577*n. Factor i(t).
-(t - 18)*(t - 16)
Let d = 350 - 345. Let j(o) = 3*o**3 + 24*o**2 - 25*o. Let a(u) = u**3 + 11*u**2 - 12*u. Let s(b) = d*a(b) - 2*j(b). Factor s(n).
-n*(n - 5)*(n - 2)
Suppose 0 = n + 6, 6*j - 4*j - 36 = 5*n. Let x(p) be the third derivative of -3*p**2 - 1/40*p**6 + 1/10*p**5 + 0 - p**j + 1/8*p**4 + 0*p. Factor x(t).
-3*(t - 2)*(t - 1)*(t + 1)
Let j be ((-76)/12)/((-7733)/814). Factor j*a**2 + 14/3*a + 4.
2*(a + 1)*(a + 6)/3
Suppose 65 = 5*w - 103*x + 108*x, 0 = -7*w - 3*x + 47. What is j in j - 1/3*j**w - 2/3 = 0?
1, 2
Factor -13/2*r - 17/4*r**2 + 0.
-r*(17*r + 26)/4
Factor 152*q + 276*q**2 - 4*q**4 + 64*q - 476*q**3 + 532*q**3.
-4*q*(q - 18)*(q + 1)*(q + 3)
Suppose 0 = -2*p + 20 - 16. Let k(n) be the first derivative of -9*n**3 + 3*n**2 + 4*n**4 - 3*n**4 + p*n**4 - 11. Determine w, given that k(w) = 0.
0, 1/4, 2
Suppose 30 + 69 = 45*r - 81. Factor 0*a + 3/5*a**5 - 12/5*a**2 + 24/5*a**3 - 3*a**r + 0.
3*a**2*(a - 2)**2*(a - 1)/5
Let i(x) be the third derivative of 1/84*x**8 - 7*x**2 + 1/6*x**4 + 8/105*x**7 + 0 + 4/15*x**5 + 0*x + 0*x**3 + 1/5*x**6. Let i(m) = 0. Calculate m.
-1, 0
Let s(r) be the first derivative of 124/7*r**3 + 0*r - 253 + 177/14*r**4 + 6/5*r**5 - 24*r**2. What is b in s(b) = 0?
-7, -2, 0, 4/7
Let p(s) = s + 1. Let f(a) = -3*a**3 + 192*a**2 - 1358*a + 1183. Let r(m) = -f(m) + 7*p(m). Suppose r(b) = 0. Calculate b.
1, 7, 56
Let h(k) be the third derivative of k**6/120 - 4*k**5/15 + 61*k**4/24 - 11*k**3 + 930*k**2. Factor h(f).
(f - 11)*(f - 3)*(f - 2)
Let g(o) be the third derivative of o**7/735 + o**6/140 - o**5/5 + 25*o**4/21 - 24*o**3/7 - 783*o**2. Factor g(y).
2*(y - 2)**3*(y + 9)/7
Let z(l) = -27*l**3 - 978*l**2 - 1278*l - 420. Let b(k) = -54*k**3 - 1955*k**2 - 2558*k - 840. Let s(w) = 3*b(w) - 7*z(w). Factor s(m).
3*(m + 35)*(3*m + 2)**2
Let f be (-2)/22 + (-193500)/(-473). Let w = 411 - f. Suppose -w*a**3 - 2/3*a**2 + 2/3 + 2*a = 0. Calculate a.
-1, -1/3, 1
Let l be ((-3)/(-6))/(1/(-1502)). Let q = -748 - l. Factor 5/2 + 3/2*j**2 + 1/2*j**q - 9/2*j.
(j - 1)**2*(j + 5)/2
Let b(k) = -28*k + 5. Let c be b(0). Factor 160*i**2 + 0*i**5 + 43899*i**3 - 43869*i**3 - 35*i**4 + 5*i**c - 160*i.
5*i*(i - 4)**2*(i - 1)*(i + 2)
Let c(r) be the third derivative of 20 - 1/210*r**6 - r**2 + 1/84*r**4 + 0*r**3 + 0*r**5 + 0*r**7 + 0*r + 1/1176*r**8. Suppose c(d) = 0. Calculate d.
-1, 0, 1
Find g, given that 1855*g**3 + 20*g**5 - 249*g**4 + 107*g**4 + 500*g**2 - 387*g**4 - 46*g**4 = 0.
-1/4, 0, 4, 25
Let q be 15/(-10) - 3/(-2). Find s such that q*s**3 + s**3 + 45*s + 18*s**2 + 24 + 2*s**3 - 6*s**3 = 0.
-1, 8
Let x be (-34)/(-51) + 30/35 + (-2)/3. Factor 38/7*o - x*o**2 - 12/7.
