Let m = -548 + 552. Solve -36*y**4 + 8 - 36*y**4 + m*y + y**5 - 5*y**3 + 74*y**4 - 5*y**2 - 5*y**2 = 0 for y.
-2, -1, 1, 2
Let g(f) = 6*f**2 + 9*f. Let r(v) = 17*v**2 + 26*v + 1. Suppose -8*k - 24 = -5*k. Let i = -5 - -8. Let s(m) = i*r(m) + k*g(m). Find o such that s(o) = 0.
-1
Let h(x) = -9*x**4 - 3*x**3 - 110*x**2 + 230*x + 5. Let u(j) = 2*j**4 + 2*j**3 + j**2 - j - 1. Let f(k) = 3*h(k) + 15*u(k). Let f(q) = 0. Calculate q.
-15, 0, 3, 5
Suppose 44 = 4*q + 4*j, 3*j = q - 0*j + 9. Let w be q/(-9) + (-140)/(-126). Factor -w*y**2 - 2/9*y**3 - 2/9*y + 0.
-2*y*(y + 1)**2/9
Let t = 4127 - 4124. Let x(o) be the second derivative of 2/5*o**5 + 0 - 11/6*o**t - o**2 - 5/6*o**4 - 5*o. Factor x(m).
(m - 2)*(2*m + 1)*(4*m + 1)
Factor 656*m + 708*m**2 - 507*m + 31*m + 279*m**3 + 21*m**4.
3*m*(m + 3)*(m + 10)*(7*m + 2)
Suppose 0 = 2*f + f - 12, 0 = -4*h + 2*f. Suppose 10*k**h - 10 + 2*k**3 - 11*k + 16*k - 6*k**3 - k**3 = 0. What is k?
-1, 1, 2
Let p(j) be the first derivative of -2*j**5/5 + 37*j**4/2 - 910*j**3/3 + 1859*j**2 - 1513. Let p(v) = 0. Calculate v.
0, 11, 13
Let q be (3 - 2)*-4 - (224/16 - 18). Let r(h) be the first derivative of -1/16*h**4 + 19 + q*h**2 + 0*h + 0*h**3 - 1/20*h**5. Let r(m) = 0. What is m?
-1, 0
Let i(x) be the third derivative of x**5/180 - 181*x**4/12 + 32761*x**3/2 + 1307*x**2. Factor i(q).
(q - 543)**2/3
Let 5/3*v**2 - 7940/3*v - 7945/3 = 0. What is v?
-1, 1589
Find b such that -25053*b + 0*b**2 + 12588*b + b**2 + 12552*b = 0.
-87, 0
Let n(y) be the second derivative of y**8/1680 - 13*y**6/360 + y**5/10 - 31*y**3/6 - 8*y + 6. Let w(g) be the second derivative of n(g). Factor w(a).
a*(a - 3)*(a - 1)*(a + 4)
Let n(w) be the second derivative of -3*w**7/14 - 157*w**6/20 - 3*w**5/5 + 459*w**4/8 - 59*w**3 - 39*w**2 + 2401*w. Find b such that n(b) = 0.
-26, -2, -1/6, 1
Let u(d) = -6*d - 21. Let h be u(-4). Find y, given that 6*y**3 + h*y**4 + 155*y + 0 - 3 - 161*y = 0.
-1, 1
Let w(p) = -p**3 + p**2 - 2*p - 7. Let j(v) = -2*v**3 - 37*v**2 - 61*v + 55. Let n(d) = j(d) - 5*w(d). Factor n(x).
3*(x - 15)*(x - 1)*(x + 2)
Let v(b) be the second derivative of -3*b**5/160 - 2013*b**4/16 - 1350723*b**3/4 - 906335133*b**2/2 + 3868*b. Let v(n) = 0. What is n?
-1342
Let f(v) = -9*v - 7. Suppose -6 = 40*k - 34*k. Let p be f(k). Suppose 6/5 - 3/5*x**p + 3/5*x = 0. What is x?
-1, 2
Let c be 104/(-800)*15/2 + 1. Let b(o) be the third derivative of 1/8*o**4 + 0*o**3 + 0*o + 0*o**5 + 11*o**2 - c*o**6 + 0. Factor b(q).
-3*q*(q - 1)*(q + 1)
Let o(a) be the third derivative of a**7/70 + a**6/8 - 59*a**5/10 + 14*a**4 + 77*a**2 - 3. Suppose o(p) = 0. What is p?
-14, 0, 1, 8
Let u(w) be the second derivative of w**5/20 + 11*w**4/6 + w**3/3 + 23*w**2 - w + 15. Let k be u(-22). Factor 0 + 2/5*q**3 - 2/5*q**k - 4/5*q.
