 4)/9
Determine b, given that 1211760*b**2 + 6722/5*b**4 + 60528*b**3 + 324000 + 9115200*b + 56/5*b**5 = 0.
-30, -1/28
Let c be (64/(-48))/(3 + (-135)/35). Let x(r) be the third derivative of 0*r - 1/30*r**5 + 9*r**2 + 0 - 23/36*r**4 - c*r**3. Find a such that x(a) = 0.
-7, -2/3
Let j(z) be the first derivative of -z**3/27 + 7*z**2/2 - 20*z + 1433. Solve j(m) = 0 for m.
3, 60
Let d(p) = -5*p**2 + 25*p - 26. Let r = 68 - 113. Let z be 144/(-108) - (-80)/15. Let f(u) = -55*u**2 + 275*u - 285. Let j(t) = r*d(t) + z*f(t). Factor j(y).
5*(y - 3)*(y - 2)
Factor -69*k + 108*k**2 + 120*k**2 + 118*k**2 - 459*k**2 + 488 + 114*k**2.
(k - 61)*(k - 8)
Let o(n) = -3*n + 64. Let l be o(18). Suppose -4*f + 2*t = -8, 3 = 2*f + f - 3*t. Factor 4*d**3 - 10 + 11*d**f - l*d**3 - 10*d - 5*d.
5*(d - 2)*(d + 1)**2
Let o(r) be the third derivative of -41*r + 2*r**2 + 0 - 1/60*r**6 - 23/60*r**4 - 7/50*r**5 - 8/15*r**3 + 1/525*r**7. Factor o(p).
2*(p - 8)*(p + 1)**3/5
Suppose -3*v + 71 = 5*b, -5*v - 4*b - 35 = -8*v. Factor -v*x + 19*x + 4 + 5*x + 2 - x**3.
-(x - 3)*(x + 1)*(x + 2)
Suppose -k - 5*y + 7 = 0, -y + 8 + 3 = 5*k. Suppose -40*v + 0*v**5 - v**5 - 1235*v**k + 4*v**3 + 1143*v**2 - 4*v**4 + 5*v**5 - 64*v**3 = 0. Calculate v.
-2, -1, 0, 5
Let l(j) be the first derivative of -3*j**4/4 - 55*j**3 - 237*j**2 - 312*j + 946. Find z such that l(z) = 0.
-52, -2, -1
Suppose 0 = 9*p + 10*p - 95. What is z in -12*z**4 - 2*z**p - 99*z**3 - 95*z**3 + 184*z**3 = 0?
-5, -1, 0
Factor -1720/7 - 4/7*j**2 + 212/7*j.
-4*(j - 43)*(j - 10)/7
Let n(o) = 5*o**3 + 2*o**2 - 21*o + 26. Suppose -21 = -11*t + 111. Let j(p) = -p**3 + p**2 - p - 2. Let a(m) = t*j(m) + 3*n(m). Determine f so that a(f) = 0.
-9, 1, 2
Let f(t) be the first derivative of -3/5*t**5 + 0*t + 4/3*t**3 - 1/6*t**6 + 67 + 0*t**4 + 0*t**2. Find r such that f(r) = 0.
-2, 0, 1
Let n(p) be the first derivative of p**4/8 - 49*p**3/6 - 337*p**2/4 + 385*p/2 + 3083. Determine z so that n(z) = 0.
-7, 1, 55
Suppose -16*g - 351 = 3073. Let y = g + 214. Solve y - 2/21*k**2 - 8/21*k = 0.
-4, 0
Let g = -33/90104 - -67611/90104. Factor 1/8*r**4 - 7/8*r**3 + 0 + g*r**2 + 0*r.
r**2*(r - 6)*(r - 1)/8
Let q(j) be the first derivative of 22*j**2 - 4/3*j**3 - 49 + 48*j. Determine z so that q(z) = 0.
-1, 12
Let u(h) be the second derivative of h**6/105 + 2*h**5/5 + 277*h**4/42 + 366*h**3/7 + 1296*h**2/7 - 1367*h. Factor u(y).
2*(y + 2)*(y + 8)*(y + 9)**2/7
Let x = -3562 + 3566. Let d(l) be the third derivative of 0*l**3 + 0*l - 2/3*l**x + 4*l**2 + 0 - 2/105*l**7 + 4/15*l**5 + 1/30*l**6. Find f such that d(f) = 0.
-2, 0, 1, 2
Let c(s) be the first derivative of -s**7/168 - s**6/9 - 7*s**5/24 + s**3/3 + s**2 - 60. Let b(u) be the third derivative of c(u). Factor b(d).
-5*d*(d + 1)*(d + 7)
Suppose -2/9*f**4 - 14/9*f**3 + 0*f + 0 - 4/3*f**2 = 0. Calculate f.
