53/8*j**2 = 0.
-17
Let g(m) = -11*m**3 - 12*m**2 + 37*m + 46. Let l(k) = 75*k**3 + 84*k**2 - 261*k - 324. Let w(d) = -27*g(d) - 4*l(d). Determine n, given that w(n) = 0.
-6, -1, 3
Suppose 5*h + 9*f - 267 - 28 = 4*f, -11*f + 11 = 0. Factor -44/5*t**4 - 2/5*t**5 - 1024/5 + 1664/5*t - 304/5*t**2 - h*t**3.
-2*(t - 1)**2*(t + 8)**3/5
Let p(i) be the first derivative of i**6/840 - 19*i**5/140 + 215*i**3/3 + 92. Let q(w) be the third derivative of p(w). Factor q(v).
3*v*(v - 38)/7
Let a(j) be the first derivative of 6*j**2 - 133 - 8/3*j**3 + 2/3*j**6 - 4*j**4 + 0*j**5 + 8*j. Factor a(h).
4*(h - 2)*(h - 1)*(h + 1)**3
Let x be ((-32430)/(-15))/(-46) + 49. Determine l, given that 0 + 14/25*l**x - 2/25*l**4 - 4/5*l + 8/25*l**3 = 0.
-2, 0, 1, 5
Let s be 1328/80 + (10 - 0). Let o = -394/15 + s. Factor -i - o + 1/3*i**2 + i**3.
(i - 1)*(i + 1)*(3*i + 1)/3
Let w(l) = 9*l**2 + 315*l + 648. Let j(h) = -35*h**2 - 1262*h - 2591. Let s(q) = 6*j(q) + 23*w(q). Suppose s(a) = 0. Calculate a.
-107, -2
Let y be (10642/(-8451))/(-3 - 100/(-36)). Let o = -284/3 + 98. Factor -o*m**2 + y*m - 8/3 + 1/3*m**3.
(m - 8)*(m - 1)**2/3
Let p(c) = c**5 + 7*c**4 - 10*c**3 - 34*c**2 - 6*c + 12. Let m(a) = -a**5 - 8*a**4 + 11*a**3 + 33*a**2 + 5*a - 10. Let b(d) = 6*m(d) + 5*p(d). Factor b(g).
-g**2*(g - 2)*(g + 1)*(g + 14)
Let i(w) be the second derivative of -7*w**6/90 + 709*w**5/60 + 310*w**4/9 - 206*w**3/9 + 1509*w. Find q, given that i(q) = 0.
-2, 0, 2/7, 103
Let l(z) be the first derivative of -z**5 + 335*z**4/4 - 650*z**3/3 + 2821. Solve l(s) = 0.
0, 2, 65
Let l(h) be the third derivative of 1/24*h**5 - 98*h**2 + 0*h - 1/8*h**4 + 1/12*h**3 + 0. Factor l(x).
(x - 1)*(5*x - 1)/2
Let l(q) be the second derivative of 11*q**7/28 + 5*q**6/4 - 81*q**5/40 - 53*q**4/8 + 8*q**3 + 9*q**2 - 616*q. What is w in l(w) = 0?
-2, -3/11, 1
Find k such that 156*k**2 + 6227*k + 4*k**3 - 12086*k + 6155*k = 0.
-37, -2, 0
Suppose 21/2 - 11/4*a - 1/4*a**2 = 0. Calculate a.
-14, 3
Let j(b) be the first derivative of b**3 + 3/28*b**4 - 101 + 45/14*b**2 + 27/7*b. Factor j(o).
3*(o + 1)*(o + 3)**2/7
Suppose 46 = 3*l + 2*i, 5*i + 4 + 7 = 3*l. Find q such that 85*q**2 + 51 + 110*q + l*q**4 - 5*q**3 - 11 - 5*q**5 - 37*q**4 = 0.
-4, -1, 2
Suppose 89 = 16*p - 55. Factor -13*d - d**2 + 8*d + 5*d**2 - p*d**2.
-5*d*(d + 1)
Factor 0 + 0*m - 125/3*m**2 - 1/6*m**3.
-m**2*(m + 250)/6
Let o = -738251/3 - -246084. Find z, given that 2/3*z**4 + 0*z**3 + o*z - 1/3*z**5 - 2/3*z**2 + 0 = 0.
-1, 0, 1
Suppose -5*z = -i - 8, -3*i + 0*z = -5*z + 4. Factor 0 + 1/2*a**i - 1/2*a - 1/2*a**4 + 1/2*a**3.
-a*(a - 1)**2*(a + 1)/2
Let u = 34/16443 - -175358/16443. Solve 80/3 + u*l**3 - 116/3*l**2 + 12*l**4 - 32/3*l = 0.