2*q*(q - 2)*(q + 1)/5
Let h(a) be the first derivative of 0*a**4 - 34/21*a**3 - 36/7*a**2 - 40/7*a - 10 + 2/35*a**5. Factor h(z).
2*(z - 5)*(z + 1)*(z + 2)**2/7
Determine x so that -69/5*x + 36/5 + 1/5*x**4 - 11/5*x**3 + 43/5*x**2 = 0.
1, 3, 4
Let p be ((-28)/20)/(-7) - (-77)/(-715). Let a(z) be the first derivative of -3/26*z**4 + 0*z - p*z**5 + 0*z**2 + 7 - 1/39*z**6 - 2/39*z**3. Factor a(j).
-2*j**2*(j + 1)**3/13
Factor 196246/5*r**2 + 1/5*r**4 - 884/5*r**3 - 389844/5*r + 194481/5.
(r - 441)**2*(r - 1)**2/5
Let t = 270207 - 810616/3. Suppose -14/3 + t*h + 1/3*h**2 = 0. What is h?
-7, 2
Let k(q) be the second derivative of 2*q**6/15 - 553*q**5/5 + 25017*q**4 + 259470*q**3 + 2*q - 8097. Factor k(i).
4*i*(i - 279)**2*(i + 5)
Let s = 322 + -320. Find t such that -44*t**2 - 55*t**3 + 96*t**2 + 140*t**4 - 47*t**s = 0.
0, 1/7, 1/4
Suppose 55*o - 2127 - 861 = -111*o. Let f(n) be the second derivative of o*n + 0 - 54*n**2 - 6*n**3 - 1/4*n**4. Find k such that f(k) = 0.
-6
Suppose 2883 + 2453 = -8*h. Let b = h - -669. Solve 0*g + 0*g**3 - 1/3*g**4 + 0*g**b + 0 = 0 for g.
0
Suppose 232*f**2 + 15312*f + 4*f**3 - 49604 + 28*f**2 + 252*f**2 - 20092 = 0. What is f?
-66, 4
Let t(w) be the second derivative of 1/102*w**4 - 49*w + 1/51*w**3 + 0 - 12/17*w**2. Determine o, given that t(o) = 0.
-4, 3
Suppose -2*m + 6 = -2, y - 2*m + 5 = 0. Suppose -1 = -y*s + 8. Factor -2/7*l**4 + 0 - 4/7*l**2 - 6/7*l**s + 0*l.
-2*l**2*(l + 1)*(l + 2)/7
Determine j, given that 218 - 60*j - 25 - 7 - 48 - 4*j**2 - 2 = 0.
-17, 2
Let c(r) be the first derivative of -r**4/8 + 10*r**3/3 - 91*r**2/4 - 935. Factor c(o).
-o*(o - 13)*(o - 7)/2
Find k, given that 58*k**3 + 202/5*k**4 + 0 - 66/5*k + 38/5*k**2 + 16/5*k**5 = 0.
-11, -1, 0, 3/8
Let l be (231/49 + -5)*(-21)/(-3). Let d be (5 - (l + 3)) + (15 - 17). Factor -50/3 - 1/6*r**d - 10/3*r.
-(r + 10)**2/6
Let m(h) be the second derivative of 55*h**2 - 37*h**3 - 1/10*h**5 + 2*h - 73 + 19/2*h**4. Let m(c) = 0. Calculate c.
1, 55
Suppose 4 + 113*b**5 + 6943*b + 136 - 3605*b**3 + 1195*b**4 + 3345*b**2 - 8*b**5 - 8123*b = 0. What is b?
-14, 2/7, 1/3, 1
Let a(x) be the second derivative of x**4/4 - 19*x**3/2 - 8540*x. Factor a(m).
3*m*(m - 19)
Determine v, given that -542/7*v**4 - 36450/7*v**2 + 2/7*v**5 + 0 + 0*v + 36990/7*v**3 = 0.
0, 1, 135
Let r(q) be the first derivative of -4/7*q + 147 + 4/21*q**3 - 1/7*q**2 + 1/14*q**4. Let r(s) = 0. Calculate s.
-2, -1, 1
Let o(v) be the first derivative of -54 + 0*v + 5*v**2 + 4*v**3 + 1/2*v**4. Factor o(u).
2*u*(u + 1)*(u + 5)
Let y(r) = 3*r**2 + 34*r + 59. Let j(v) = -9*v**2 - 104*v - 175. Let t(a) = 2*j(a) + 7*y(a). Factor t(b).
3*(b + 3)*(b + 7)
Let b = -3202/87 - -211136/957. Let o = 184 - b. Let -4/11*l - o*l**2 - 2/11 = 0. What is l?