-6, -1, 0
Let v(w) be the third derivative of -1/10*w**5 - 17/420*w**7 + 1/6*w**4 + 0*w - 1/224*w**8 - 1/8*w**6 - 7 + 4*w**2 + 0*w**3. Let v(r) = 0. What is r?
-2, 0, 1/3
Let t(d) be the second derivative of -d**7/735 + d**6/140 + d**5/210 - d**4/28 - 58*d**2 + 180*d. Let g(c) be the first derivative of t(c). Factor g(l).
-2*l*(l - 3)*(l - 1)*(l + 1)/7
Let p(i) be the first derivative of 12*i**2 + 0*i + 65 - 20/3*i**3 - i**4. Solve p(y) = 0 for y.
-6, 0, 1
Let u be ((-56)/6)/(-4 - (-12954)/3240). What is a in -12 + 840*a**3 - u*a**4 + 2360*a**2 + 2160*a**5 + 615*a - 12 + 69 = 0?
-1/3, -1/6, 3/2
Solve -6/7*s**4 - 24/7 - 20/7*s**3 + 10/7*s**2 + 40/7*s = 0 for s.
-3, -2, 2/3, 1
Let -1376/13*b + 2/13*b**3 + 1384/13 + 26*b**2 = 0. What is b?
-173, 2
Let i = 1765 - 1762. Let w(q) be the first derivative of -14 - 20/3*q**i + 0*q + 5/2*q**2. Factor w(c).
-5*c*(4*c - 1)
Let r(l) be the third derivative of 0 + 1/30*l**5 + 9*l**2 - 19/12*l**4 + 34/3*l**3 + 9*l. Let r(p) = 0. What is p?
2, 17
Let p be ((-1)/4)/(24/(-288)). Let a(n) be the first derivative of 0*n**5 + 0*n + 0*n**2 + 1/39*n**6 + 4/39*n**p - 3/26*n**4 - 16. Factor a(q).
2*q**2*(q - 1)**2*(q + 2)/13
Let q(m) be the first derivative of 3/2*m**4 + 51 + 1/5*m**5 - 5/2*m**2 - 3*m + 2/3*m**3 - 1/6*m**6. Let q(s) = 0. What is s?
-1, 1, 3
Let r(o) be the second derivative of -1/84*o**7 + 0*o**2 - 11/24*o**4 + 2 - 1/60*o**6 + 9/40*o**5 - 21*o + 1/3*o**3. Solve r(c) = 0 for c.
-4, 0, 1
Let 0 - 12*i**4 - 3*i**2 + 9/2*i**5 + 0*i + 21/2*i**3 = 0. What is i?
0, 2/3, 1
Suppose 16*o**3 + 228*o**2 - 2*o - 43*o**2 + 18*o**4 + 37*o**3 - 85*o**2 - 67*o**2 = 0. Calculate o.
-2, -1, 0, 1/18
Factor 11637*f**2 + 388*f - 384 + 11637*f**2 - 23278*f**2.
-4*(f - 96)*(f - 1)
Find b such that 0*b + 1/6*b**3 + 15/2*b**2 + 0 = 0.
-45, 0
Let c(r) be the first derivative of -r**6/1440 + r**5/480 - r**3 + 17. Let f(q) be the third derivative of c(q). Factor f(p).
-p*(p - 1)/4
Let c(h) be the third derivative of h**6/280 - 37*h**5/140 + 11*h**4/4 + 96*h**3/7 + h**2 + 264. Find l, given that c(l) = 0.
-1, 6, 32
Suppose 22*s - 17*s - 2*z - 6 = 0, -z = -5*s + 8. Factor 1 - 2*u - 5*u**2 - 2 + 3*u**s + 3 + 2*u**3.
2*(u - 1)**2*(u + 1)
Let 46672*l**3 - 46674*l**3 + 48*l**2 - 144*l**2 - 814*l = 0. What is l?
-37, -11, 0
Factor -200/7*v - 24/7*v**3 + 138/7*v**2 - 1/7*v**4 + 87/7.
-(v - 3)*(v - 1)**2*(v + 29)/7
Let r(k) be the second derivative of -3/4*k**2 - 5/6*k**4 - k - 1/12*k**6 - 3/8*k**5 - 30 - 1/168*k**7 - 25/24*k**3. Factor r(n).
-(n + 1)**4*(n + 6)/4
Let i be -7 + 18 + 6 + -16 + 2 + 0. Solve 0 - 1/9*v**5 + 0*v**i + 2/9*v**4 + 1/9*v - 2/9*v**2 = 0.
