
-4*(m - 40)*(m + 1)*(m + 2)**2
Let k(n) be the third derivative of n**7/1400 - n**6/100 + 9*n**5/200 - 15*n**3/2 + 9*n**2 - 1. Let i(g) be the first derivative of k(g). Factor i(z).
3*z*(z - 3)**2/5
Let y(g) be the first derivative of -54 + 0*g - 70/3*g**3 - 20*g**2 - 35/4*g**4 - g**5. Factor y(o).
-5*o*(o + 1)*(o + 2)*(o + 4)
Factor 96*l + l**3 - 61/2*l**2 - 81/2.
(l - 27)*(l - 3)*(2*l - 1)/2
Let v(a) = a**3 - 31*a**2 + 107*a + 29. Let n be ((-54)/1)/(-2) + (-270 - -270). Let j be v(n). Factor -1/5*b**3 + 0 + 7/5*b**j - 6/5*b.
-b*(b - 6)*(b - 1)/5
Let v(p) be the first derivative of 5/8*p**4 - 5/6*p**3 + 2*p - p**2 + 37 - 1/12*p**6 + 1/10*p**5. Determine g, given that v(g) = 0.
-2, -1, 1, 2
Let a = 1250 - 1048. Suppose 0 = 198*d - a*d + 16. Factor 32/5*t + d*t**2 + 4/5*t**3 + 16/5.
4*(t + 1)*(t + 2)**2/5
Let i(n) be the second derivative of n**6/90 - n**5/60 - 229*n**4/18 + 752*n**3/3 - 1200*n**2 + 3*n + 1016. Factor i(r).
(r - 12)**2*(r - 2)*(r + 25)/3
Let g(r) be the first derivative of r**4 - 64*r**3 + 1080*r**2 - 3584*r - 4844. What is d in g(d) = 0?
2, 14, 32
Determine y, given that 64*y**2 + 0*y + 0 + 240/7*y**3 + 36/7*y**4 + 1/7*y**5 = 0.
-28, -4, 0
Let -9/2 + 93/8*o - 3/8*o**4 + 27/8*o**3 - 81/8*o**2 = 0. What is o?
1, 3, 4
Suppose 0 = -4*o + 44 + 228. Suppose 12 = o*g - 62*g. Find v, given that 1/2 - v**g + 7/4*v = 0.
-1/4, 2
Let f(c) be the third derivative of -5*c**7/6 + 103*c**6/12 - 21*c**5 - 35*c**4/3 + 80*c**3/3 + 178*c**2 + 5*c. Suppose f(g) = 0. What is g?
-2/5, 2/7, 2, 4
Let l(u) be the second derivative of -160801*u**4/42 + 802*u**3/21 - u**2/7 + 4978*u. Solve l(o) = 0 for o.
1/401
Let y(b) = -11*b**3 + 211*b**2 - 339*b - 26. Let l(t) = -5*t**3 + 105*t**2 - 172*t - 12. Let v(n) = 13*l(n) - 6*y(n). Factor v(x).
x*(x - 2)*(x + 101)
Let b(p) be the first derivative of 0*p - 38 + 2/15*p**5 + 96*p**3 + 6*p**4 + 576*p**2. Factor b(f).
2*f*(f + 12)**3/3
What is l in -1701*l**2 + 54*l - 114*l**4 + 132*l - 732*l**3 + 2*l**5 - 1194*l + 205*l**2 = 0?
-2, 0, 63
Let k(m) = 39*m**3 + 383*m**2 + 246*m - 2152. Let o(t) = -14*t**3 - 128*t**2 - 81*t + 717. Let c(n) = 3*k(n) + 8*o(n). Factor c(r).
5*(r - 2)*(r + 3)*(r + 24)
Let k(z) be the second derivative of -3*z**5/80 - 5*z**4/16 + z**3/4 + 9*z**2 - 638*z. Let k(a) = 0. What is a?
-4, -3, 2
Let b be -5 - 102/(-15) - 20381/12595. Determine i so that -b*i**5 + 0 + 0*i + 6/11*i**3 - 4/11*i**4 + 0*i**2 = 0.
-3, 0, 1
Let a(i) be the third derivative of 0*i + 1/6*i**4 + 96*i**2 - 1/420*i**7 + 1/40*i**5 + 1/3*i**3 - 1/120*i**6 + 0. Factor a(s).
-(s - 2)*(s + 1)**2*(s + 2)/2
Let v(y) be the second derivative of -1 - 961/7*y**2 - 3/2*y**4 + 96*y + 1/70*y**5 + 341/7*y**3. Suppose v(s) = 0. Calculate s.
1, 31
Let p be ((-24)/10)/((-29)/(2320/32)). Factor -2*z**2 + 3 - 9 + p - 22*z.
