/2
Determine s so that 0 + 0*s + 3/7*s**4 + 264/7*s**2 - 267/7*s**3 = 0.
0, 1, 88
Let f(s) be the second derivative of s**5/30 + 68*s**4/9 + 1628*s**3/3 + 5808*s**2 - 2816*s. Suppose f(l) = 0. Calculate l.
-66, -4
Let t be (-3204)/(-288) - 2/16. Let s be t/4 - (-24)/(-32). Let 0*k**3 - 2*k**s + 2/3*k**4 - 4/3*k + 0 = 0. Calculate k.
-1, 0, 2
Let v(g) = -49*g + 2551. Let x be v(52). Factor -1/2*b**4 - 4*b + 4*b**x + 8 - 15/2*b**2.
-(b - 4)**2*(b - 1)*(b + 1)/2
Let c(k) be the third derivative of -k**5/270 - 103*k**4/6 - 31827*k**3 + 6*k**2 - k + 2. Factor c(b).
-2*(b + 927)**2/9
Let v(y) be the second derivative of -y**6/10 + 7*y**5/12 - 7*y**4/6 + 8*y**3/9 + 613*y. Factor v(n).
-n*(n - 2)*(n - 1)*(9*n - 8)/3
Suppose 5*o = 10*o + x - 176, -4*o + 2*x = -152. Let g be (5 + 1)*((-128)/o)/(-2). Suppose -8*w**2 + 8/3*w**3 - 1/3*w**4 + g*w - 16/3 = 0. What is w?
2
Suppose 2*o - 4*g - 3940 = 0, -3*o + 4*g - 411 = -6325. Let h = o + -7895/4. Factor 1/4*j**4 + h*j**3 - 1/4*j + 0 - 1/4*j**2.
j*(j - 1)*(j + 1)**2/4
Let q(n) be the second derivative of n**6/15 - 18*n**5/5 - 295*n**4/6 - 86*n**3 - 1862*n. Let q(u) = 0. Calculate u.
-6, -1, 0, 43
Let z be ((-42)/10)/(13/(-65)). Factor 0*c - 3*c + 3*c - 24*c**3 + z*c**3.
-3*c**3
Let k be 33/12*(23/(-46) - (-30)/20). What is x in 5/2*x**3 + k*x**2 + 0 + 1/4*x = 0?
-1, -1/10, 0
Let -2309*k**3 - k + 4*k**2 - 36 + 17*k**2 + 1156*k**3 + 13*k + 1156*k**3 = 0. Calculate k.
-6, -2, 1
Let f(a) be the second derivative of a**7/420 - a**6/45 + a**5/60 + a**4/2 + 28*a**3/3 + 42*a - 2. Let i(z) be the second derivative of f(z). Solve i(t) = 0.
-1, 2, 3
Let x(t) be the third derivative of -t**7/70 + 15*t**6 - 599*t**5/20 + 3394*t**2. Find g, given that x(g) = 0.
0, 1, 599
Let u(q) be the second derivative of 2*q**6/5 - 13*q**5/5 + 14*q**4/3 + 2*q + 86. Solve u(p) = 0.
0, 2, 7/3
Let l(w) = 2*w**2 + 42*w + 110. Let o be l(-18). Let s(i) be the second derivative of 1/70*i**5 + 4/7*i**o - 27*i + 8/21*i**3 + 5/42*i**4 + 0. Factor s(f).
2*(f + 1)*(f + 2)**2/7
Let u(b) = 2*b**2 + 14*b + 3. Let p be u(-7). Solve 44*f**2 + 63*f + 32 + 9*f - f**4 - p*f**4 = 0 for f.
-2, -1, 4
Let b(m) be the second derivative of m**7/105 - 11*m**6/75 - 59*m**5/50 + 199*m**4/30 + 526*m**3/15 + 56*m**2 + 874*m - 2. What is g in b(g) = 0?
-5, -1, 4, 14
Factor -2/11*d**3 - 8/11*d - 2*d**2 + 120/11.
-2*(d - 2)*(d + 3)*(d + 10)/11
Let f(c) = 2*c**2 + 11*c + 3. Let v(i) = -4*i**2 - 23*i - 5. Let z be (-3 + -3)/(4/(-4)). Let y(a) = z*v(a) + 14*f(a). Factor y(x).
4*(x + 1)*(x + 3)
Let u be 112/860 + 207/2967. Suppose -11/5*b - u*b**2 - 2 = 0. What is b?
-10, -1
Let t(h) be the second derivative of -1 + 2*h**2 - 4/3*h**3 + 1/3*h**4 + 20*h. Factor t(r).
4*(r - 1)**2
Let w = 73364 - 73362. Determine n, given that -26/3*n - 58/9*n**w - 4 - 2/9*n**4 - 2*n**3 = 0.