-2*(o - 6)*(3*o - 1)/7
Let v(x) be the third derivative of 1/24*x**6 - 5/12*x**5 + 5/8*x**4 + 15/2*x**3 + 0 + 0*x + 48*x**2. Let v(n) = 0. Calculate n.
-1, 3
Find t such that -10236501235 - 30900*t**2 - 13433068900 + 5*t**3 + 63654000*t - 9965429732 - 10074080133 = 0.
2060
Factor -19/2*k**2 - 5*k**3 + 15*k - 1/2*k**4 + 0.
-k*(k - 1)*(k + 5)*(k + 6)/2
Find k such that 0 - 2/5*k**4 - 768/5*k**2 + 88/5*k**3 - 4608/5*k = 0.
-4, 0, 24
Let x(p) = -p**2 - 6*p + 2. Let d be x(-6). Let s(q) = 23*q + 130. Let m be s(-5). Factor -13*c + 15*c**2 + 5*c**d - 3 - m*c - 4*c**3 + 15.
-4*(c - 3)*(c - 1)**2
Let -4160*v**2 - 260*v**2 - 3167*v**3 - 1283*v**3 - 1115*v**4 + 40*v = 0. Calculate v.
-2, 0, 2/223
Let x be (-8)/10*(-2)/4. Suppose -219*b + 214*b = 25, -b - 5 = 5*s. Factor x*l**4 + 6/5*l**2 + s + 6/5*l**3 + 2/5*l.
2*l*(l + 1)**3/5
What is i in 1/9*i**2 - 638/9 - 317/9*i = 0?
-2, 319
Suppose -33/4*d**3 - 3/4*d**5 - 27/4*d**4 - 21 + 75/4*d**2 + 18*d = 0. What is d?
-7, -2, 1
Solve 1192*o - 3577/3 + 1/3*o**2 = 0 for o.
-3577, 1
Factor -51*x + 16*x**2 + 6*x**2 - 8*x**3 + 8*x**3 - 72 + x**3.
(x - 3)*(x + 1)*(x + 24)
Let x(i) be the second derivative of 1/150*i**6 + 44 + 2*i + 4/5*i**2 - 11/100*i**5 + 9/20*i**4 - 5/6*i**3. Factor x(c).
(c - 8)*(c - 1)**3/5
Suppose -57 = 4*s + 57 + 65 - 191. Factor 3/2*u**2 + 7 - 23/2*u - 1/2*u**4 + 7/2*u**s.
-(u - 7)*(u - 1)**2*(u + 2)/2
Let o(d) be the third derivative of -1/5*d**6 + 0*d**7 + 8/15*d**5 - 1/2*d**4 + d**2 + 1/84*d**8 + 0 - 16*d + 0*d**3. Find w, given that o(w) = 0.
-3, 0, 1
Let l(i) be the first derivative of 3*i**6/280 + i**5/7 + 25*i**4/42 + 113*i**2/2 + 98. Let z(w) be the second derivative of l(w). Factor z(n).
n*(3*n + 10)**2/7
Factor 0*s + 1/12*s**2 - 1/12*s**4 - 1/12*s**3 + 0 + 1/12*s**5.
s**2*(s - 1)**2*(s + 1)/12
Let m = 18 + -14. Let n be 2 - (-4)/m*0. Factor -n + 3*v**2 - 9*v**3 + 2*v**3 + 13*v - v**2 - 6*v.
-(v - 1)*(v + 1)*(7*v - 2)
Let o = -178464/35 + 5099. Let i(y) be the third derivative of 1/735*y**7 + 2/21*y**4 + 0 + 17*y**2 - o*y**5 - 1/7*y**3 + 0*y + 0*y**6. Factor i(d).
2*(d - 1)**3*(d + 3)/7
Let o(f) = 72*f - 3. Let k(g) = 530*g + 0 + 5 - 368*g - g**2 - 308*g. Let r(s) = -3*k(s) - 5*o(s). Factor r(z).
3*z*(z + 26)
Let w(h) be the second derivative of h**7/21 - 7*h**6/15 + 19*h**5/10 - 25*h**4/6 + 16*h**3/3 - 4*h**2 + 1984*h. What is l in w(l) = 0?
1, 2
Let a(n) be the first derivative of 2/21*n**3 - 15 + 16/7*n**2 + 8*n. Find p such that a(p) = 0.
-14, -2
Let k = 388 + -385. Determine l so that -4*l**3 + 2*l**k + 8*l + l**4 - 6*l**2 - 4*l**3 + 3*l**3 = 0.
-2, 0, 1, 4
Let w(h) be the third derivative of -1/12*h**5 + h**2 - 1/3*h**4 + 0*h - 2/3*h**3 + 0 - 1/120*h**6. Factor w(t).
-(t + 1)*(t + 2)**2
What is m in -72/7*m**2 + 27/7 - 645/7*m = 0?
-9, 1/24
Let f = 15839/4167 + -731/463. Factor -388/9*d**2 + 0 + 152/9*d + f*d**3.