-2, -1, 1, 10/9
Let u be (53 - -17)*(-2)/(-4). Suppose -174*f**2 + 2 - 10*f - u*f - 88*f**3 - 39*f = 0. What is f?
-1, 1/44
Let f(q) = -19*q + 75. Let w be f(19). Let j = -283 - w. Determine i, given that -1/8*i**2 + 1/8*i**4 - 1/8*i + 0 + 1/8*i**j = 0.
-1, 0, 1
Let y(g) be the first derivative of -g**4/20 + 2546*g**3/5 - 9723174*g**2/5 + 16503467336*g/5 + 6244. Determine n, given that y(n) = 0.
2546
Factor 186*i**2 + 2*i**3 - 88*i**2 - 136 + 274*i - 238*i**2.
2*(i - 68)*(i - 1)**2
Let c be (-24 + 0/(-1))*14/(-21). Let j be (120/c - 10) + 4 + -1. Factor 0 - 1/4*u**2 + 1/4*u**3 - j*u.
u*(u - 2)*(u + 1)/4
Suppose 4*g - 14 = 2. Let c be 6 + ((-28)/(-5))/(-25*(-402)/(-8375)). Suppose 2*j**g + 8/3*j**3 + 0 - 2/3*j**2 - c*j = 0. What is j?
-1, 0, 2/3
Factor -8/3 + 2/9*l**5 + 2/3*l**3 - 46/9*l**2 - 64/9*l + 14/9*l**4.
2*(l - 2)*(l + 1)**3*(l + 6)/9
Let l be ((-7)/(-22) + (-4)/(-22))*10. Factor -3*j**2 - 3785*j + 3*j**2 - l*j**2 + 3800*j - 10.
-5*(j - 2)*(j - 1)
Let a = 35 + -16. Factor -16*y + 13*y**2 - 7 - 4 + a - 3*y**3 - 4.
-(y - 2)**2*(3*y - 1)
Let t(b) = 57*b**4 - 3*b**3 + 6*b**2 + 12*b + 24. Let x(h) = -5*h**4 - h - 2. Let j(k) = -t(k) - 12*x(k). Determine d, given that j(d) = 0.
-2, 0, 1
Let z(j) = -j**3 - 15*j**2 - 26*j + 5. Let y = -4 - 9. Let d be z(y). Factor -61*k - d*k**2 + 5*k + 26*k.
-5*k*(k + 6)
Let p(c) be the second derivative of 3/2*c**3 + 110*c - 1/8*c**4 - 27/4*c**2 - 2. Factor p(k).
-3*(k - 3)**2/2
Let l(z) be the third derivative of z**7/42 + z**6/40 - 287*z**5/60 + 263*z**4/8 - 45*z**3 - 3*z**2 + 10*z + 40. What is k in l(k) = 0?
-9, 2/5, 3, 5
Let a be ((-2)/(-12))/(382/(-1146)) + 278/12 + -2. Factor -2/3*z**5 + 392/3 - 1232/3*z - 566/3*z**3 + 1346/3*z**2 + a*z**4.
-2*(z - 14)**2*(z - 1)**3/3
Let c(x) = 13*x - 324. Let y be c(24). Let r be (-14)/4*((-960)/70 - y). Factor r*h + 0 - 4*h**2 + 2/3*h**3.
2*h*(h - 3)**2/3
Let w(z) be the third derivative of -3*z**6/160 - 101*z**5/80 + 619*z**4/32 - 195*z**3/8 + 1384*z**2. Let w(m) = 0. Calculate m.
-39, 1/3, 5
Suppose -4*w = -3*n + 20 + 2, -3*n = 2*w + 2. Determine l, given that 359*l + 0*l**2 - 24 - 3*l**n - 184*l - 202*l = 0.
-8, -1
Let x(u) be the third derivative of u**6/1080 + u**5/180 + 299*u**3/6 - 169*u**2. Let v(o) be the first derivative of x(o). Let v(w) = 0. Calculate w.
-2, 0
Let h(x) = -44*x**3 + 204*x**2 + 620*x - 264. Let j(d) = d**3 + 8*d**2 - 2*d. Let l(t) = -h(t) - 12*j(t). Factor l(w).
4*(w - 11)*(w + 2)*(8*w - 3)
Let a = -5329333/8 + 666167. Suppose -a*x + 6*x**5 + 0 + 51/8*x**4 - 45/8*x**3 - 51/8*x**2 = 0. Calculate x.
-1, -1/16, 0, 1
Suppose -2*r = 3*r - h - 315, 252 = 4*r - 3*h. Let b be (-32)/(-18) + 14/r. Factor 21*k**b + k - 16*k**2 - 5*k**3 + 9*k.
