t v = -4228 + 4232. Find s, given that 0*s**3 - 1/3*s**2 + 0*s + 0 + 1/3*s**v = 0.
-1, 0, 1
Let f = -72 - -95. Suppose -f = -3*v - 14. Factor 0*g + 2/5*g**v + 0 + 2/5*g**2.
2*g**2*(g + 1)/5
Let 486*w + 27*w**2 + 1/2*w**3 + 2916 = 0. What is w?
-18
Suppose -3*g - 304 = -6*z + z, 5*z + g - 312 = 0. Let i = 65 - z. Let 2/7*m**2 + 2/7*m**5 + 0 + 0*m - 2/7*m**i - 2/7*m**4 = 0. Calculate m.
-1, 0, 1
Let a(f) be the third derivative of -f**6/120 - 8*f**2 - f. Factor a(d).
-d**3
Let l(d) = -8*d**2 - 2*d**3 - 8*d**2 + 2*d - 2 + 4*d**4 + 2. Let t(k) = -k**4 - k**3 + k**2 - k. Let u = 2 - -4. Let q(s) = u*t(s) + l(s). Factor q(c).
-2*c*(c + 1)**2*(c + 2)
Let r(o) = -7*o**4 + 8*o**3 - 6*o**2 - 6*o. Let g(x) = -15*x**4 + 17*x**3 - 13*x**2 - 13*x. Let l(m) = -6*g(m) + 13*r(m). Factor l(w).
-w**3*(w - 2)
Let k(x) = 7*x**2 - 56*x - 75. Let n(m) = 16*m**2 - 140*m - 188. Let y(t) = 12*k(t) - 5*n(t). Suppose y(p) = 0. What is p?
-5, -2
Factor 132*j**2 + 1250/11 - 104/11*j**3 - 2600/11*j + 2/11*j**4.
2*(j - 25)**2*(j - 1)**2/11
Let p(b) be the second derivative of 2/15*b**2 - 7/45*b**3 - 2/45*b**4 - 4*b + 0. Solve p(d) = 0 for d.
-2, 1/4
Let x = 1685 - 1680. Let k(p) be the third derivative of 1/15*p**x + 0*p - 7*p**2 + 0 + 8/3*p**3 - 2/3*p**4. Let k(h) = 0. Calculate h.
2
Suppose -27*c + 26 = 52 - 26. Determine n, given that 0*n + c + 0*n**4 + 2/9*n**3 - 2/9*n**5 + 0*n**2 = 0.
-1, 0, 1
Let w(j) = -j**3 + 8*j**2 - 17. Let p be w(7). Factor p*a**2 + 6*a**4 + 23*a**3 - 3*a**3 + 11*a + 5*a - 2*a**4.
4*a*(a + 1)*(a + 2)**2
Let b(r) be the second derivative of r**5/5 - 13*r**4/3 + 8*r**3 - 2*r - 10. Factor b(f).
4*f*(f - 12)*(f - 1)
Factor 1/3*y**2 - y - 4/3.
(y - 4)*(y + 1)/3
Let a(b) be the second derivative of 32/105*b**6 + 32/7*b**2 + 31/7*b**4 + 0 + 16*b - 128/21*b**3 - 1/49*b**7 - 17/10*b**5. Solve a(k) = 0 for k.
2/3, 1, 4
Let w be 14/(-8)*(20/150 - 146/420). Determine c so that w*c**2 - 3 + 3/4*c = 0.
-4, 2
Let r be 28 - 9/(270/(-1720)). Factor 64/3*j - r - 4/3*j**2.
-4*(j - 8)**2/3
Let k(t) be the first derivative of -t**6/8 + 81*t**5/20 - 765*t**4/16 + 1025*t**3/4 - 1125*t**2/2 - 576. Factor k(p).
-3*p*(p - 12)*(p - 5)**3/4
Let a(h) be the third derivative of -101/36*h**5 - 5*h**2 - 8*h**3 + 0 + 73/120*h**6 - 3/70*h**7 + 0*h + 1/1008*h**8 + 19/3*h**4. Factor a(m).
