n**5 - 12*n**2. Factor u(v).
-4*(v - 6)*(v - 1)*(v + 1)**2
Let i(t) = -t**5 - 18*t**4 + 47*t**3 - 9*t**2 - 48*t + 30. Let p(l) = 2*l**5 - l**3 - 3*l**2 + l. Let a(v) = i(v) + p(v). Determine h so that a(h) = 0.
-1, 1, 2, 15
Suppose -2*h = 5*n - 66, -2*h = 29*n - 30*n + 18. Solve -23*p**2 + 114*p**2 - 110*p**3 + 5*p**4 + n*p**2 = 0 for p.
0, 1, 21
Determine t so that t**2 - 45*t - 57 + 4*t**2 + 49 - 71 - 101 = 0.
-3, 12
Let w(s) be the third derivative of -s**7/840 + 7*s**6/24 - 30*s**5 + 5000*s**4/3 - 160000*s**3/3 - 7498*s**2. Factor w(q).
-(q - 40)**3*(q - 20)/4
Let m(w) = -17*w - 516. Let q be m(-31). Let k(s) be the second derivative of -3/4*s**4 + 3/20*s**5 + 6*s**2 + q*s + 0*s**3 + 0. Factor k(v).
3*(v - 2)**2*(v + 1)
Let i(v) be the second derivative of -1/30*v**4 + 0 - 4/5*v**2 + 4/15*v**3 + 39*v. Let i(s) = 0. Calculate s.
2
Suppose -11*q = -3*q - 24. Suppose -69*a**3 + 136*a**q + 16 - 71*a**3 + 24*a**2 - 36*a = 0. Calculate a.
1, 4
Let z(x) be the second derivative of -3/20*x**5 - 77*x + 1/4*x**4 + 5*x**3 + 0 + 12*x**2. Determine k, given that z(k) = 0.
-2, -1, 4
Let u(k) be the first derivative of 4*k**2 - 5/3*k**3 - 4*k - 40 + 1/4*k**4. Let u(r) = 0. What is r?
1, 2
Let t(b) = -4*b**2 - 48*b - 13. Let n(i) be the first derivative of -i**3 - 51*i**2/2 - 12*i + 164. Let r(d) = -5*n(d) + 6*t(d). Factor r(c).
-3*(c + 3)*(3*c + 2)
Let c(y) be the third derivative of -2*y**7/105 - 19*y**6/30 - 7*y**5/3 - 17*y**4/6 + 1111*y**2. Factor c(x).
-4*x*(x + 1)**2*(x + 17)
Let h = 67817/2 + -100825/3. Let w = h + -300. Find j, given that 0 + 0*j**3 - 1/6*j - 1/3*j**4 + w*j**5 + 1/3*j**2 = 0.
-1, 0, 1
Let j(s) = s**3 - s**2 - s - 7. Let x(f) = -2*f**3 + 74*f**2 - 142*f + 62. Let a(p) = j(p) - x(p). Factor a(v).
3*(v - 23)*(v - 1)**2
Let m(i) = -i**3 - i**2 + 3*i - 6. Let h be m(-3). Find y, given that -2*y**h + 4*y**3 - 210*y + 208*y = 0.
-1, 0, 1
Let a = -119 - -193. Suppose -a = -f - f. Factor 34*n**2 - 3 - 19*n**2 + 26*n + 30*n**3 + f*n**2 + 7.
2*(n + 1)*(3*n + 1)*(5*n + 2)
Suppose -4392 = 4*u + a - 4401, -u - 9 = 4*a. Let 5*n**u + 0 + 1/3*n**2 - 1/3*n**4 - 5*n = 0. Calculate n.
-1, 0, 1, 15
Factor 79/5*l + 154/5 + 1/5*l**2.
(l + 2)*(l + 77)/5
Let w be (-1 - 4)*(-630)/225. Suppose -399*a + 392*a + w = 0. Factor 3/7*n**a + 6/7*n + 0.
3*n*(n + 2)/7
Let k(u) be the second derivative of -u**5/40 + 11*u**4/4 - 123*u**3/4 + 135*u**2 - 11472*u. Let k(t) = 0. Calculate t.
3, 60
Let f(j) = j**3 + 17*j**2 - 2*j - 31. Let t be f(-17). Factor -2336 + 70*b - 34*b**2 - 17*b**2 + 2*b**t + 2384.
(b - 24)*(b - 2)*(2*b + 1)
Determine h, given that 864/7 + 366/7*h**2 + 57/7*h**3 + 3/7*h**4 + 960/7*h = 0.
-9, -4, -2
Let s = -126 - -131. Factor 832 + 2*o**2 - 900 - 35*o + s*o.
