e k.
-4, 1
Let j be 7/14 + (-298)/52. Let z = j + 1072/195. Suppose 0 + z*k + 2/5*k**2 = 0. Calculate k.
-2/3, 0
Suppose -254 = -3*m - 230. Determine c, given that m*c + 21*c**3 - 9*c - 7*c**2 + 7 - 20*c**3 = 0.
-1, 1, 7
Factor 158*u**3 + 0*u + 6*u**2 + 3344/3*u**4 + 2888/3*u**5 + 0.
2*u**2*(u + 1)*(38*u + 3)**2/3
Let r(f) be the third derivative of f**7/1050 + 31*f**6/600 + 14*f**5/15 + 49*f**4/10 - 2*f**2 - 1442. Factor r(z).
z*(z + 3)*(z + 14)**2/5
Let u(y) be the second derivative of -y**4/3 + 2*y**3/3 + 4*y**2 + 180*y + 7. Determine l, given that u(l) = 0.
-1, 2
Let f(u) = 13*u**2 - 78*u + 4. Let d be f(6). Let o be (12/9)/((-10)/(-15)). What is y in 8*y - 4 - 2 - 6*y**3 + d*y**4 + 16*y - 2 - 14*y**o = 0?
-2, 1/2, 1, 2
Let i(p) be the second derivative of 71/9*p**3 + 96 - p + 17/3*p**4 + 2/3*p**2. Factor i(v).
2*(3*v + 2)*(34*v + 1)/3
Let b(j) = 5*j + 13. Let p be b(6). Factor -15*f**3 - 144*f**2 + 150 - 131*f - p*f - 141*f.
-3*(f + 5)**2*(5*f - 2)
Let a(o) be the third derivative of 0 + 0*o - 9/2*o**3 - 1/20*o**5 + 46*o**2 + 5/4*o**4. Factor a(n).
-3*(n - 9)*(n - 1)
Suppose -3*a + 18 = 3*v, -4*a + 0*a + v = -14. Find o such that -o**2 + o**2 - 4*o + o**3 - a*o + 5*o - 2*o**2 = 0.
-1, 0, 3
Let b = 10038/29 + -49262/145. Factor -b + 6*r**2 + 48/5*r - 10*r**3.
-2*(r + 1)*(5*r - 4)**2/5
Let s(n) be the first derivative of -2*n**3/27 + 15*n**2 - 1046. Factor s(z).
-2*z*(z - 135)/9
Solve 1/3*i**2 - 161/2*i + 241/6 = 0.
1/2, 241
Let q be -2 + 262/2 + 1. Let r = 658/5 - q. Factor r*g - 1/5*g**2 - 16/5.
-(g - 4)**2/5
Let m(i) be the first derivative of i**4/8 - 23*i**3/6 + 41*i**2/2 + 240*i + 1678. Suppose m(w) = 0. What is w?
-3, 10, 16
Let t(z) be the first derivative of z**8/168 - 11*z**7/105 + z**6/6 - 169*z**2/2 + 20. Let l(p) be the second derivative of t(p). Determine u so that l(u) = 0.
0, 1, 10
Find q, given that 1/3*q**5 + 173756/3*q + 236/3*q**4 - 84950/3*q**2 - 117128/3 + 13201/3*q**3 = 0.
-121, 2
Let d(t) = -7*t**5 - 11*t**4 - 19*t**3 + 33*t**2 + 68*t + 34. Let u(j) = -j**5 - 2*j**3 - j**2 + 2. Let s(z) = -d(z) + 5*u(z). Find w such that s(w) = 0.
-3, -2, -1/2, 2
Let z(h) be the third derivative of -h**8/588 - 9*h**7/245 + 4*h**6/105 + 9*h**5/70 - h**4/6 - 4*h**2 + 4*h. Let z(a) = 0. Calculate a.
-14, -1, 0, 1/2, 1
Let f(i) = -10*i**2 - 7*i + 781. Let y(k) = -2*k**2 - 2*k + 156. Let u(z) = 4*f(z) - 22*y(z). Factor u(x).
4*(x - 7)*(x + 11)
Let j be (-16)/(-2)*((25 - (-7429)/(-828)) + -16). Factor 0 + 8/3*r - j*r**3 + 8/9*r**2.
-2*r*(r - 6)*(r + 2)/9
Let z = 3909 - 35179/9. Let x(q) be the third derivative of -1/45*q**6 + z*q**3 - 26*q**2 + 1/9*q**4 - 2/315*q**7 + 0 + 0*q + 0*q**5. What is w in x(w) = 0?
-1, 1
Let t(z) be the second derivative of -z**7/42 - z**6/12 + z**5/4 + 49*z**2 + 9*z + 2. Let w(k) be the first derivative of t(k). Factor w(c).