-2*z*(z + 11)
Let k(c) be the first derivative of -c**5/15 + 415*c**4/3 - 688900*c**3/9 + 1276. Factor k(h).
-h**2*(h - 830)**2/3
Let g(o) = -o**4 - 27*o**3 + 348*o**2 - 542*o + 4. Let k(d) = -d**4 - 3*d**3 + d - 2. Let x(n) = g(n) + 2*k(n). Factor x(w).
-3*w*(w - 5)*(w - 2)*(w + 18)
Suppose -6*p - 16 - 44 = 0. Let h be (p/(-4))/((110/(-8))/(-11)). Solve 4*j**2 + 2*j - h*j - 5*j**3 + 9*j**3 = 0 for j.
-1, 0
Let b(w) be the first derivative of w**6/16 + 3*w**5/8 + 3*w**4/4 + w**3/2 - 1507. Solve b(s) = 0.
-2, -1, 0
Let c(l) be the third derivative of l**6/40 + 83*l**5/20 - 43*l**4/4 - 84*l**3 + 10917*l**2. Suppose c(v) = 0. What is v?
-84, -1, 2
Let j be 582/(-388) - (-2)/(4/9). Let d(u) be the second derivative of 11/3*u**j + 0 - 3/2*u**4 - 4*u - 2*u**2. Factor d(c).
-2*(c - 1)*(9*c - 2)
Let g(t) = 8*t**2 + 27*t - 28. Let s(q) be the third derivative of -q**5/60 - q**2 - 16. Let c(a) = -2*g(a) - 14*s(a). Factor c(j).
-2*(j - 1)*(j + 28)
Find o, given that -2/3*o**2 + 6*o**3 + 26/3*o**4 + 10/3*o**5 + 0 - 4/3*o = 0.
-1, 0, 2/5
Let f(m) be the first derivative of -3*m**4/4 - 13*m**3 + 144*m**2 + 324*m - 11212. Determine n so that f(n) = 0.
-18, -1, 6
Suppose -5*d = b + 15, -3*b - 2*d = -0*d + 19. Let o be 1/b - 336/(-80). Factor -r**2 + 12*r**3 + 2*r**2 - 5*r**2 - 12*r**o + 4*r**5.
4*r**2*(r - 1)**3
Let u(m) be the third derivative of -m**6/300 + 269*m**5/75 + 18*m**4 - 242*m**2 - 5*m + 2. Factor u(k).
-2*k*(k - 540)*(k + 2)/5
Let k(h) be the first derivative of -5*h**4/2 + 24364*h**3/3 - 7422492*h**2 + 5934096*h + 1825. Factor k(d).
-2*(d - 1218)**2*(5*d - 2)
Factor -9*h**2 - 13*h**2 + 9*h**2 - 9*h**2 + 24*h + 4*h**3 + 2*h**2.
4*h*(h - 3)*(h - 2)
Let s be ((584/60)/(-73))/(1/(5/(-1))). Let l(t) be the first derivative of -s*t**3 - 9/5*t**2 + 4/5*t + 7. Suppose l(u) = 0. Calculate u.
-2, 1/5
Suppose 0 = 2*z - 6*n + 2*n + 8, 0 = 4*z + 5*n - 23. Solve -6*b + z*b**4 - 5*b**4 - 16*b**2 + 25*b**2 + 0*b**4 = 0 for b.
-2, 0, 1
Let p be 4/(-10) + (-12)/(-5). Factor -18 - 3*w**3 - 8010*w + p*w**2 + 2*w**3 + 8019*w.
-(w - 3)*(w - 2)*(w + 3)
Suppose 11262*y + 24 = 11270*y. Let x(u) be the first derivative of -1/6*u**6 - 2 + 2/3*u**y + u**4 + 0*u - 2/5*u**5 - 3/2*u**2. Factor x(c).
-c*(c - 1)**2*(c + 1)*(c + 3)
Let c(p) be the first derivative of 0*p - 1/6*p**6 + 3/4*p**4 + 10/3*p**3 - 4/5*p**5 - 4*p**2 - 178. Determine a so that c(a) = 0.
-4, -2, 0, 1
Let d(g) be the third derivative of -1/90*g**5 - 5/9*g**4 - 13*g**2 + 0 + 7/3*g**3 + 3*g. Solve d(v) = 0 for v.
-21, 1
Let b(z) = 461*z + 1385. Let m be b(-3). Let o(t) be the first derivative of 2/45*t**5 - 2/9*t**m - 16 - 2/27*t**3 + 0*t + 1/9*t**4. Factor o(r).
