49
Let x(l) be the first derivative of l**5/5 + 15*l**4/4 + 25*l**3/3 - 15*l**2/2 - 26*l - 684. Find t such that x(t) = 0.
-13, -2, -1, 1
Suppose -3*s + 3*g = -24, -2*s - 4*g = -5*s + 26. Let o be (-13)/(-6) + (1/s)/(-1). Let -40*j + 128 + 97*j**o + 8*j - 95*j**2 = 0. What is j?
8
Let d(z) be the second derivative of -z**5/70 - 75*z**4/14 - 608*z**3 - 1792*z**2 - 427*z. Find a, given that d(a) = 0.
-112, -1
Let i(d) be the first derivative of d**6/1440 - 7*d**5/120 + 49*d**4/24 + d**3/3 + 45*d**2/2 + 69. Let u(m) be the third derivative of i(m). Factor u(k).
(k - 14)**2/4
Let k = 438 + -434. Suppose a - 3*a + 8 = 0, k*g - 3*a - 8 = 0. Factor 0 - 6/7*v**g + 0*v**3 + 0*v**2 - 6/7*v**4 + 0*v.
-6*v**4*(v + 1)/7
Let w(q) be the first derivative of -5*q**4/4 - 835*q**3/3 + 5145*q**2/2 - 7785*q + 2898. Solve w(y) = 0.
-173, 3
Let c(r) = 41*r**4 - 692*r**3 + 667*r**2 + 8*r + 8. Let f(s) = -26*s**4 + 461*s**3 - 445*s**2 - 5*s - 5. Let i(k) = 5*c(k) + 8*f(k). Factor i(t).
-3*t**2*(t - 75)*(t - 1)
Let q(i) be the first derivative of 8*i**5/5 - 77*i**4/2 - 794*i**3/3 + 1208*i**2 - 552*i + 8268. Determine r so that q(r) = 0.
-6, 1/4, 2, 23
Let t(n) be the first derivative of 2/15*n**3 - 123 + 16/5*n - 9/5*n**2. Suppose t(o) = 0. What is o?
1, 8
Let x = 3133 - 3133. Let w(h) be the first derivative of 1/7*h**2 + x*h + 2/21*h**3 - 6. Let w(y) = 0. What is y?
-1, 0
Suppose 3 = 4*l - 3*t, l - 2 = 62*t - 60*t. Let g(q) be the first derivative of 2/25*q**5 - 4/5*q**3 + 0*q**2 - 1/10*q**4 + l*q - 24. What is k in g(k) = 0?
-2, 0, 3
Let r(o) be the third derivative of -o**8/3360 - o**7/252 - o**6/60 - 59*o**4/24 - 145*o**2. Let k(d) be the second derivative of r(d). Factor k(s).
-2*s*(s + 2)*(s + 3)
Let w(i) be the third derivative of i**5/180 + 1567*i**4/72 - 784*i**3/9 + 4*i**2 + 42*i + 4. Let w(t) = 0. Calculate t.
-1568, 1
Factor 81*i + 3/4*i**4 - 6*i**3 - 27/4*i**2 + 81.
3*(i - 6)**2*(i + 1)*(i + 3)/4
Let q = 824070/7 + -2470082/21. Let -8/3*v**5 + 72*v**3 - q*v**2 - 44/3*v**4 - 12 + 176/3*v = 0. What is v?
-9, 1/2, 1
Let y be (-1457)/705 + (-60)/(-25). Let t(m) be the second derivative of y*m**3 - 1/4*m**4 + 21*m + 1/20*m**5 + 0 + 0*m**2. Factor t(f).
f*(f - 2)*(f - 1)
Let f(a) be the second derivative of -a**7/945 - a**6/60 - 2*a**5/45 - 43*a**4/12 - 28*a + 2. Let y(p) be the third derivative of f(p). Factor y(b).
-4*(b + 4)*(2*b + 1)/3
Let a = 36265 + -181324/5. Factor -a*n**5 - 4/5*n - 2/5*n**4 + 0 + 4/5*n**2 + 3/5*n**3.
-n*(n - 1)**2*(n + 2)**2/5
Let v(k) be the first derivative of 0*k + 1/9*k**3 - 1/12*k**2 + 13 - 1/24*k**4. Factor v(f).
-f*(f - 1)**2/6
Let d(r) be the second derivative of -39/10*r**3 + 169/5*r**2 - 2/5*r**4 + 0 - 34*r - 1/100*r**5. Solve d(o) = 0 for o.
-13, 2
Let q = 6262 + -12523/2. Let j(l) be the third derivative of 0*l + 12*l**3 + 36*l**2 - q*l**4 - 23/30*l**5 - 1/210*l**7 - 13/120*l**6 + 0. Solve j(o) = 0.