-5*k*(k - 2)*(k + 1)
Suppose 25 = w + 22. Solve 18*n**5 + 19*n**2 + 6*n**3 - 20*n**5 + 8*n - 4*n**4 - w*n**2 = 0 for n.
-2, -1, 0, 2
Suppose 50 = 25*v - 25. Determine h so that 4*h**2 - 3*h**3 - h**2 + 15*h**v - 3*h - 13*h**3 + 1 = 0.
1
Factor -580/3*u + 0 + 5/3*u**2.
5*u*(u - 116)/3
Let w be (-3134*(-3)/(-96))/((-10)/40). Let k = 392 - w. Factor 3/4*g**3 - k*g**5 - 1/2*g**2 + 0*g + 0*g**4 + 0.
-g**2*(g - 1)**2*(g + 2)/4
Let o(d) be the second derivative of 32*d**6/45 + 204*d**5/5 + 2491*d**4/3 + 98315*d**3/18 - 148877*d**2/4 - 503*d - 2. Determine m, given that o(m) = 0.
-53/4, 3/2
Let v(c) be the first derivative of c**7/70 + 3*c**6/10 + 21*c**5/20 + 5*c**4/4 - 13*c**2 + 2*c - 192. Let r(y) be the second derivative of v(y). Factor r(h).
3*h*(h + 1)**2*(h + 10)
Let v(l) be the second derivative of 1/120*l**5 + 15/2*l**2 - 2*l - 5/12*l**3 + 0 + 1/12*l**4. Let z(q) be the first derivative of v(q). Factor z(h).
(h - 1)*(h + 5)/2
Let n = 0 + 2. Let y be (1 + (-104)/39)*-3*1. Solve 450*o**n + 852 - 80*o**3 - 1000*o + y*o**4 - 150 - 77 = 0 for o.
1, 5
Let b(p) be the first derivative of -2*p**7/21 + 4*p**6/5 - 9*p**5/5 + 4*p**4/3 + 168*p + 58. Let l(z) be the first derivative of b(z). Factor l(r).
-4*r**2*(r - 4)*(r - 1)**2
Let c(q) be the first derivative of 8 + 95/4*q**4 + 20*q + 5/6*q**6 + 7*q**5 + 40*q**2 + 125/3*q**3. Determine i so that c(i) = 0.
-2, -1
Let f(j) = 6*j**5 + 26*j**4 - 29*j**3 - 59*j**2 - 5*j. Let m(a) = -5*a**5 - 27*a**4 + 30*a**3 + 60*a**2 + 4*a. Let i(u) = -4*f(u) - 5*m(u). Factor i(s).
s**2*(s - 2)*(s + 1)*(s + 32)
Solve 16/19*n + 168/19 - 2/19*n**2 = 0 for n.
-6, 14
Let g be (-19)/152*(-48)/2. Suppose 2*x - 2 = 2. Factor -3 - 45 + 50*f + g*f**4 - x*f - 12*f**3.
3*(f - 2)**3*(f + 2)
Suppose -81*r + 24*r + 1995 = 0. Let a be 70/15*30/r*1. Determine o so that a*o - 2/11*o**2 - 22 = 0.
11
Let m be ((-516)/(-430))/(2/(-5)). Let v(p) = 2*p**3 - p**2. Let x(y) = -4*y**4 + 13*y**3 + 2*y**2. Let u(j) = m*v(j) + 3*x(j). Factor u(i).
-3*i**2*(i - 3)*(4*i + 1)
Let t(i) be the third derivative of 131*i**2 - 97/480*i**6 + 0*i - 66/5*i**5 - 1120/3*i**4 - 1/840*i**7 + 0 - 4096/3*i**3. Factor t(s).
-(s + 1)*(s + 32)**3/4
Let z = 217 + -215. Let f be 3 + 3/(9/(-3)). Find g such that 141 - g**2 - 135 + 0*g - 3*g**f + z*g = 0.
-1, 3/2
Let l(a) be the second derivative of -4320*a**2 - 15*a**4 - a + 2 + 1/4*a**5 + 360*a**3. Suppose l(p) = 0. Calculate p.
12
Let d be ((4/(-5))/2)/(-4). Let m(f) be the second derivative of 0*f**2 - 1/10*f**4 + 0 - 4*f + d*f**3. Find g such that m(g) = 0.
0, 1/2
Let n be -9 - ((-3411)/133 + 0 - (137368/(-539))/(-223)). Find q such that 0*q + 390/19*q**4 + n*q**5 + 2/19*q**2 + 0 + 54/19*q**3 = 0.
-1, -1/13, 0
Let h(d) be the second derivative of d**4/60 + 8*d**3/15 + 39*d**2/10 - 773*d. Factor h(q).
(q + 3)*(q + 13)/5
Let a(k) = -k**3 + 3*k**2 + k. Let b(s)