6523. Let r(p) be the second derivative of 0*p**2 + 0*p**4 + 0*p**q + 0 - 1/5*p**6 - 25*p + 3/20*p**5 + 1/14*p**7. Factor r(a).
3*a**3*(a - 1)**2
Let n = -4727/52 + 379/4. Let x = 184092 - 184089. Factor -22/13*w**2 + 8/13 - 24/13*w + 60/13*w**x + n*w**4.
2*(w + 1)**2*(5*w - 2)**2/13
Let o = -48409/2 + 24205. Let t(k) be the third derivative of 47*k**2 + 0*k**3 - 1/40*k**6 + 0*k + 0 + o*k**4 + 3/20*k**5. Solve t(w) = 0 for w.
-1, 0, 4
Let b be 6 + (3 + (-96)/28)*7. Suppose b*h = 19*h - 7*h. Suppose 2/11*l**2 + h - 12/11*l = 0. What is l?
0, 6
Suppose n + 7 = -3*a, -1070 + 1068 = -4*n - 2*a. Factor 1/8*o**n + 0 - 9/8*o.
o*(o - 9)/8
Let o = 29345/4 - 7334. Let b(r) be the first derivative of 0*r + 9/5*r**5 - 19 + 0*r**2 + o*r**4 + r**3 + 1/2*r**6. Factor b(s).
3*s**2*(s + 1)**3
Let o be 8691/(-28970)*(-1 - 3/1). Factor 6/5 - o*b**2 + 1/5*b - 1/5*b**3.
-(b - 1)*(b + 1)*(b + 6)/5
Let n(u) = -3*u**3 - 296*u**2 + 3275*u - 8498. Let f(k) = 35*k**3 + 3555*k**2 - 39300*k + 101975. Let c(x) = -2*f(x) - 25*n(x). Let c(b) = 0. What is b?
-68, 5
Let f(h) = -14*h**3 - h**2 + 5*h + 6. Let b be f(-1). Let v = b - 14. Suppose -3/8*z**4 + 3/4*z**3 + v*z - 3/8*z**2 + 0 = 0. Calculate z.
0, 1
Let y(v) be the first derivative of 30 - 9/5*v**2 - 27/5*v - 1/5*v**3. Determine n so that y(n) = 0.
-3
Suppose 7*g - 17700 = -23*g. Let p = 1185/2 - g. Let -3*l + p + 1/2*l**2 = 0. Calculate l.
1, 5
Let l(a) be the second derivative of -a + 266 + 0*a**2 + 8/9*a**3 + 10/9*a**4 + 1/10*a**6 + 11/20*a**5. Factor l(y).
y*(y + 1)*(3*y + 4)**2/3
Let y(a) = -13*a - 39. Let o(f) = -f + 1. Let p(w) = -4*o(w) + y(w). Let c be p(-5). Let -6/7*s + 0 - 2/7*s**c = 0. Calculate s.
-3, 0
Factor -99/5*o**3 - 3216/5*o + 3/5*o**4 + 180*o**2 + 4032/5.
3*(o - 21)*(o - 4)**3/5
Suppose -27*r + 28 = -13*r. Find u, given that -7*u**4 + 3 - 2*u**5 - 9 - 3*u**4 - 8*u**3 + 18*u**4 + r - 4*u**2 + 10*u = 0.
-1, 1, 2
Suppose 0 = -2*m + 3*m - 2*u, -7 = -5*m + 3*u. Suppose m*k = 0, -6*q = -3*q + 2*k - 6. Factor -12 + q*a**2 + 49 + 53 - 24*a - 18.
2*(a - 6)**2
Let j(t) be the first derivative of -t**4/10 + 434*t**3/15 - 216*t**2/5 + 13476. What is q in j(q) = 0?
0, 1, 216
Let m(g) be the first derivative of -15*g**4/4 - 15580*g**3/3 - 4050795*g**2/2 - 2693610*g + 1640. Factor m(p).
-5*(p + 519)**2*(3*p + 2)
Suppose d - 5*n + 5 = 0, 70 = 5*d + 4*n + 8. Let v be (-40)/(-15)*((-21)/d + 3). Let v*m + 6/5*m**2 - 3/5*m**3 - 24/5 = 0. What is m?
-2, 2
Let p be ((-25248)/28404)/((-2)/21). Suppose p*k**2 + 8*k + 0 + 0*k**3 - 4/3*k**4 = 0. Calculate k.
-2, -1, 0, 3
Let o(g) be the second derivative of 5*g**4/12 + 935*g**3/3 + 1860*g**2 - 149*g - 11. Determine q so that o(q) = 0.
