4*c(o) - 6*i(o). Factor s(w).
4*w*(w - 13)*(w + 1)*(2*w + 1)
Let u(o) be the first derivative of o**5/140 + o**4/6 + 15*o + 70. Let v(q) be the first derivative of u(q). Factor v(a).
a**2*(a + 14)/7
Factor -80 + 2/9*c**2 + 134/9*c.
2*(c - 5)*(c + 72)/9
Suppose 42*n + 94 = 89*n. Let z(p) be the second derivative of p**3 - 1/6*p**4 + 0*p**n - 10*p + 0. Factor z(m).
-2*m*(m - 3)
Let 8/5*o**2 + 4/5*o**3 + 0*o + 0 = 0. Calculate o.
-2, 0
Let k = 185204 + -185054. Suppose -10/3*l**4 + 172/3*l**2 - 110*l + 44/3*l**3 - 2/3*l**5 - k = 0. What is l?
-5, -1, 3
Find u, given that 686000/3*u + 140*u**3 + 2/3*u**4 + 9800*u**2 + 0 = 0.
-70, 0
Let k(o) = -o**2 - o. Let p(x) = 24*x + 40. Let j(d) = -d**2 - 9*d - 16. Let b be j(-5). Let r(s) = b*k(s) - p(s). Determine g so that r(g) = 0.
-5, -2
Let k(l) be the second derivative of -l**7/840 + l**6/120 + l**5/20 - l**4/3 - 13*l**3 - 3*l + 18. Let j(w) be the second derivative of k(w). Factor j(g).
-(g - 4)*(g - 1)*(g + 2)
Let p(r) = 68*r**3 + 88*r**2 - 320*r - 1248. Let x(l) = -23*l**3 - 29*l**2 + 107*l + 396. Let b(d) = -5*p(d) - 16*x(d). Factor b(z).
4*(z - 2)*(z + 2)*(7*z + 6)
Let u(o) be the third derivative of o**7/1512 - 5*o**6/216 + o**4/8 + 12*o**2. Let d(c) be the second derivative of u(c). Factor d(h).
5*h*(h - 10)/3
Let z = 1564 + -1515. Suppose 0 = z*w - 198 + 51. Factor 1 - 5/4*c**2 + 1/4*c**4 + 3/4*c - 3/4*c**w.
(c - 4)*(c - 1)*(c + 1)**2/4
Let b(t) be the first derivative of -28*t**3/3 - 3258*t**2 + 1864*t + 8218. Factor b(f).
-4*(f + 233)*(7*f - 2)
Let d(z) = z**2 + 11*z - 2. Let u be d(-15). Let q be 2/(-9) - u/(-18). Factor -12*f**2 + 6*f + 70*f**q + 3*f**2 - 67*f**3.
3*f*(f - 2)*(f - 1)
Let 14080/7 - 3776/7*b - 4/7*b**3 + 284/7*b**2 = 0. What is b?
8, 55
Let q(s) be the first derivative of 2*s**3/3 + 5271*s**2/4 - 659*s - 13476. Suppose q(v) = 0. Calculate v.
-1318, 1/4
Let u(i) = i**3 + 9*i**2 + 11*i - 7. Let s be u(-7). Factor -16*k + 30 - k**2 + 3*k + s*k.
-(k - 6)*(k + 5)
Let m be (-364)/572 + (-6505)/(-110). Factor 3/2*u**3 - 63/2*u**2 - 57/2 + m*u.
3*(u - 19)*(u - 1)**2/2
Let i(h) be the first derivative of -35/2*h**2 + 10 - 25/3*h**3 - 5/4*h**4 - 15*h. Factor i(u).
-5*(u + 1)**2*(u + 3)
Let s = 162855/1303352 + 8/162919. Factor -11/8 - s*c**2 + 3/2*c.
-(c - 11)*(c - 1)/8
Suppose 4*v + 236 = n - 3*n, v - 3*n = -45. Let q = v + 115/2. Suppose 2 - q*m**2 + 3/2*m = 0. Calculate m.
-1, 4
Let o(f) = -f**2 - 26*f - 65. Let n be o(-23). Determine v, given that 2*v**n + 7*v**2 + 29*v**2 - 8*v**2 + 2*v**4 + 12*v + 20*v**3 = 0.
-3, -1, 0
Suppose 32 = 5*h - 18. Determine o, given that -h*o - o**2 - 20 + 20 = 0.
-10, 0
Let h(j) be the first derivative of j**3/3 + 71*j**2/2 + 448*j + 13036. Factor h(v).
