4/36 - 133*k**3/27 + 15*k**2 - 2170. Factor l(b).
-b*(b - 2)*(b + 135)/9
Let t(u) be the second derivative of 0 + 0*u**2 - u**3 - 77*u - 7/15*u**4 + 1/50*u**5. Factor t(d).
2*d*(d - 15)*(d + 1)/5
Let o = -887 + 710. Let d = 180 + o. Find h such that -2/7*h**5 + 0*h + 8/7*h**4 + 4/7*h**2 + 0 - 10/7*h**d = 0.
0, 1, 2
Let j(t) be the first derivative of -t**5/10 - 11*t**4/8 - 37*t**3/6 - 45*t**2/4 - 9*t - 2535. Find y, given that j(y) = 0.
-6, -3, -1
What is l in 4/3*l**2 + 1/6*l**5 - 4/3*l**4 + 0 + 11/6*l**3 - 2*l = 0?
-1, 0, 1, 2, 6
Let c(i) = -i**2 - 1195*i + 43086. Let h be c(35). Factor 0 - h*a - 26*a**2 - 40/9*a**3 - 2/9*a**4.
-2*a*(a + 2)*(a + 9)**2/9
Let p(w) be the second derivative of 0*w**2 + 23/4*w**4 - 11/2*w**3 - 6 + 2*w - 39/20*w**5 + 1/10*w**6. Factor p(c).
3*c*(c - 11)*(c - 1)**2
Let j be (-53 - (-23872)/448)/(15/14 - 1). Find g such that 0 - 2/11*g**5 + 0*g**3 + 0*g**j + 0*g**2 + 0*g = 0.
0
Let b(s) = -9*s**3 + 33*s**2 - 3*s + 6. Let v(y) = -25*y**3 + 103*y**2 - 8*y + 16. Let h(q) = 8*b(q) - 3*v(q). Factor h(l).
3*l**2*(l - 15)
Solve 33*v**4 - 88*v**2 + 90*v**3 + v**5 + 78*v**2 + 6*v**2 - 120*v = 0 for v.
-30, -2, 0, 1
Let d(u) = 2*u**3 + 132*u**2 - 288*u + 24. Let q(y) = 2*y - 3. Let n(g) = d(g) + 8*q(g). Suppose n(b) = 0. What is b?
-68, 0, 2
Let f(j) = 2*j**2 - 54*j + 280. Let k(y) = 2*y**2 - 58*y + 280. Let a(q) = -4*f(q) + 6*k(q). Determine o, given that a(o) = 0.
5, 28
Let x(u) be the second derivative of -u**7/42 + 17*u**5/10 + 23*u**4/3 + 29*u**3/2 + 14*u**2 - 155*u. Factor x(m).
-(m - 7)*(m + 1)**3*(m + 4)
Suppose 0 = 3*g - 4*f - 15, 5*g - 6 - 19 = -4*f. Let t(q) be the first derivative of -1/8*q**4 + 1/4*q**2 - 12 - 1/4*q + 0*q**3 + 1/20*q**g. Factor t(x).
(x - 1)**3*(x + 1)/4
Let z(d) = -d**2 - 74*d - 467. Let g be z(-67). Let j(v) be the first derivative of 7/8*v**4 + 10 + 9/10*v**5 + v**g + 0*v - 10/3*v**3. Factor j(q).
q*(q - 1)*(q + 2)*(9*q - 2)/2
Factor 117*n**2 + 5824 - 1440*n + 229*n**2 - 350*n**2.
-4*(n - 4)*(n + 364)
Let j(x) be the third derivative of -x**5/160 - 57*x**4/64 + 45*x**3/4 + 1338*x**2. Find a, given that j(a) = 0.
-60, 3
Factor 92307 - 34495*t**3 + 34493*t**3 + 660*t**2 - 55104*t + 15277.
-2*(t - 164)**2*(t - 2)
Let m(x) be the second derivative of 2*x**6/15 - 233*x**5/5 + 692*x**4/3 - 920*x**3/3 + 17*x - 22. Factor m(q).
4*q*(q - 230)*(q - 2)*(q - 1)
Let c be (3 + -26)/(22/374). Let u = c + 395. Factor 7/3*t**3 + 0 - 5*t**2 + 3*t - 1/3*t**u.
-t*(t - 3)**2*(t - 1)/3
Let r(x) be the first d