2*r*(r - 1)*(r + 1)*(r + 2)/9
Let l be 237/(-237)*(-16)/1*1. Factor 0 - l*j - 2/3*j**3 + 28/3*j**2.
-2*j*(j - 12)*(j - 2)/3
Let j(i) = 100*i + 105. Let b be j(-1). Let n(c) be the first derivative of 7/5*c**b - 2/3*c**3 + 0*c**2 + 1 - 5/4*c**4 + 0*c. Suppose n(s) = 0. What is s?
-2/7, 0, 1
Let u(i) be the third derivative of i**5/48 - 5*i**4/32 - 25*i**3/3 + 2*i**2 - 5841. Factor u(y).
5*(y - 8)*(y + 5)/4
Let h(k) = -12*k - 3 + 3 - 21*k. Let q be h(-1). Determine p so that 14*p + 22*p - 6*p**3 - q*p + 3*p**5 = 0.
-1, 0, 1
Let a = -1/92285 + 184591/1937985. Factor 0 + 0*v - 4/21*v**2 - a*v**4 - 2/7*v**3.
-2*v**2*(v + 1)*(v + 2)/21
Let k = -28298 - -28301. Let v(n) be the first derivative of 45 - 4*n - 5*n**2 - 8/3*n**k - 1/2*n**4. What is c in v(c) = 0?
-2, -1
Determine p, given that -1296/19 - 3096/19*p + 206/19*p**3 - 6/19*p**4 - 1588/19*p**2 = 0.
-1, -2/3, 18
Let i be 40/15 - 4/(-3). Suppose -i*b + 0*b = -8. Factor 26*u + 22*u - 12 - 33*u - u**b - 2*u**2.
-3*(u - 4)*(u - 1)
Let h(g) be the first derivative of -g**6/180 + 29*g**5/180 + 5*g**4/18 - 53*g**3/3 + 12. Let f(c) be the third derivative of h(c). Solve f(p) = 0 for p.
-1/3, 10
Let k(b) be the third derivative of b**6/1080 - b**5/360 + 31*b**3/3 - 3*b**2 + 21. Let h(t) be the first derivative of k(t). Factor h(l).
l*(l - 1)/3
Let r(d) be the second derivative of -d**6/75 + 9*d**5/50 - 13*d**4/30 - 3*d**3 + 10*d**2 + 43*d - 2. Solve r(x) = 0.
-2, 1, 5
Suppose -512/5*o**2 + 1/5*o**4 + 0 + 25*o**3 + 516/5*o = 0. Calculate o.
-129, 0, 2
Let l(a) be the third derivative of a**5/75 + 153*a**4 + 702270*a**3 - 3*a**2 - 1229*a. Solve l(p) = 0.
-2295
Suppose 0 = 103*x + 80 - 207 - 182. Determine c, given that 8/9*c**x - 20/9*c**4 + 0 + 16/9*c**2 + 0*c + 2/3*c**5 = 0.
-2/3, 0, 2
Suppose 35 = x - 5*h + 28, -4 = -3*x - 2*h. Factor -4*n**2 + 3*n**2 + 30*n - 27 + 0*n**2 - x*n**2.
-3*(n - 9)*(n - 1)
What is g in 0 - 358/11*g**3 + 16800/11*g + 10/11*g**4 + 2320/11*g**2 = 0?
-21/5, 0, 20
Let m(c) = 9*c**2 + 4*c - 6. Let h be m(2). Let 4*x - 4*x**2 - 5*x + h*x + 15*x = 0. Calculate x.
0, 13
Solve 100*n - 2*n**2 - 27*n + 533 + 297 + 39*n - 598 = 0 for n.
-2, 58
Suppose -4*a + 169 - 89 = 0. Suppose 3 = 4*h - 5. Factor -a*o**2 + 10*o**3 - o - 16*o + h*o - 15*o**3.
-5*o*(o + 1)*(o + 3)
Let b(r) be the second derivative of r**7/105 + 8*r**6/75 - 12*r**5/25 - 19*r**4/15 + 23*r**3/15 + 6*r**2 + 4044*r. Let b(w) = 0. Calculate w.
-10, -1, 1, 3
Let f be 3447/(-21831)*28/(-6). Let -6/19*o**2 + 0 + 0*o + f*o**3 - 4/19*o**4 = 0. What is o?
0, 1/2, 3
Let a(j) be the first derivative of -j**5/5 - 9*j**4/2 - 80*j**3/3 + 9*j**2 + 81*j - 1629. Factor a(n).
-(n - 1)*(n + 1)*(n + 9)**2
Let k(w) be the third derivative of -1 - 61/120*w**6 + 23/30*w**5 - 35*w**2 - 64/3*w**3 - 1/336*w**8 - 8/105*w**7 + 20/