(v + 7)*(v + 64)
Let v = -3973397/80 + 49672. Let s(z) be the second derivative of 43*z - 6*z**3 - 165/16*z**4 - v*z**5 - 3/2*z**2 + 0. Solve s(h) = 0 for h.
-1, -2/11
Determine x so that -95 + 39*x**2 - 81*x**2 - 505 + 39*x**2 - 90*x = 0.
-20, -10
Let n(q) be the third derivative of q**7/175 + 53*q**6/75 + 341*q**5/150 - 14*q**4/3 - 92*q**3/5 + 6*q**2 - 429*q. Let n(v) = 0. Calculate v.
-69, -2, -2/3, 1
Let l(d) be the first derivative of 3*d**5/4 + 9*d**4/8 - 9*d**3/4 - 3*d**2/4 - 1664. Determine n, given that l(n) = 0.
-2, -1/5, 0, 1
Let z(v) be the second derivative of 0*v**3 - 1/42*v**7 + 0*v**2 + 1/20*v**5 - 1/15*v**6 - 4 + 1/6*v**4 + 24*v. Solve z(q) = 0 for q.
-2, -1, 0, 1
Let i(x) be the second derivative of x**7/14 + 24*x**6/5 + 933*x**5/10 + 276*x**4 + 529*x**3/2 - 1302*x. Factor i(c).
3*c*(c + 1)**2*(c + 23)**2
Let o(i) be the first derivative of 0*i - 80 + 0*i**3 + 1/6*i**4 + 0*i**2. Factor o(x).
2*x**3/3
Let i be (-46)/(-60) - 16/24. Let v(l) be the second derivative of i*l**5 - 1/3*l**4 + 0*l**2 - 15*l + 1/3*l**3 + 0. What is c in v(c) = 0?
0, 1
Let q(y) be the third derivative of -y**7/8820 - y**6/140 - 27*y**5/140 + y**4/24 + 28*y**3/3 - 99*y**2. Let k(r) be the second derivative of q(r). Factor k(h).
-2*(h + 9)**2/7
Factor 384 + 58*z - 361019*z**2 - z**3 + 360954*z**2 + 2*z**3.
(z - 64)*(z - 3)*(z + 2)
Let y(b) be the third derivative of b**8/1176 + b**7/735 - 47*b**6/420 - 173*b**5/210 - 103*b**4/42 - 80*b**3/21 + 3*b**2 + 52. Suppose y(f) = 0. What is f?
-5, -2, -1, 8
Let j(x) = -197*x**3 + 464*x**2 - 6737*x + 6294. Let n(l) = -1725*l**3 + 4175*l**2 - 60635*l + 56645. Let y(s) = -35*j(s) + 4*n(s). Factor y(q).
-5*(q - 74)*(q - 17)*(q - 1)
Let n(r) be the first derivative of 4*r**2 - 4/3*r**3 - 4*r + 70. Solve n(v) = 0 for v.
1
Let o = 755/3 - 2263/9. Let w(c) be the first derivative of -2*c + 1/6*c**4 - 5/3*c**2 + 11 - o*c**3. Find l such that w(l) = 0.
-1, 3
Let g(w) be the third derivative of -w**7/2100 - 113*w**6/1200 - 377*w**5/75 + 841*w**4/20 + 620*w**2 + 2. Solve g(m) = 0.
-58, 0, 3
Let y(h) be the first derivative of -h**4/2 - 6*h**3 - 14*h**2 - 1215. Find d, given that y(d) = 0.
-7, -2, 0
Let y(k) be the second derivative of -k**7/14 - 117*k**6/40 - 51*k**5/80 + 343*k**4/16 - 147*k**3/8 - 87*k**2/4 - 769*k. Solve y(h) = 0.
-29, -2, -1/4, 1
Let h(p) = -2*p**4 - p**3 + p**2 - p + 1. Let o(f) = 1530*f**4 + 5949*f**3 - 7989*f**2 + 3156*f - 402. Let c(t) = -3*h(t) + o(t). Factor c(q).
3*(q + 5)*(8*q - 3)**3
Let v be 60/(-72)*((-12)/(-21))/(28/(-294)). Find c such that 14/11*c**3 + 2/11*c**2 + 8/11 - 10/11*c**4 - 16/11*c + 2/11*c**v = 0.
-1, 1, 2
Let p(s) = 18 - 6*s - 35*s**2 + 34*s**2 + 27 - 15. Let n be p(-9). Suppose 156*a + 0*a**n - 5*a**3 - 156*a = 0. What is a?
0
Suppose 79*b + 30 - 60 = 128. Factor -1/9*c**b - 9 + 2*c.