-5*c**2*(c - 1)*(c + 3)
Let y(q) = 3*q**2 + 65*q - 146. Let z(t) be the third derivative of t**4/24 - 2*t**3/3 - 216*t**2. Let f(w) = -y(w) + 2*z(w). Determine g, given that f(g) = 0.
-23, 2
Let g be 9671/57 + -18 - 20/4. Factor -94*m**2 - g*m - 2/3*m**4 - 200/3 - 44/3*m**3.
-2*(m + 1)**2*(m + 10)**2/3
Let t(r) be the second derivative of r**4/36 + r**3/9 - 28*r**2 + 2625*r. Solve t(b) = 0.
-14, 12
Factor -84*p - 4/5*p**2 + 0.
-4*p*(p + 105)/5
Let m(d) be the third derivative of -3*d**6/80 - d**5/5 + 33*d**4/16 + 45*d**3/2 - 1466*d**2. Factor m(g).
-3*(g + 3)**2*(3*g - 10)/2
Let s be 2*(-8)/240*3190/72. Let l = 62/27 - s. Factor -27/2*z**3 + 33/2*z**2 + l*z**4 + 9/4 - 3/4*z**5 - 39/4*z.
-3*(z - 3)*(z - 1)**4/4
Let d(n) be the first derivative of n**5/35 - 8*n**4/7 + 142*n**3/21 - 96*n**2/7 + 81*n/7 - 434. Factor d(a).
(a - 27)*(a - 3)*(a - 1)**2/7
Let u(q) = q**2 - 109*q + 787. Let s(t) = 5872 - 546*t - 86*t**2 + 47*t**2 + 45*t**2 - 1938. Let z(c) = -3*s(c) + 14*u(c). Factor z(k).
-4*(k - 14)**2
Let d = 38411 - 38399. Factor d - 3/4*j**2 - 9/2*j.
-3*(j - 2)*(j + 8)/4
What is x in 413140/3*x - 206116/3 + 910/3*x**3 - 1/3*x**4 - 69311*x**2 = 0?
1, 454
Let s be 255/680 - 6/16. Determine m, given that -18/13*m + s - 16/13*m**2 + 2/13*m**3 = 0.
-1, 0, 9
Let w(c) be the third derivative of -c**7/315 + c**6/10 - 47*c**5/90 - 47*c**4/6 - 24*c**3 - 3*c**2 - 507*c. Find j, given that w(j) = 0.
-2, -1, 9, 12
Suppose -114 = 5*q + 186. Let n = -56 - q. What is w in -3*w**2 - w**n + 15*w**2 - 11*w**2 = 0?
-1, 0, 1
Let w(z) = -2*z - 2. Suppose 3*i - 6 = 4*d, 3*d + 4*i = i - 15. Let t be w(d). Solve -t*k**2 - k**2 - 25*k + 25*k = 0.
0
Let k(s) be the second derivative of -62*s + 47/3*s**3 - 2209/2*s**2 - 1/12*s**4 + 0. Factor k(o).
-(o - 47)**2
Let u(m) = m**4 - m**2. Suppose 0 = -16*g + 9*g - 42. Let k(b) = 3*b**4 - 9*b**3 + 16*b**2 + 4*b - 24. Let o(y) = g*u(y) + 3*k(y). What is h in o(h) = 0?
-1, 2, 6
Let j(k) be the first derivative of 39 + 53/14*k**2 - 2/7*k**3 + 9/7*k. Factor j(h).
-(h - 9)*(6*h + 1)/7
Let g(b) be the first derivative of b**4/12 + 4*b**3/3 + 23*b**2/6 - 12*b + 4054. Let g(s) = 0. What is s?
-9, -4, 1
Let f be (29/(-15))/(2/(-5)). Let z = -14/3 + f. Factor 0 + 1/6*x**5 + 0*x - 1/2*x**4 + 1/2*x**3 - z*x**2.
x**2*(x - 1)**3/6
Let p(u) be the second derivative of u**5/4 + 25*u**4/6 + 85*u**3/6 + 20*u**2 + 1077*u. Factor p(t).
5*(t + 1)**2*(t + 8)
Let q(p) be the first derivative of 45 + 0*p + 2/75*p**5 - 2/45*p**3 - 1/45*p**6 + 1/10*p**4 - 2/15*p**2. Let q(l) = 0. What is l?
-1, 0, 1, 2
Let s(y) = -22*y**2 - 4422*y - 319754. Let n(x) = -15*x**2 - 2950*x - 213170. Let h(o) = -7*n(o) + 5*s(o). Solve h(f) = 0.
