be the third derivative of 0*f - 1/270*f**6 - 40*f**2 - 32/27*f**3 + 7/135*f**5 - 4/27*f**4 + 0. Factor j(d).
-4*(d - 4)**2*(d + 1)/9
Let c(u) be the second derivative of 0 - 1/24*u**4 + 5/6*u**3 + 0*u**2 - 1/240*u**5 + 42*u + 1/720*u**6. Let i(b) be the second derivative of c(b). Factor i(l).
(l - 2)*(l + 1)/2
Let t(b) = -20*b + 78. Let s be t(4). Let z be ((-17)/(-17 - 442))/(s/(-12)). Factor 20/9*r - z*r**2 - 50/9.
-2*(r - 5)**2/9
Let k(n) be the second derivative of n**5/100 + 13*n**4/20 - 97*n**3/30 - 123*n**2/2 + 1896*n. Factor k(u).
(u - 5)*(u + 3)*(u + 41)/5
Let y(g) be the third derivative of 12*g**2 - 5 + 7/75*g**5 + 1/300*g**6 - 49/60*g**4 + 0*g + 34/15*g**3. Find p such that y(p) = 0.
-17, 1, 2
Factor 49/2*i**4 + 0*i**2 + 0 + 0*i + 0*i**3 - 1/4*i**5.
-i**4*(i - 98)/4
Suppose -11*p - 65 = -6*p. Let w be (11 + p)/((-4)/6). Factor 3*r**2 - 3 + 10 - 20*r + 4*r**w - 4*r**4 + 1 + 9*r**2.
-4*(r - 1)**3*(r + 2)
Let v(u) be the third derivative of 0 - 1/15*u**5 + 0*u - 135*u**2 - 5/84*u**8 - 2/35*u**7 + 17/30*u**6 - 2*u**4 + 8/3*u**3. Determine d so that v(d) = 0.
-2, -1, 2/5, 1
Let p(u) be the first derivative of 2*u**5/5 + 13*u**4 + 224*u**3/3 + 150*u**2 + 126*u + 586. Determine j so that p(j) = 0.
-21, -3, -1
Find y, given that -5792*y**2 - 5793*y**2 + 11580*y**2 + 850*y - 36125 = 0.
85
Suppose -53*r**4 + 140608*r + 2860*r**3 + 0 + 1/3*r**5 - 164944/3*r**2 = 0. Calculate r.
0, 3, 52
Let s(a) be the second derivative of -4*a**5/5 + 17*a**4/3 - 40*a**3/3 + 8*a**2 - 16*a - 25. Factor s(f).
-4*(f - 2)**2*(4*f - 1)
Let h be (-3)/2*(-9 + 5). Factor 0*y - h*y + 77*y**3 - 73*y**3 + 2*y - 12 + 12*y**2.
4*(y - 1)*(y + 1)*(y + 3)
Let w be (-4)/(-98) + (-44145)/(-96138). Factor -h**3 - 3/2*h**2 + w*h**4 - 2 + 4*h.
(h - 2)*(h - 1)**2*(h + 2)/2
Let j be ((-20)/(-63))/(-5) + (6 - (-1520)/(-266)). Solve -j*p**3 + 2*p**2 + 40/9 - 16/3*p = 0 for p.
2, 5
Suppose -20 - 69/5*j**2 + 72*j - 529/5*j**3 = 0. What is j?
-1, 10/23
Let p(a) be the second derivative of a**8/8400 + a**7/2100 - a**6/600 - a**3/3 - 10*a. Let h(i) be the second derivative of p(i). Find c, given that h(c) = 0.
-3, 0, 1
Let z = -7989 - -39948/5. Factor -z + 0*g + 3/5*g**2.
3*(g - 1)*(g + 1)/5
Let v(a) be the third derivative of a**7/98 + 37*a**6/280 + 9*a**5/140 - 37*a**4/56 - a**3 - 2*a**2 + 319*a. Suppose v(b) = 0. What is b?
-7, -1, -2/5, 1
Let g(y) = y**3 - 188*y**2 + 379*y - 1300. Let q be g(186). Factor 5/2*m + 1/2*m**q + 0.
m*(m + 5)/2
Let v(h) be the third derivative of -5*h**7/14 - 13*h**6 - 886*h**5/5 - 1092*h**4 - 3528*h**3 + 7*h**2 - 66*h. Determine q so that v(q) = 0.
-42/5, -2
Let s(r) be the second derivative of 3*r**5/80 - 2781*r**4/16 + 2577987*r**3/8 - 2389793949*r**2/8 - 4403*r. Factor s(f).
3*(f - 927)**3/4
Suppose 4 + 87 + 820 - 40*v**2 - 357*v - v**3 - 29 = 0. Calculate v.