-1
Let z(n) be the first derivative of 1/5*n**2 - 101 + 1/5*n - 1/25*n**5 + 0*n**3 - 1/10*n**4. Let z(u) = 0. Calculate u.
-1, 1
Let q(m) be the first derivative of -25*m**4/4 - 215*m**3/9 + 5*m**2 + 1948. Suppose q(p) = 0. What is p?
-3, 0, 2/15
Let r(d) be the second derivative of -d**5/5 + 127*d**4/3 + 514*d**3/3 + 258*d**2 - 3*d + 1467. Factor r(s).
-4*(s - 129)*(s + 1)**2
Let q(b) be the first derivative of 5*b**6/12 + 6*b**5 + 115*b**4/4 + 50*b**3 + 125*b**2/4 + 2032. Factor q(n).
5*n*(n + 1)**2*(n + 5)**2/2
Let q(g) = -g**2 - g + 6. Let f be q(-2). Let u(d) = 28*d**2 + 41*d - 249. Let x(v) = -13*v**2 - 21*v + 124. Let y(l) = f*u(l) + 9*x(l). Factor y(r).
-5*(r - 3)*(r + 8)
Suppose 0 = 3*b - 15, -2*u + 6 = 3*b + 1. Let w(x) = 32*x**2 - 1332*x + 21792. Let n(o) = 13*o**2 - 533*o + 8717. Let l(h) = u*w(h) + 12*n(h). Factor l(v).
-4*(v - 33)**2
Factor 4017/4 - 3/4*k**2 + 2007/2*k.
-3*(k - 1339)*(k + 1)/4
Let v(g) = -g**2 - 15*g + 56. Let u be v(0). Factor -219*m**2 - u - 4*m + 4*m**3 + 4 + 152*m**2 + 119*m**2.
4*(m - 1)*(m + 1)*(m + 13)
Let m(v) be the first derivative of -v**3/3 - 573*v**2/2 - 572*v - 8327. Factor m(b).
-(b + 1)*(b + 572)
Let z(i) = 2*i**2 - 13*i - 3. Let b be z(7). Suppose -62 = b*g - 82. Find m such that -111 + 111 - 5*m**g - 8*m**4 - 4*m**3 + m**5 = 0.
-1, 0
Let z = 1461819/5 - 292361. Let 14/5 - 2/5*f + 2/5*f**3 - z*f**2 = 0. What is f?
-1, 1, 7
Let s be -4 + 3 + -4 - -9. Let i(b) be the second derivative of 0 - 14/3*b**s + 0*b**2 - 4/3*b**3 - 49/10*b**5 - 12*b. What is w in i(w) = 0?
-2/7, 0
Factor -329/4*a - 1/2*a**3 + 165/2 - 661/4*a**2.
-(a + 1)*(a + 330)*(2*a - 1)/4
Suppose -14*k + 6*k = -24. Determine f, given that -5*f - 198*f**k + 57*f**3 - 130*f**4 - 15*f**3 + 148*f**2 - 18 + 11*f + 150*f**5 = 0.
-1, -1/3, 3/5, 1
Suppose -3*p + 3*i = -i - 21, 5*p = 3*i + 24. Suppose p*v + 2 = r + 12, 3*r + 18 = 3*v. Solve 6*s + s**4 + 3*s**v + 2*s**4 + 3*s + 0*s**3 - 9*s**3 - 6 = 0.
-1, 1, 2
Suppose 1 = 2*c + 3*q, -99*c - 3*q - 1 = -98*c. Factor 252/5*r**c - 54/5*r**4 - 216/5*r**3 - 88/5*r + 2.
-2*(r + 5)*(3*r - 1)**3/5
Suppose 2*i = -121 + 121. Let u(n) be the first derivative of 1/5*n**3 + 4 - 3/5*n**4 + i*n + 3/5*n**2 - 9/25*n**5. Factor u(x).
-3*x*(x + 1)**2*(3*x - 2)/5
Let c be (((-5330)/90)/41)/(10/(-3) + 3). Factor -c*u**2 - 16/3*u + 1 + 2*u**3.
(u - 3)*(u + 1)*(6*u - 1)/3
Suppose -20*l + 9*l = -13*l. Let w be l + 1*7/((-14)/(-4)). Determine z, given that -3/7*z**5 - 6/7*z**4 + 6/7*z**w + 0*z + 3/7*z**3 + 0 = 0.
-2, -1, 0, 1
Suppose 320*y = 88 + 872. Let 1/3*d**y - 13/3*d + 7/3 + 5/3*d**2 = 0. Calculate d.
-7, 1
Determine f so that -784 + 13*f**2 + 1/4*f**3 + 140*f = 0.
-28, 4
Let b = 238 + -241. Let u be b/(-2)*(-276)/(-207). Find h s