-3, -2, -1
Let m = 3003 - 2999. Factor -1/5*n**5 + 6/5*n**m + 9/5*n + 0 + 24/5*n**3 + 26/5*n**2.
-n*(n - 9)*(n + 1)**3/5
Factor 8 + n**3 + 2*n + 0 - 28204*n**2 + 28199*n**2.
(n - 4)*(n - 2)*(n + 1)
Let x = -353366 + 2473634/7. Factor -8/7*f**5 - 312/7*f**3 + x*f**2 + 14*f**4 + 0*f + 0.
-2*f**2*(f - 6)**2*(4*f - 1)/7
Let u(g) be the first derivative of -g**6/40 + g**4/8 - 39*g**2/2 - 49. Let r(q) be the second derivative of u(q). Factor r(t).
-3*t*(t - 1)*(t + 1)
Let s = -83 + 89. Suppose -23*j + 24*j = s. Factor -j*y**5 - 8 + 2 + 7 - y + 2*y**3 - 2*y**2 + y**4 + 5*y**5.
-(y - 1)**3*(y + 1)**2
Let p be 73/(-584)*(2/6 - (-57)/(-171)). Determine m so that -1/4*m**5 + m**2 + p - 3/4*m**3 - m**4 + m = 0.
-2, -1, 0, 1
Solve 10609*n + 788768 + 2*n**2 - 20305*n + 7184*n = 0.
628
Suppose -15*n - 56 = -461. Suppose -3*b + 3 = 15*t - 10*t, n = 5*t - 3*b. Factor 4/3*v**5 - 8/3*v**2 + 8/3*v**t + 4*v**4 - 4/3 - 4*v.
4*(v - 1)*(v + 1)**4/3
Suppose 386362875/7 + 2295225/7*z + 4545/7*z**2 + 3/7*z**3 = 0. Calculate z.
-505
Let h(k) be the first derivative of 21*k**5/5 + 309*k**4/4 + 396*k**3 + 858*k**2 + 816*k - 718. Let h(r) = 0. What is r?
-68/7, -2, -1
Let j be 9/30 + (-180)/1350. Let q(p) be the third derivative of 20*p**2 + 0 - 2/75*p**5 + 0*p + 8/15*p**3 + j*p**4 - 1/50*p**6. Factor q(n).
-4*(n + 1)**2*(3*n - 4)/5
Let j be (57 - (1 - (-6486)/115))/(16/(-10) + 1). Factor -4/3*r - j - 2/3*r**2.
-2*(r + 1)**2/3
Let z(i) = 8315*i - 124723. Let d be z(15). Factor 5*l**4 + 34*l + 37*l**d + 1/2*l**5 + 39/2*l**3 + 12.
(l + 1)*(l + 2)**3*(l + 3)/2
Suppose 3*v + 2*s - s = 2, 4*s + 10 = -3*v. Factor 16 + 39*x**4 - v*x**3 - 2*x**5 - 116*x**4 + 8*x - 20*x**2 + 40*x**4 + 45*x**4.
-2*(x - 2)**3*(x + 1)**2
Let r(c) be the first derivative of -c**5/330 + 5*c**4/66 + c**3/3 - 33*c**2/2 - 45. Let d(q) be the second derivative of r(q). Factor d(v).
-2*(v - 11)*(v + 1)/11
Let v(l) = -7*l**2 + 7*l + 8. Let r be (((-36)/(-10))/(-3))/(30/(-200)). Let f(z) = 6 - 5 + 6 - 8*z**2 + r*z. Let b(u) = 2*f(u) - 3*v(u). Factor b(o).
5*(o - 2)*(o + 1)
Let l(a) = -6*a + 38. Let d be l(6). Determine k, given that -42*k + 40 + k**2 + d*k**2 - k**2 = 0.
1, 20
Determine r so that 12/13*r**4 - 8/13*r**3 - 36/13*r**2 + 10/13*r + 24/13 - 2/13*r**5 = 0.
-1, 1, 3, 4
Let h(k) be the first derivative of 3 + 12/19*k - 58/57*k**3 - 23/19*k**2. Factor h(b).
-2*(b + 1)*(29*b - 6)/19
Let c(o) be the first derivative of 5*o**3/9 - 19*o**2/2 - 12*o - 1090. Factor c(s).
(s - 12)*(5*s + 3)/3
Let z(w) be the second derivative of w**6/35 + w**5/14 - 89*w**4/42 - 61*w**3/21 + 30*w**2/7 + 1043*w. Solve z(l) = 0 for l.
-6, -1, 1/3, 5
Let a(c) be the first derivative of 26/3*c**3 + 3/2*c**4 + 144 + 6*c + 13*c**2. Factor a(p).