-1, 0, 1
Let h(v) = 0 - 12 - 3*v - 13 + 5. Let f be h(-8). Find j such that 2 + 4*j**3 + 8*j + f*j**4 - 6 - 12*j**3 = 0.
-1, 1
Let h = 144447 - 433319/3. Solve 2/3*b**4 + 4*b**3 - 2/3*b**5 - 2 + h*b - 28/3*b**2 = 0 for b.
-3, 1
Let t(x) be the second derivative of x**4/72 + 115*x**3/36 - 58*x + 2. Find g such that t(g) = 0.
-115, 0
Let g(i) = 9*i**2 - 23*i - 5. Let a(m) = -m**2 + 2*m - 1. Let j(d) = d**2 - 3*d + 2. Let h(q) = -5*a(q) - 3*j(q). Let r(z) = g(z) - 5*h(z). Factor r(o).
-o*(o + 18)
Let 2664/13*d - 2/13*d**2 - 887112/13 = 0. Calculate d.
666
Let t(i) = -50*i**3 + 8415*i**2 + 34440*i + 34535. Let m(g) = -7*g**3 + 1203*g**2 + 4920*g + 4934. Let q(a) = 15*m(a) - 2*t(a). Factor q(l).
-5*(l - 247)*(l + 2)**2
Let d(p) be the second derivative of -6*p**7/7 - 54*p**6/5 - 10*p**5 + 180*p**4 + 16*p**3 - 448*p**2 - 87*p - 7. Let d(q) = 0. Calculate q.
-7, -4, -2/3, 2/3, 2
Let x = -41 - -51. Suppose 4*s - y - 18 = 4*y, -4*s + y + x = 0. Factor 89*i**2 - s - 3 - 94*i**2 - 10*i.
-5*(i + 1)**2
Let a = -30/17167 + -6326673/4549255. Let x = -42/53 - a. Find h such that 0 + 0*h + 3/5*h**2 - x*h**5 + 3/5*h**3 - 3/5*h**4 = 0.
-1, 0, 1
Let x = 53 - 52. Suppose g + 935 = 3*w, -g - x = -2*g. Factor 3*y**2 - 3*y - 312 + w.
3*y*(y - 1)
Let y(w) = w**2 + 18*w - 25. Let f(b) = b**2 + 14 - b + b - 12. Let c(o) = 2*f(o) + y(o). Factor c(u).
3*(u - 1)*(u + 7)
Let t(z) be the first derivative of -z**4/120 + 3*z**3/20 - 45*z - 72. Let b(a) be the first derivative of t(a). Suppose b(v) = 0. What is v?
0, 9
Let c(l) be the third derivative of -5*l**5/18 - 133*l**4/6 + 64*l**3/9 + 3486*l**2. Factor c(g).
-2*(g + 32)*(25*g - 2)/3
Let x = -2/13697 - -54806/123273. Let a(h) be the first derivative of x*h**3 + 2*h**2 + 0*h - 16. Find q, given that a(q) = 0.
-3, 0
Let p be (-14)/4*30*(-78)/28665. Factor 8/7*u + 0*u**2 + 0 - 6/7*u**3 + p*u**4.
2*u*(u - 2)**2*(u + 1)/7
Suppose 32 - 4 = 7*z. Find m such that -5 - 105*m**2 + 72*m - 17*m + 5*m**z + 5 + 45*m**3 = 0.
-11, 0, 1
Suppose -35 = -14*t - 147. Let h be (-7)/(-14)*(-14)/t. Solve -1/4 - 5/8*a**3 - 1/8*a**4 - h*a - 9/8*a**2 = 0.
-2, -1
Suppose 681/2 + 2729/4*h**2 + 3407/4*h + 685/4*h**3 + 1/4*h**4 = 0. What is h?
-681, -2, -1
Solve -9/5*x**5 - 33/5*x**3 + 24 + 567/5*x**2 + 546/5*x - 183/5*x**4 = 0.
-20, -1, -1/3, 2
Let o(u) be the third derivative of -15 + u**2 - 1/17*u**3 + 11/510*u**5 + 0*u + 2/51*u**4. Factor o(f).
2*(f + 1)*(11*f - 3)/17
Let f(h) be the second derivative of -h**5/4 + 85*h**4/12 - 125*h**3/2 + 495*h**2/2 - 25*h + 14. Factor f(n).
-5*(n - 11)*(n - 3)**2
Factor 0*j - 2*j**2 + 0 + 1/2*j**3.
j**2*(j - 4)/2
Let f(r) = 6*r - 181. Let m be f(34). Let b be 2/6*m/((-1150)/(-140)). Factor -2/3*j**4 - b*j**2 + 2/15*j**5 + 6/5*j**3 + 0 + 4/15*j.
2*j*(j - 2)*(j - 1)**3/15
Let l(a) be the third derivat