2*(o - 17)*(o + 2)
Let v(r) = -1147*r + 1151. Let x be v(1). Find k such that -108/5*k + 8/5*k**3 - 16*k**2 + 24/5*k**x - 8 + 4/5*k**5 = 0.
-5, -1, 2
Let w(o) = 211*o - 1475. Let t be w(7). Let m(u) be the second derivative of 1/3*u**3 - 1/12*u**4 + 0*u**t + 0 + 18*u. Factor m(s).
-s*(s - 2)
Let z(q) be the second derivative of 1/10*q**4 + 26*q + 0 + 1/50*q**5 + 0*q**2 + 2/15*q**3. Suppose z(v) = 0. Calculate v.
-2, -1, 0
Suppose -88*y = -94*y + 12. Factor 104*l**2 - 7*l + 84*l**y - 194*l**2 + l**3.
l*(l - 7)*(l + 1)
Let k(w) be the first derivative of 10201*w**4/4 + 13736*w**3 + 810*w**2 + 16*w + 1736. Determine t so that k(t) = 0.
-4, -2/101
Let k(u) = -u**3 + 37*u**2 - 70*u + 4. Let z be k(35). Factor 10*b**4 + 6*b**3 + 11*b**z - 24*b**2 - 18*b**4.
3*b**2*(b - 2)*(b + 4)
Factor -369 - d**3 - 70*d**2 + 117 + 7*d**3 + 19*d**2 - 240*d - 3*d**3.
3*(d - 21)*(d + 2)**2
Let l = -1786 - -1786. Let o(p) be the second derivative of l - 11*p - 5/12*p**4 + 5/2*p**2 + 0*p**3. Let o(s) = 0. Calculate s.
-1, 1
Factor -121*j**2 + 498*j**2 - 120*j - 125*j**2 - 124*j**2 + 315 - 123*j**2.
5*(j - 21)*(j - 3)
Suppose -r + r + 7*r = 0. Suppose r = 37*t - 75 - 36. Find a such that 6/5*a**4 + 0 - 2/5*a**2 + 0*a + 4/5*a**t = 0.
-1, 0, 1/3
Suppose 28*v - 704 = -56*v - 92*v. Let -40/3*a - v*a**2 - 112/9 - 2/9*a**3 = 0. What is a?
-14, -2
Let a(h) = 152*h + 3. Let i be a(0). Let z(u) be the first derivative of -8/5*u + 10 - 1/10*u**4 - 11/5*u**2 + 2/25*u**5 - 6/5*u**i. Solve z(b) = 0 for b.
-1, 4
Let g be (4/(-10)*1)/(1/15). Let w be (-1)/(1/g)*2/3. Suppose 5*t**3 - 29*t**3 - 32 + 24*t + 28*t**2 + 0*t**3 + 4*t**w = 0. Calculate t.
-1, 1, 2, 4
Let r(v) = -5*v**2 - 1. Let m(l) be the third derivative of 17*l**5/15 + 11*l**4/12 - 23*l**3/3 - 70*l**2. Let p(o) = 2*m(o) + 28*r(o). Factor p(h).
-4*(h - 6)*(h - 5)
Determine p so that -90*p**2 + p**3 - 12505 + 4*p**3 + 12505 = 0.
0, 18
Let z = -939 - -959. Let g(o) be the first derivative of z*o + o**5 - 5/2*o**4 + 10*o**2 + 18 - 5*o**3. Factor g(q).
5*(q - 2)**2*(q + 1)**2
Let k(w) = 2*w - 13. Let y be k(9). Let t be 8*(-11 + 1248/112). Factor t*f**2 + 4/7*f**y + 0 - 4/7*f - 8/7*f**4 + 0*f**3.
4*f*(f - 1)**3*(f + 1)/7
Let i(y) = 17 - 21*y - 2*y + 10 - 12*y + 3*y**2. Let n(h) = 2*h**2 - 18*h + 14. Suppose -6*r = 9*r - 75. Let o(x) = r*n(x) - 2*i(x). Factor o(m).
4*(m - 4)*(m - 1)
Let x(u) = 3*u**3 + 126*u**2 + 4094*u. Let b(w) = -7*w**3 - 251*w**2 - 8187*w. Let d(l) = 4*b(l) + 10*x(l). Factor d(j).
2*j*(j + 64)**2
Suppose -2/19*p**2 + 108/19 + 6/19*p = 0. Calculate p.
-6, 9
Let v = 198754 - 1391251/7. Let -3/7*h**5 - 108/7 + 69/7*h**2 + 72/7*h + v*h**4 - 81/7*h**3 = 0. Calculate h.
-1, 2, 3
Let p(c) = -3*c**2 + c. Suppose 0 = 2*r + 14 - 10. Let v(a) = 3*a**2. Let s(b) = r*v(b) - 3*p(b). Factor s(j).