-(c - 9)**2/9
Let y(m) = -m + 20. Let h be y(15). Factor -3*a**3 + 8*a**2 - 10*a**2 + h*a**2.
-3*a**2*(a - 1)
Let a(y) = y**3 - 26*y**2 + 16*y. Let o be a(26). Factor 19*f + 49*f + o*f**2 - 412*f**2.
4*f*(f + 17)
Let a(j) be the first derivative of -j**4/4 + 13*j**3/2 - 18*j**2 - 108*j - 134. Let k(w) be the first derivative of a(w). Factor k(l).
-3*(l - 12)*(l - 1)
Let v = -61164 - -61168. Factor -9/4*n**2 + 0*n - 1/4*n**v + 0 - 5/2*n**3.
-n**2*(n + 1)*(n + 9)/4
Let v(x) be the first derivative of -2*x**5/125 - 37*x**4/25 - 128*x**3/5 - 182*x**2 - 590*x - 5464. Factor v(y).
-2*(y + 5)**3*(y + 59)/25
Let m be 12 + 16/6*(-468)/104 - 1/(-2). Suppose 9 = 3*w - 4*o - 7, 2*o = -8. Suppose 1/4*s**5 + 0*s**3 + w - 1/4*s - 1/2*s**2 + m*s**4 = 0. What is s?
-1, 0, 1
Suppose 0 = 20*t - 15*t + 4*o + 29, -3*t - 4*o - 35 = 0. Determine i so that 15*i + 85/2*i**2 + 0 - 15/2*i**t = 0.
-1/3, 0, 6
Suppose -24*w = -7*w + 170. Let v(h) = -2*h**2 - 23*h - 28. Let z be v(w). Factor -3/2 - 6*r**3 + 21/2*r**z - 3*r.
-3*(r - 1)**2*(4*r + 1)/2
Suppose -2*b = 4*v - 114, b - 366 = -5*v - 291. Let z be ((-2)/(-2) + -30)*-7. Determine u, given that 26 + 3*u**3 + 144*u - 37 - b*u**2 + z = 0.
-1, 8
Let t(k) be the second derivative of -k**8/3360 + 3*k**7/560 - k**6/36 - 11*k**3/6 + 7*k**2/2 - 143*k. Let y(p) be the second derivative of t(p). Factor y(f).
-f**2*(f - 5)*(f - 4)/2
Let d(t) = -4*t**2 + 2080*t - 90820. Suppose -a + 33 = 41. Let o(j) = -j**2 + 693*j - 30273. Let l(m) = a*o(m) + 3*d(m). Factor l(y).
-4*(y - 87)**2
Let w(h) be the first derivative of 0*h + 32/11*h**3 - 42/55*h**5 - 84 - 12/11*h**4 - 1/11*h**6 + 0*h**2. Factor w(x).
-6*x**2*(x - 1)*(x + 4)**2/11
Let s(i) be the third derivative of 23*i**7/56 - 231*i**6/80 + i**5/10 + 2*i**2 + i - 2. Factor s(b).
3*b**2*(b - 4)*(115*b - 2)/4
Let l = -193 - -4055/21. Let f(h) be the first derivative of 2/35*h**5 + 0*h + 1/14*h**4 - 1/7*h**2 + 10 - l*h**3. Factor f(a).
2*a*(a - 1)*(a + 1)**2/7
Let c = -7775/1218 + 373/58. Let w(l) be the second derivative of 4/35*l**5 + 1/147*l**7 - 2/35*l**6 + 4/7*l**2 + 0 - 37*l - 3/7*l**3 + c*l**4. Factor w(z).
2*(z - 4)*(z - 1)**3*(z + 1)/7
Suppose 0 = -13*p + 1480 - 1428. Let s(g) be the third derivative of 7*g**2 - 5/24*g**p + 2*g + 0*g**3 - 1/12*g**5 + 0. Solve s(v) = 0 for v.
-1, 0
Let w(j) be the first derivative of 4*j**3/3 + 96*j**2 + 1404*j + 762. Factor w(h).
4*(h + 9)*(h + 39)
Let g be 5/20*((-7)/5 - 19952/(-430)). Factor g*d**2 + 15*d**3 + 0 + 5/4*d**4 - 55/2*d.
5*d*(d - 1)*(d + 2)*(d + 11)/4
Let i(y) be the second derivative of -y**5/4 + 1285*y**4/12 + 215*y**3 + 172*y + 3. Solve i(x) = 0 for x.
-1, 0, 258
Find k, given that -63 + 33*k**3 - 9/4*k**4 - 579/4*k**2 + 177*k = 0.
2/3