-146
Let l = 16 + -12. Let m be l + (9 - (-265)/(-25)). Suppose -18/5*d - m*d**2 - 2/5*d**3 - 8/5 = 0. What is d?
-4, -1
Let n(o) = -100*o**3 - 573*o**2 - 1077*o - 662. Let z(k) = -250*k**3 - 1432*k**2 - 2692*k - 1656. Let x(y) = 12*n(y) - 5*z(y). Suppose x(g) = 0. What is g?
-2, -42/25
Factor -618*m - 686*m + 4*m**2 + 85029 - 17969 + 39216.
4*(m - 163)**2
Let y(z) be the first derivative of 0*z**3 - 2/15*z**5 - 1/2*z**4 + 0*z + 0*z**2 + 33. Factor y(v).
-2*v**3*(v + 3)/3
Suppose 4*b = -l + 28, 2*b + 0*b = 8. Determine c, given that 5*c**3 - l*c**2 - 11*c - 31 + 85 - 48 = 0.
-1, 2/5, 3
Suppose -j - 2*q + 11 = 2, 2*q = 0. Let i be (j/2)/(6/36). Factor -10*o**3 - 2*o**3 - 15*o + 8 - 4*o**4 - 8*o**2 + i*o + 4*o**2.
-4*(o - 1)*(o + 1)**2*(o + 2)
Let f(g) be the second derivative of g**7/840 + g**6/80 - g**5/240 - g**4/16 - 19*g**2 + 5*g + 13. Let s(l) be the first derivative of f(l). Factor s(m).
m*(m - 1)*(m + 1)*(m + 6)/4
Let n(d) be the first derivative of 10648*d**4 + 6776*d**3 + 1617*d**2 + 343*d/2 - 1259. Factor n(h).
(44*h + 7)**3/2
Let y(a) = -7*a**3 - 52*a**2 - 170*a + 264. Let c(l) = l**3 - 4*l**2 - 4*l. Let t(d) = -5*c(d) - y(d). What is b in t(b) = 0?
-33, -4, 1
Let f = 286/5077 + 18306/35539. Factor -f*l**4 - 4/7*l + 0 - 12/7*l**3 - 12/7*l**2.
-4*l*(l + 1)**3/7
Let b(d) = 15*d - 9. Let q be b(3). Factor -44*j**3 + 5 - 10*j**5 + 16*j**2 - 1 - 32*j**2 + 6*j - q*j**4.
-2*(j + 1)**4*(5*j - 2)
Let b(s) be the second derivative of -s**6/600 - 9*s**5/100 - 7*s**4/5 + 98*s**3/15 + 17*s**2 - 2*s - 4. Let k(z) be the first derivative of b(z). Factor k(m).
-(m - 1)*(m + 14)**2/5
Let x = 95 - 92. Let -9*a**5 + 38070*a**3 + 12*a**2 - 21*a**4 - 38070*a**x = 0. Calculate a.
-2, -1, 0, 2/3
Factor -298931*g + 299035*g - 348 + 4*g**2 + 0*g**2.
4*(g - 3)*(g + 29)
Let j(t) be the first derivative of t**6/4 - t**5/2 - 5*t**4/8 + 5*t**3/6 + t**2/2 - 947. Solve j(m) = 0.
-1, -1/3, 0, 1, 2
Let o(n) be the third derivative of -12/5*n**3 + 17/150*n**5 - 65*n**2 + 0 - 1/200*n**6 - 7/10*n**4 + 0*n. Factor o(g).
-(g - 6)**2*(3*g + 2)/5
Factor -1/2*y**3 + 19*y + 37/2*y**2 + 0.
-y*(y - 38)*(y + 1)/2
Suppose -8*n + 478 = 454. Factor 4*p**5 + 1064*p**n - 108*p**4 + 1189*p**2 + 7680*p - 4096 - 3657*p**2 + 138*p**2 - 2214*p**2.
4*(p - 8)**3*(p - 2)*(p - 1)
Let x = -882993 - -882993. Let r be (-3)/(-35) + 3/15. Factor 6/7*h - r*h**2 + x.
-2*h*(h - 3)/7
Let r = -41 - -44. Let i = 7 + r. Let -18*c**3 - i*c**3 + 7*c**4 - 8 - 6*c**4 + 4*c + 7*c**4 + 24*c**2 = 0. What is c?
-1/2, 1, 2
Solve -658 - 826*r - r**2 + 601 - 25 - 743 = 0 for r.
-825, -1
Let p be 43/(-3) - 44/66. Let b be ((-33)/176*-8)/(p/(-52)). Factor -12/5*k**3 - b*k**2 - 24/5*k - 8/5 - 2/5*k**4.
-2*(k + 1)**2*(k + 2)**2/5
Let w(l) be the second der