-6, -2, 1
Let z(v) be the third derivative of -v**7/315 - 3*v**6/20 - 4*v**5/5 + 770*v**2 - 3. What is d in z(d) = 0?
-24, -3, 0
Solve -176/7 - 44/7*j**4 + 220/7*j**2 + 4/7*j**5 + 16/7*j - 20/7*j**3 = 0.
-2, -1, 1, 2, 11
Let 19*p**2 + 0 - 4 - 186*p - 6 - 42*p**2 - 6 = 0. What is p?
-8, -2/23
Let x(t) = 2*t + 12. Let w be (-396)/77 - (-2)/14. Let f be x(w). Factor -2 - 30*h**2 + 28*h**f + 0*h - 5*h + h.
-2*(h + 1)**2
Let y(a) be the third derivative of 0 + 4*a - 2/135*a**6 + 5*a**2 + 2/315*a**7 - 1/1512*a**8 + 4/9*a**4 - 32/27*a**3 - 8/135*a**5. Factor y(g).
-2*(g - 2)**4*(g + 2)/9
Let t(f) be the second derivative of -8/3*f**2 + 29/54*f**4 - 29/45*f**5 + 0 + 64*f + 58/27*f**3 - 1/27*f**6. Solve t(r) = 0.
-12, -1, 2/5, 1
Let b(y) be the second derivative of 0 - 1/140*y**5 + 19/84*y**4 - 32/21*y**3 - 155*y + 30/7*y**2. Factor b(v).
-(v - 15)*(v - 2)**2/7
Let c = 22226 + -133355/6. Let q(n) be the first derivative of 16/9*n**3 + 16/3*n**2 - 31 + c*n**4 + 0*n. Factor q(d).
2*d*(d + 4)**2/3
Let i(g) be the first derivative of 3*g**5/5 - 141*g**4/4 + 612*g**3 - 3210*g**2 - 8400*g - 9206. Find t, given that i(t) = 0.
-1, 10, 28
Let l(z) = 7*z + 28. Let b be l(-1). Let y be b/6 - (-5 - 54/(-12)). Factor -78*s + 9/2*s**y + 17*s**3 - 35/2*s**2 + 18.
(s - 2)*(s + 3)**2*(9*s - 2)/2
Let p = 4486 - 4481. Let o(u) be the third derivative of 0*u**3 + 0*u + 24*u**2 - 37/120*u**6 - 2/21*u**7 + 2/15*u**p + 1/6*u**4 + 0. Factor o(n).
-n*(n + 2)*(4*n + 1)*(5*n - 2)
Let w(v) be the third derivative of v**6/280 - 1181*v**5/140 + 337*v**4/8 - 1179*v**3/14 + 33*v**2 + 4*v + 7. Factor w(j).
3*(j - 1179)*(j - 1)**2/7
Let n(r) be the first derivative of r**3/33 - 86*r**2 + 2541. Factor n(s).
s*(s - 1892)/11
Let r(x) = -20*x**4 - 42476*x**3 + 12168*x**2 - 8*x - 16. Let b(z) = 19*z**4 + 42477*z**3 - 12172*z**2 + 9*z + 18. Let y(j) = 8*b(j) + 9*r(j). Factor y(q).
-4*q**2*(q + 1517)*(7*q - 2)
Suppose -3*t + 7 + 10 = 5*p, -5*t + 24 = 4*p. Solve 0*x**2 + 61 + x**2 - 61 - x**t = 0.
-1, 0, 1
Let y(m) be the second derivative of 0 - 1/60*m**5 - 169/6*m**3 - 13/12*m**4 + 35*m - 2197/6*m**2. Factor y(l).
-(l + 13)**3/3
Let d be 0 - (-123 + 3) - 3. Suppose -215 = -2*y - 211. Factor d*z - 235*z - 2*z**y + 106*z.
-2*z*(z + 6)
Let j(i) = i**2 + 47*i - 1. Let r(o) = 6*o**2 - 83*o + 344. Let v(x) = -j(x) + r(x). Factor v(h).
5*(h - 23)*(h - 3)
Let z(l) = 96*l**2 + 24630*l + 24300. Let x(s) = 5*s**2 + 1296*s + 1279. Let p(c) = -39*x(c) + 2*z(c). Solve p(n) = 0 for n.
-427, -1
Let u be (-62)/(-1426) - (-481)/46. Factor u - 33/4*o**2 - 225/4*o.
-3*(o + 7)*(11*o - 2)/4
Let k = -182830/3 + 62193. Let w = k + -1249. Suppose -4/9*u - 2/9*u**2 + w = 0. Calculate u.