4*d*(d - 19)*(5*d - 2)/9
Let b = -1/80 + 1971/132080. Let q = b - -13196/4953. Determine l, given that -2/3*l**2 - q - 10/3*l = 0.
-4, -1
Let g be (1 - 0 - -21)/((-340)/9810). Let s = g - -635. Suppose -6/17*v**2 + s - 10/17*v = 0. Calculate v.
-2, 1/3
Suppose 5*t - x = 112, 5*t + 70*x - 100 = 75*x. Let u(c) be the first derivative of 1/5*c**2 - 1/10*c**4 - 2/5*c + 2/15*c**3 - t. Factor u(m).
-2*(m - 1)**2*(m + 1)/5
Let v be (-13)/2*1*(16 - 20). Factor 98*a**4 - 12*a**2 - v*a**4 - 32*a**4 - 37*a**4.
3*a**2*(a - 2)*(a + 2)
Let r be (27/((-108)/(-40)) - 12) + 11/((-110)/(-28)). Factor -r*o**4 + 343/5 - 83/5*o**3 - 567/5*o**2 - 245*o.
-(o + 7)**3*(4*o - 1)/5
Let a(w) be the third derivative of w**6/90 + 13*w**5/30 - 13*w**3/6 + 33*w**2. Let y(x) be the first derivative of a(x). Factor y(k).
4*k*(k + 13)
Let m be ((-28)/12 - -4)*(-11 + (-602)/(-56) - -1). Factor 3/4*n + 0 + m*n**2.
n*(5*n + 3)/4
Let g be (0 - -2) + (-21 - -21). Factor -35*h**3 + 2*h**4 - 5*h**4 - g*h**4 - 50*h**2.
-5*h**2*(h + 2)*(h + 5)
Suppose 2*o + 2*q - 2 = 0, -3*q + 0 = -3. Suppose 5*j - 4*z - 15 = 0, z - 2*z = o. Factor 30*s + 2 + 0 - 8 + 1 + 20*s**j - 45*s**2.
5*(s - 1)**2*(4*s - 1)
Suppose 0 = 27*a - 25*a - 914. Let p = 1373/3 - a. Find n such that -4/3 - p*n + 2/3*n**2 = 0.
-1, 2
Let m(s) be the first derivative of 15*s**4/4 - 145*s**3/3 - 30*s**2 + 100*s - 1154. Factor m(c).
5*(c - 10)*(c + 1)*(3*c - 2)
Let o be ((184/(-828))/((-8)/9))/((-21)/(-120)). Let -6/7*t**5 + o*t**4 - 32/7*t + 8*t**3 + 8/7*t**2 + 0 = 0. Calculate t.
-2, -1, 0, 2/3, 4
Let c(r) = r**3 - 299*r**2 + 2018*r + 190. Let u be c(7). Factor 86/3*g**2 - 5/3*g**3 + 0 - u*g - 7/3*g**4.
-g*(g - 3)*(g + 4)*(7*g - 2)/3
Let a be (-70)/12*(-2)/(-50)*(-838)/11732. Let u(z) be the third derivative of a*z**5 + 29*z**2 - 1/12*z**4 + 0*z + 0*z**3 + 0. Solve u(f) = 0.
0, 2
Suppose -9*d + 116 = -7*d. Suppose t - d = -56. Factor -n - n**3 - 4*n - 10*n**t - n**3 - 3*n**3.
-5*n*(n + 1)**2
Let k(l) be the second derivative of 0 - 1/15*l**5 + 1/2*l**3 + 4/3*l**4 + 20*l + 1/720*l**6 + 0*l**2. Let s(b) be the second derivative of k(b). Factor s(n).
(n - 8)**2/2
Let w = -314 - -316. Factor 15*m**3 - 32*m**w - 18*m**2 + 70*m**2 - 34*m**4 + 14*m**4 - 15*m.
-5*m*(m - 1)*(m + 1)*(4*m - 3)
Factor 800/3*i**3 - 182/9*i**4 - 2/9*i**5 + 0*i + 0 - 824*i**2.
-2*i**2*(i - 6)**2*(i + 103)/9
Find v such that 364/9*v + 80 + 2/9*v**2 = 0.
-180, -2
Let r = -311 - -313. Find c, given that 2096*c + 18*c**3 + 5*c**2 + 38 - 3*c**4 - 2108*c - 2 - 32*c**r = 0.
-1, 2, 3
Let z be 1*((-3700)/(-15))/20 + -7. Factor 4/3*k**2 + 4 - z*k.
4*(k - 3)*(k - 1)/3
Let d(u) be the first derivative of -2*u**3/45 + 797*u**2/15 - 212*u + 1859. Factor d(n).
-2*(n - 795)*(n - 2)/15
Let p(i) = 2*i