-21, 2
Let p = -33878 + 33880. Let v(t) be the second derivative of -5/24*t**4 - 5*t**p + 21*t + 5/3*t**3 + 0. Determine u so that v(u) = 0.
2
Factor -336/13 - 340/13*j**2 + 674/13*j + 2/13*j**3.
2*(j - 168)*(j - 1)**2/13
Let u = -1287 - -1258. Let b be (-83)/747 - u/18. What is k in -b*k**4 + 3/2*k - 3 - 3/2*k**3 + 9/2*k**2 = 0?
-2, -1, 1
Let g be -6 + (2 - 0) + 31096/1014. Find d such that 5*d**2 + g*d - 20 = 0.
-6, 2/3
Solve -65 + 1490*h - 31 + 110*h**2 + 16*h**3 - 2*h**3 - 1518*h = 0 for h.
-8, -6/7, 1
Let y(n) be the first derivative of -n**4 + 1792*n**3 - 1204224*n**2 + 359661568*n + 2892. Factor y(o).
-4*(o - 448)**3
Let t(v) = v**3 - 36*v**2 - 111*v - 232. Let n be t(39). Factor -4 - 1/5*r**4 + n*r**3 - 33/5*r**2 + 44/5*r.
-(r - 5)*(r - 2)**2*(r - 1)/5
Let f(r) = 2*r**3 + 164*r**2 - 1366*r. Suppose -773*w - 9 = -776*w. Let o(t) = t**3 + 54*t**2 - 456*t. Let u(g) = w*f(g) - 8*o(g). Factor u(z).
-2*z*(z - 15)**2
Let g(o) be the third derivative of 12 + 0*o - 1/2016*o**8 + 1/315*o**7 + 5/144*o**4 - 1/180*o**6 - 1/180*o**5 - 5*o**2 - 1/18*o**3. Factor g(x).
-(x - 2)*(x - 1)**3*(x + 1)/6
Let m be -22*(3 - (-1 - (-405)/10)). Let p = m - 799. Solve -2/3*w**p - 4/3*w**3 - 8/3 + 2*w**2 + 8/3*w = 0.
-2, 1
Let r = 481 + -17315/36. Let t(d) be the first derivative of 1/12*d**2 + 1/9*d**3 + r*d**6 - 1/30*d**5 - 12 - 1/12*d**4 - 1/6*d. Let t(n) = 0. Calculate n.
-1, 1
Let h(p) be the third derivative of p**7/1050 + 71*p**6/600 + 127*p**5/60 + 305*p**4/24 - 2*p**2 - 2*p - 976. Factor h(d).
d*(d + 5)**2*(d + 61)/5
Suppose 19057*x**3 + 13*x**2 + 56*x**4 - 19461*x**3 + 71*x**2 = 0. Calculate x.
0, 3/14, 7
Let y(j) be the second derivative of j**7/147 - 3*j**6/35 + 11*j**5/70 + 39*j**4/14 - 144*j**3/7 + 432*j**2/7 - 10*j + 92. Suppose y(q) = 0. What is q?
-4, 3, 4
Let a(h) be the first derivative of 56 + 15*h - 5/3*h**3 + 5*h**2. Factor a(q).
-5*(q - 3)*(q + 1)
Let m = 2197860/11 + -199804. Solve -2/11*k + 8/11*k**4 - m*k**2 - 2/11*k**5 + 4/11*k**3 + 8/11 = 0 for k.
-1, 1, 4
Factor -41*l**3 - 259922*l + 43*l**3 - 2022*l**2 + 286319*l - 76545506 + 655017*l.
2*(l - 337)**3
Let w(v) = -v**2 - 29*v - 10. Let m(t) = -3*t. Let o(q) = 6*m(q) - w(q). Let b be o(-10). Find x, given that 3/4*x**3 + b - 3/4*x + 0*x**2 = 0.
-1, 0, 1
Factor -2273/3*y + 910/3 - 3190/3*y**2 - 7/3*y**3.
-(y + 1)*(y + 455)*(7*y - 2)/3
Let s = 752 - 683. Let k = 277/4 - s. Let -1/4 - 1/2*b - k*b**2 = 0. Calculate b.
-1
Let w(x) be the third derivative of -2 + 1/15*x**5 - 1/3*x**4 + 2/3*x**3 + 0*x + 19*x**2. Find m, given that w(m) = 0.
1
Let s(r) be the third derivative of -74*r**7/105 - 94*r**6/15 - 274*r**5/15 - 22*r**4 - 6*r**3 + 2*r**2 + 8618. Solve s(q) = 0.
-3, -1, -3/37
Find k, given that -2178*k**2 - 6*k**4 - 13872/7 + 1518/7*k**3 + 27642/7*k = 0.