-3, 1
Solve -12*b**4 - 73*b**2 - 12 - 26*b**2 + 7*b + 28*b**3 - 4*b**3 + 53*b + 36*b**3 = 0.
1/2, 2
Let g = 8403103/589692 - -2/147423. Let -3 - 39/2*d**2 - g*d - 33/4*d**3 = 0. Calculate d.
-1, -4/11
Let o(q) be the second derivative of -q**4/30 + 18*q**3 - 3645*q**2 + 684*q. Determine k so that o(k) = 0.
135
Let w = -143 + 138. Let p(r) = -r**2 - 2*r - 1. Let k(f) = -2*f**2 + 2*f - 4. Let t(c) = w*p(c) + 5*k(c). Factor t(u).
-5*(u - 3)*(u - 1)
Let z be (-18)/(-84) - 147/686. Factor -8*m**4 + 32/5*m**3 - 12/5*m**5 + 0*m**2 + z*m + 0.
-4*m**3*(m + 4)*(3*m - 2)/5
Let n be (-18 + 1 + 11)/(2/(-1)). Factor -6*o**n + 50/3*o**2 + 0 + 4*o.
-2*o*(o - 3)*(9*o + 2)/3
Let a(y) be the second derivative of 0*y**2 - 2/15*y**6 - 98/3*y**3 + 0 - 3*y**5 - 21*y**4 + 146*y. Let a(b) = 0. Calculate b.
-7, -1, 0
Solve 208/5*u + 2/5*u**2 + 160 = 0 for u.
-100, -4
Let n = 176906/3 - 58968. Let q be 0/((-9)/(-5 - -2)). Factor 0 + q*a**3 + 0*a - n*a**2 + 2/3*a**4.
2*a**2*(a - 1)*(a + 1)/3
Let l(g) be the second derivative of g**6/24 - g**5/2 + 5*g**4/8 + 15*g**3 - 675*g**2/8 - 69*g - 2. Solve l(t) = 0.
-3, 3, 5
Let x be -6*(-3)/(-9)*-1*1. Let f(k) be the first derivative of -1/40*k**4 - 1/5*k**3 - 2/5*k + 12 - 9/20*k**x. Factor f(r).
-(r + 1)**2*(r + 4)/10
Factor -2/7*m**2 - 306/7 - 52/7*m.
-2*(m + 9)*(m + 17)/7
Let f = 60904 + -60902. Find u, given that 0 - 2*u**3 - 3*u**f - 1/3*u**4 - 4/3*u = 0.
-4, -1, 0
Let o(g) be the first derivative of -45*g**4/4 + 350*g**3/3 + 1565*g**2/2 + 330*g + 6092. Factor o(p).
-5*(p - 11)*(p + 3)*(9*p + 2)
Suppose 717*o - 1059 = 513 - 138. Solve 1 + 5/2*c + 2*c**o + 1/2*c**3 = 0 for c.
-2, -1
Find w such that -2787 + 21*w**2 - 55*w**2 + 3367*w - 577*w + 31*w**2 = 0.
1, 929
Let r = -18948 - -18952. Let 74/7*h**3 + 64/7*h**2 - 2*h**r - 24/7*h + 0 = 0. What is h?
-1, 0, 2/7, 6
Suppose -2*a + 3*m = -4*a + 21, -3*m - 84 = -5*a. Suppose 4*g**3 - 9*g**2 - a*g**2 - 19 + 12*g + 59 + 0*g**2 = 0. Calculate g.
-1, 2, 5
Suppose -1158242/9 + 3044/9*j - 2/9*j**2 = 0. What is j?
761
Let g(j) = -2 + 7*j**2 - 3*j + 21 - 15*j + 2*j - 3*j. Let z(p) = 3*p**2 - 9*p + 10. Let y(o) = 4*g(o) - 10*z(o). Solve y(m) = 0 for m.
3, 4
Let g(x) be the third derivative of x**7/210 + x**6/24 - x**5/10 - 1481*x**2. Factor g(a).
a**2*(a - 1)*(a + 6)
Let q(t) = 8*t**2 - 4*t + 14. Suppose -3*h - z = -8, -2*z + 2 + 8 = 3*h. Let f(d) = -d**2 - d - 4. Let i(y) = h*q(y) + 18*f(y). Suppose i(x) = 0. What is x?
-11, -2
Let i = -80359 + 564162/7. Let f = 236 - i. Factor -3/7*b + 0*b**4 + 6/7*b**3 + 0*b**2 + 0 - f*b**5.
-3*b*(b - 1)**2*(b + 1)**2/7
Let c = -7696/35 - -1542/7. Let -c*u + 6/5*u**2 - 6/5 + 2/5*u**3 = 0. Calculate u.
-3, -1, 1
Let c = -417