-372, -2
Let n(f) = 37*f - 108. Let l be n(3). Let h(s) be the first derivative of -5/3*s**l - 10*s**2 - 15*s + 8. Suppose h(v) = 0. What is v?
-3, -1
Let c(p) be the first derivative of p**4/12 - 10*p**3/9 + 3*p**2/2 + 56. Factor c(i).
i*(i - 9)*(i - 1)/3
Let i(s) be the second derivative of -s**6/120 - 3*s**5/20 + 15*s**4/16 - 15*s + 4. Let i(n) = 0. Calculate n.
-15, 0, 3
Solve -52/5*x**2 + 0 - 10*x - 2/5*x**3 = 0 for x.
-25, -1, 0
Let s = 11 + -9. Find p such that -16428 + 4*p**2 - 2*p**2 - 444*p + 3*p**2 - 8*p**s = 0.
-74
Let v(d) be the third derivative of d**2 + 1/60*d**6 + 0 + 110*d + 0*d**4 + 0*d**3 + 0*d**5 - 1/315*d**7. Determine b, given that v(b) = 0.
0, 3
Find p, given that -2*p**2 + 345*p - 155*p - 145*p + 240 - 119*p = 0.
-40, 3
Suppose 24*l + s + 306 = 29*l, -59 = -l - 2*s. Factor 36*w**4 + 609*w - l*w**2 - 144 - 1281*w - 15*w**2 + 152*w**3.
4*(w - 2)*(w + 3)**2*(9*w + 2)
Let d = 285088 - 285086. Factor -1/6*h**d - 2*h - 10/3.
-(h + 2)*(h + 10)/6
Let j(h) = -h**3 - 17*h**2 - 25*h + 3. Let f be j(-19). Let m = f + -1198. Factor -1/2*s**m + 0 + 1/2*s.
-s*(s - 1)/2
Let v(o) be the second derivative of o**5/20 + 181*o**4/12 + 2929*o**3/2 + 52983*o**2/2 + 6823*o. Solve v(g) = 0.
-87, -7
Let v(r) be the first derivative of 5*r**6/6 + 40*r**5 + 555*r**4/4 + 1234. Find w such that v(w) = 0.
-37, -3, 0
Let q(b) be the first derivative of -17 + 0*b + 11/21*b**2 - 2/21*b**3. Factor q(s).
-2*s*(3*s - 11)/21
Let j(f) be the third derivative of -2/3*f**4 + 0*f**3 + 1/30*f**6 + 22*f**2 + 0 + 0*f**5 + 0*f. Factor j(x).
4*x*(x - 2)*(x + 2)
Let i = 193 - 1157/6. Let s(n) be the second derivative of -3*n**2 + 0 + 8*n - i*n**4 - 4/3*n**3. Factor s(k).
-2*(k + 1)*(k + 3)
Let s(i) be the second derivative of i**6/6 + 15*i**5/2 + 785*i**4/12 - 850*i**3 + 2890*i**2 + 5260*i. Factor s(l).
5*(l - 2)**2*(l + 17)**2
Let q(u) be the first derivative of -1/6*u**6 + 0*u - u**5 + 21/4*u**4 + 111 + 4*u**2 - 23/3*u**3. Solve q(n) = 0 for n.
-8, 0, 1
Let o(i) be the third derivative of 0 - 4/3*i**3 - 5/3*i**4 + 17/105*i**7 + 1/42*i**8 + 0*i + 143*i**2 + 4/15*i**6 - 13/30*i**5. Find k, given that o(k) = 0.
-2, -1, -1/4, 1
Let q(p) be the third derivative of -p**8/560 - 4*p**7/175 - 7*p**6/200 + 5*p**2 + 25. Determine x, given that q(x) = 0.
-7, -1, 0
Let j(w) be the first derivative of 2*w**3 + 51*w**2/2 + 24*w - 536. Find p, given that j(p) = 0.
-8, -1/2
What is g in -501*g**3 + 8*g**2 - 1127*g**3 - 121*g + 121*g = 0?
0, 2/407
Let d(y) = -6*y**3 + 57*y + 57. Let z be d(-1). Suppose -11*p - 6 = -15*p + 5*l, -p + 5*l = z. Factor 0*w - 1/3*w**p + 0 - 4/3*w**2 - 5/3*w**3.
-w**2*(w + 1)*(w + 4)/3
Let g(r) = r**2 + 3*r + 5. Let d be g(-3). Let 4*o**2 - 13*o + 39 - 32*o + d*o - 3 = 0. What is o?
1, 9
Factor 84/5 + 272/5*y + 144/5*y**2.
4*(2*y + 3)*(18*y + 7)/5
Let l = -73 + 72. Let p be 10/(2*(0 - l)). Let -6*i**4 + 12*i**5 - 2*i**2 - 6*i**3 - 9*i**5 - 5*i**p = 0. What is i?