2*(p + 1)*(p + 3)*(3*p + 1)
Factor 12 + 7/4*d**3 + 79/4*d**2 + 95/2*d.
(d + 3)*(d + 8)*(7*d + 2)/4
Suppose -83 - 28*j**2 + 305*j - 27*j**2 - 54 + 45*j**2 - 13 = 0. Calculate j.
1/2, 30
Let r(a) = 485*a**2 + 15*a. Let f(x) = -x. Let t = 371 - 370. Let q(w) = t*r(w) + 5*f(w). Factor q(z).
5*z*(97*z + 2)
Let -6*v + 2/11*v**2 + 0 = 0. What is v?
0, 33
Find w such that -7/9*w**4 - 1/9*w**5 - 16/9 + 8/9*w + 23/9*w**2 - 7/9*w**3 = 0.
-4, -1, 1
Suppose 9 = s - 4. Suppose -x + 4*d + s = 2*d, -3*d = 15. Factor 8*h + 4*h**2 + 4*h**5 - 13*h**4 - 12*h**x + 9*h**4 + 0*h**3.
4*h*(h - 2)*(h - 1)*(h + 1)**2
Suppose 195*a - 45*a = -742*a + 1744 + 40. Solve 0 + 0*l + 8/15*l**4 - 2/15*l**5 - 2/3*l**3 + 4/15*l**a = 0.
0, 1, 2
Let t(i) be the first derivative of 1125*i**2 + 115/2*i**4 + 400*i**3 + 3*i**5 - 33 + 625*i. Determine p, given that t(p) = 0.
-5, -1/3
Let h(s) = -s**4 + 4*s**3 + 10*s**2 - 30*s + 17. Let v(r) = -r**4 + 4*r**3 + 10*r**2 - 31*r + 18. Let a(z) = 3*h(z) - 2*v(z). Factor a(n).
-(n - 5)*(n - 1)**2*(n + 3)
Let y be (-6)/48*12*(-244)/3. Suppose y - 122 = -7*b. Determine z so that b + 1/2*z**3 - z**2 + 1/2*z = 0.
0, 1
Let y(w) be the first derivative of -7*w**4/2 + 256*w**3/3 - 36*w**2 - 2001. Factor y(k).
-2*k*(k - 18)*(7*k - 2)
Let b(o) be the first derivative of -3*o**4/4 - 701*o**3 - 367497*o**2/2 + 369603*o + 1169. Suppose b(q) = 0. What is q?
-351, 1
Suppose 0 = 7*l + 3*q - 28484 + 28483, l + 2*q + 14 = 0. Determine z, given that -76/5*z**2 + 16/5*z**l + 4*z**3 + 12/5 + 28/5*z = 0.
-3, -1/4, 1
Let i be (2148/9 - 5)/(2/(-6)). Let y = -13315/19 - i. Suppose 14/19*s - 16/19*s**2 + 4/19*s**4 + y*s**3 - 2/19*s**5 - 4/19 = 0. Calculate s.
-2, 1
Let r(g) = g**4 - 270*g**3 - 1255*g**2 - 1050*g. Let i(c) = c**4 - 135*c**3 - 625*c**2 - 525*c. Let m(d) = 11*i(d) - 6*r(d). Suppose m(a) = 0. What is a?
-21, -5, -1, 0
Let s(x) be the second derivative of -2*x**6/75 - 43*x**5/100 - 11*x**4/10 - 9*x**3/10 + 1390*x - 2. Solve s(v) = 0 for v.
-9, -1, -3/4, 0
Let w(y) be the first derivative of -5*y**2 + 80/3*y**3 + 3*y**5 - 15*y - 35/2*y**4 + 5. Find m, given that w(m) = 0.
-1/3, 1, 3
Let j = 14023 - 98158/7. Let 6/7*f**2 + j + 12/7*f - 12/7*f**3 - 9/7*f**4 = 0. What is f?
-1, -1/3, 1
Let w(z) be the second derivative of -z**5/50 + z**4/10 + 8*z**3/5 + 28*z**2/5 - 5*z. Factor w(l).
-2*(l - 7)*(l + 2)**2/5
Solve -242*s - 5463 + 5463 - s**2 = 0.
-242, 0
Let t(v) be the second derivative of v**7/10080 - v**6/1440 - v**5/160 - 91*v**4/12 + 76*v. Let f(m) be the third derivative of t(m). Factor f(a).
(a - 3)*(a + 1)/4
Let g = 4056 + -12158/3. Let k(s) be the second derivative of 0 + 4*s**2 - g*s**3 - 11*s + 2/3*s**4. Suppose k(i) = 0. Calculate i.
1/2, 2
Suppose -29 = -13*