1, 8/7, 17
Factor -7*t - 1/5*t**2 - 306/5.
-(t + 17)*(t + 18)/5
Suppose -2*d + 4*i - 6 = -0*d, 0 = -2*d + i + 3. Factor 1672*o**4 + 30*o - 17 + 36*o**2 - 1675*o**4 - 30*o**d - 16.
-3*(o - 1)**2*(o + 1)*(o + 11)
Let g(x) = 12*x**2 + 211*x + 585. Let k(h) = 48*h**2 + 846*h + 2340. Let a(r) = 15*g(r) - 4*k(r). Factor a(l).
-3*(l + 15)*(4*l + 13)
Let s(l) be the second derivative of l**6/135 + l**5/30 - 71*l**4/54 + 59*l**3/9 - 110*l**2/9 + 2*l + 596. Determine m, given that s(m) = 0.
-11, 1, 2, 5
Let m(l) be the second derivative of -147*l**5/20 - 91*l**4/4 + 783*l**3/8 + 2187*l**2/4 + 17*l + 119. Solve m(v) = 0.
-27/14, 2
Let b(h) = -h**2 + 3*h - 8. Let s be b(2). Let q be (-13)/(-5) + s/(-15). Factor -12 + 75*d**q + 63*d + 2*d**2 - 63*d**3 - 65*d**2.
3*(d - 4)*(d - 1)*(4*d - 1)
Let b(r) be the third derivative of 0*r + 0*r**3 - 1/6*r**5 - 5/8*r**4 + 0 + 7*r**2 + 1/24*r**6. Determine o, given that b(o) = 0.
-1, 0, 3
Let m = -64163/276 - -16196/69. Let 0 + m*k**2 - k = 0. Calculate k.
0, 4/9
Let s(y) be the second derivative of y**6/15 - 8*y**5/5 + 15*y**4/2 + 54*y**3 + 2*y + 204. Factor s(p).
2*p*(p - 9)**2*(p + 2)
Let l = 45103/5 - 180307/20. Determine g, given that -117*g - 267/4*g**3 - 465/2*g**2 - l*g**4 + 54 = 0.
-6, -1, 2/7
Let p = -12 + 16. Suppose 2*i - 5*b + 14 = 0, 4*b - 11 - 20 = -5*i. Factor 6*y**4 - y**5 - 8*y**p + 2*y**4 - y**4 + 2*y**i.
-y**3*(y - 1)*(y + 2)
Let s = 139613/11170 + 6/5585. Factor -s + 5/4*c**3 + 25/2*c**2 - 5/4*c.
5*(c - 1)*(c + 1)*(c + 10)/4
Let n be (-70)/(-12) + 4/(-168)*-7. Suppose n*v = 40 + 20. Find x, given that -8*x**2 + 15*x**4 - 5*x**3 + v - 10*x**4 - 7*x**2 + 5*x = 0.
-1, 1, 2
Let h be 136/51 + (-2)/(-6). Factor 1875*y**2 + y**4 + 21458*y + 41*y**3 - 5833*y + 33*y**h + y**3.
y*(y + 25)**3
Suppose 2*w + 5*p + 12 = 0, -p = -6*w + 7*w. Suppose -3*b = -3*x - 18, 12 = -10*b + 8*b - w*x. Factor 2/3*v**b + 0*v + 2/3*v**4 + 4/3*v**3 + 0.
2*v**2*(v + 1)**2/3
Let j(z) = -6*z**2 - 12*z - 2. Let x be j(-1). Factor y**4 + 6*y**2 - 13*y**3 + 20*y**3 + 9*y**2 - x*y**2 + 5*y.
y*(y + 1)**2*(y + 5)
Let w = -757 + 292. Let r = 3263/7 + w. Let r*z**2 - 2/7 - 6/7*z = 0. Calculate z.
-1/4, 1
Let z = 429803/5 - 85935. Determine j so that -192/5 + 236/15*j**2 + 2/15*j**4 + 46/15*j**3 - z*j = 0.
-12, -1, 2
Let r(q) = q**2 - 18*q + 39. Let h be r(16). Factor 5*n**3 - 5*n**4 + 160 - 170 + h*n**2 + 8*n**2 - 5*n.
-5*(n - 2)*(n - 1)*(n + 1)**2
Let u be (1 - (-15)/(-20))/((-9)/(-108)). Suppose 3*v - 7 + 13 = 3*x, v - u*x = -12. Let 2/7*p + 2/7*p**2 - 2/7*p**v + 0 - 2/7*p**4 = 0. What is p?
-1, 0, 1
Let d = 163/1265 - -18/253. Factor d*y**2 + 0*y - 1/5.
(y - 1)*(y + 1)/5
Let s(f)