-1, 0
Let k = -138 + 418. Suppose 3*q = k - 280. Solve -4/3*c**2 + 2/9*c**3 + q + 0*c = 0.
0, 6
Determine i, given that -7473 + 4*i**4 + 169*i**3 - 12686 + 7710*i - 5*i**4 - 7389*i**2 + 13289*i + 6381 = 0.
1, 2, 83
Let i be 4 - (43/8 - 78/208). Let x(r) = 21*r**2 + 15*r - 2. Let u be x(i). Determine t so that 1/5*t**u - 2/5*t + t**2 + 0 - 4/5*t**3 = 0.
0, 1, 2
Factor 3/4*i**3 - 81/4 - 3/4*i + 81/4*i**2.
3*(i - 1)*(i + 1)*(i + 27)/4
Suppose 6 = -5*v - 14, 3*v = 4*i - 6736. Find p, given that 1681 - i - 4*p**3 - 4*p**2 = 0.
-1, 0
Let v(j) = 2*j**3 + 46*j**2 - 198*j + 158. Let b(u) = -2*u + 54. Let n be b(25). Let c(a) = -a**3 - 2*a**2 + 1. Let i(d) = n*c(d) + v(d). Factor i(g).
-2*(g - 9)**2*(g - 1)
Let q = -1/96673 - -290024/483365. Find u such that -27/5*u - 42/5 - q*u**2 = 0.
-7, -2
Let y = 3067/164646 - 1/9147. Let d(z) be the second derivative of 0 + y*z**4 + 12*z - 1/27*z**3 + 0*z**2. Let d(c) = 0. Calculate c.
0, 1
Let y(m) be the first derivative of -5/16*m**2 + 151 - 1/40*m**5 - 3/32*m**4 + 3/8*m**3 + 0*m. Determine w, given that y(w) = 0.
-5, 0, 1
Let k(q) = -117*q - 15091. Let v be k(-129). Factor -1/6*n**v - 5/3*n - 3/2.
-(n + 1)*(n + 9)/6
Suppose -71*q + 2*o = -68*q - 29, -3*o - 3 = 0. Let f(j) be the first derivative of 1/3*j**3 + q + 2/3*j**2 + 1/3*j. Suppose f(x) = 0. What is x?
-1, -1/3
Let g(b) = 188*b + 13348. Let t be g(-71). Factor 0 - 2/9*h**4 + 0*h + 1/9*h**5 + 0*h**2 + t*h**3.
h**4*(h - 2)/9
What is a in -222/7*a**2 - 220/7 + 63*a + 1/7*a**3 = 0?
1, 220
Let o(z) be the first derivative of 0*z - 41 + 5/18*z**4 + 14/27*z**3 + 2/45*z**5 + 1/3*z**2. Factor o(x).
2*x*(x + 1)**2*(x + 3)/9
Let x = 108 - -5. Suppose 122*z - x*z - 18 = 0. Factor 1 + 3/2*q + 1/2*q**z.
(q + 1)*(q + 2)/2
Let o(t) = -23*t**2 + 882*t - 1726. Let r(l) = -66*l**2 + 2644*l - 5177. Let z(k) = -17*o(k) + 6*r(k). Factor z(s).
-5*(s - 172)*(s - 2)
Factor -46/21*c**2 - 74/7*c - 2/21*c**3 + 90/7.
-2*(c - 1)*(c + 9)*(c + 15)/21
Let c(n) = -n**3 + 14*n**2 - 16*n + 40. Let a be c(8). Let o = a - 296. Factor -1/2*i**2 + o + i.
-i*(i - 2)/2
Let s(b) = -b**4 - b**2 - b. Let m(u) = -10*u**5 - 46*u**4 - 50*u**3 - 2*u**2 + 32*u + 16. Let y be -2 - 4/5*(-150)/20. Let k(x) = y*s(x) - m(x). Factor k(o).
2*(o + 1)**3*(o + 2)*(5*o - 4)
Let u be 1230/(-82)*((-156)/8 - 0). Let u*i**2 - 43*i + 2 - 3375/4*i**4 - 2025/4*i**3 = 0. Calculate i.
-1, 2/15
Let j(z) = -5*z**3 + 48*z**2 - 684*z - 4. Let v(h) = -11*h**3 + 95*h**2 - 1370*h - 9. Let g(s) = 9*j(s) - 4*v(s). What is y in g(y) = 0?
0, 26
Let l be 34/(-17)*6/(-4). Suppose -3*j - 5*c = -17, l*j + c + 2 = 15. Factor 8 - 13 - 10*p**3 + 3*p + 7*p + 5*p**j.
5*(p - 1)**3*(p + 1)
Le