3*j*(j - 1)
Let m = 3213 - 3210. Let q(r) be the second derivative of -1/6*r**m + 0 + 0*r**2 + 1/20*r**5 + 1/3*r**4 - 2/15*r**6 - 14*r. Let q(u) = 0. Calculate u.
-1, 0, 1/4, 1
Suppose 2*d - 4*d + 242 = 0. Solve -7*m**2 - 3*m**2 + d*m - m**2 + m**3 - 11*m**2 = 0.
0, 11
Let q(m) = -18*m**3 + 89*m**2 + 213*m - 319. Let i(w) = -46*w**3 + 222*w**2 + 532*w - 798. Let d(j) = 7*i(j) - 18*q(j). Factor d(b).
2*(b - 26)*(b - 1)*(b + 3)
Suppose 5*c + 23 = 4*l, -1763*l + 1768*l = 4*c + 22. Factor -2/9*n**l - 4/3 + 10/9*n.
-2*(n - 3)*(n - 2)/9
Let b(z) be the third derivative of 0*z + 1 - 1/105*z**7 + 1/30*z**5 + 0*z**3 + 1/6*z**4 - 14*z**2 - 1/30*z**6. Determine u so that b(u) = 0.
-2, -1, 0, 1
Suppose 35/3*q**3 + 6 + 25/3*q - q**4 - 25*q**2 = 0. Calculate q.
-1/3, 1, 2, 9
Factor -295/2*j - 1/2*j**2 + 297.
-(j - 2)*(j + 297)/2
Let d(r) be the first derivative of 25*r**3/3 - 495*r**2 - 400*r + 3985. Factor d(l).
5*(l - 40)*(5*l + 2)
Suppose 268*v + 19 = 3*w + 269*v, -5*w = -v - 13. Determine u, given that 16/5 - 68/5*u**3 + 68/5*u + 18/5*u**w - 34/5*u**2 = 0.
-1, -2/9, 1, 4
Let l(n) = -13*n - 110. Let f be l(-10). Suppose -4*h = -3*t + 1, -18*t = -f*t - 4*h + 14. Solve 0 + 4/5*r**2 - 4/5*r**4 - 2/5*r**t + 0*r + 2/5*r**5 = 0.
-1, 0, 1, 2
Factor -1/6*n**2 - 53*n + 0.
-n*(n + 318)/6
Let p(g) be the third derivative of -13*g**2 - 1/18*g**4 + 0 - 4*g + 0*g**3 - 1/360*g**5. Factor p(o).
-o*(o + 8)/6
Let b = -83722 + 83726. Determine d, given that 0*d - 9/2*d**b + 3/2*d**5 - 15/2*d**2 - 27/2*d**3 + 0 = 0.
-1, 0, 5
Let m = -737 - -745. Suppose 22*l - m*l - 42 = 0. Determine i, given that 1/5*i**5 + 0*i + 0 + 0*i**2 - 4/5*i**4 + 3/5*i**l = 0.
0, 1, 3
Factor -1879 - 1345 + 32425*d - 32621*d + 4*d**2.
4*(d - 62)*(d + 13)
Let p be 2 - (2568/(-510) - -7). Let g = 829/595 + p. Determine y, given that -6/7*y + g*y**2 - 2/7*y**3 - 18/7 = 0.
-1, 3
Let b(m) = -4461*m**5 - 8*m**4 - 171*m**3 + 9*m. Let n(z) = -2231*z**5 - 4*z**4 - 95*z**3 + 5*z. Let l(j) = -5*b(j) + 9*n(j). Factor l(u).
2*u**4*(1113*u + 2)
Let r(o) be the third derivative of -o**5/15 - 103*o**4/6 - 264*o**3 - 1585*o**2. Solve r(u) = 0 for u.
-99, -4
Let q(j) be the third derivative of 0*j**4 + 98 - 3/35*j**7 + j**2 + 1/20*j**5 + 0*j + 0*j**3 + 1/80*j**6 + 9/224*j**8. Solve q(a) = 0.
-1/3, 0, 2/3, 1
Let r(g) be the first derivative of 4*g**5/15 - 7*g**4/4 - 91*g**3/9 + 4*g**2 + 287. Factor r(t).
t*(t - 8)*(t + 3)*(4*t - 1)/3
Let u(j) = -j**3 + j + 1. Let i(z) = 18 - 27*z + z**3 - 116*z**2 + 7*z**3 - 4*z**3 + 103*z. Let k(a) = -2*i(a) - 36*u(a). Let k(r) = 0. Calculate r.
-9, -2/7, 1
Solve 0*o - 4/7*o**5 + 0 - 40/7*o**2 + 24/7*o**4 - 12/7*o**3 = 0.
-1, 0, 2, 5
Let l(t) be the first derivative of -2*t**5/5 + 452*t**3/3 - 450*t - 5087. Determin