(m - 12)**2*(m - 1)**3/3
Let t(u) = 3*u - 21. Let g be t(12). Let v be -15 + g + 16*1. Factor -3*p**2 + 16 - 4*p - v + p.
-3*p*(p + 1)
Let y be (2800/45)/10 + 4/(-18). Factor -y*r**2 - 6*r**2 + 2*r**2 + 0 + 5 - 5*r.
-5*(r + 1)*(2*r - 1)
Factor -4/5*w**2 + 36/5*w - 56/5.
-4*(w - 7)*(w - 2)/5
Let b = 17 - 16. Suppose 0 = g - 3*j - b, g + 39 = 4*g + 3*j. Find x, given that -g + 3*x**2 - 3*x - x**3 + 8 + 3 = 0.
1
Suppose -109*x = 68*x - 354. Factor -12/13*k + 18/13 + 2/13*k**x.
2*(k - 3)**2/13
Let j(p) be the first derivative of -p**4/2 - 8*p**3/3 - 5*p**2 - 4*p + 132. What is n in j(n) = 0?
-2, -1
Suppose 5*c - 4*h + 16 = 0, 4*c + 27*h = 23*h + 16. Let x(z) be the second derivative of 6*z + 0 + 0*z**2 + c*z**4 - 1/6*z**3 + 1/20*z**5. Factor x(y).
y*(y - 1)*(y + 1)
Let s(r) be the first derivative of 2/9*r + 2/27*r**3 + 2/9*r**2 + 6. Solve s(m) = 0 for m.
-1
Find n such that 4*n**2 + 4*n**2 + 1002*n - 998*n + 4*n**3 + 3 - 3 = 0.
-1, 0
Let q be 6 - (-2 - (90/(-20) + 5)*-10). Factor 6*v**3 + q*v + 15/2*v**2 + 0 + 3/2*v**4.
3*v*(v + 1)**2*(v + 2)/2
Let h be (-20)/(-12) + -4 - 154/(-66). Find m, given that 0*m**2 - 3/5*m**3 + 0 + 3/5*m**4 + h*m = 0.
0, 1
Let y(m) be the first derivative of -m**7/1540 - m**6/220 - 32*m**3/3 + 25. Let f(o) be the third derivative of y(o). Find d, given that f(d) = 0.
-3, 0
Suppose 2*o = w + 2, 4 = 5*o + 4*w - 1. Let n be (-6 - -10)*o/2. Solve 6*v**2 + n*v + 3*v - 2*v**4 - 6*v - 3*v = 0 for v.
-2, 0, 1
Let f(x) be the second derivative of -x**6/180 - x**5/40 + x**4/12 + x**3/3 - 15*x. Let u(l) be the second derivative of f(l). Factor u(k).
-(k + 2)*(2*k - 1)
Let z be ((-10)/(-35))/((-4)/(-56)). Let k(m) be the first derivative of 3 + 2*m**2 + 0*m - 4/3*m**3 + 4/5*m**5 - m**z. Let k(d) = 0. Calculate d.
-1, 0, 1
Let m(f) be the third derivative of 1/12*f**4 + 0*f**5 + 0 - 7*f**2 + 0*f - 1/60*f**6 + 0*f**3. Factor m(s).
-2*s*(s - 1)*(s + 1)
Let t be 2/7 + (-416)/(-112). Let -4*m + 3*m**2 + 0*m**2 + 3*m - t*m**2 = 0. Calculate m.
-1, 0
Let u(m) = -m**4 - m**3 + m + 1. Let p be ((-12)/15 - 0)/((-1)/(-10)). Let y(j) = 10*j**4 + 8*j**3 - 12*j**2 + 8*j - 14. Let h(a) = p*u(a) - y(a). Factor h(f).
-2*(f - 1)**3*(f + 3)
Let b be (-483)/3 + (2 + -3 - 0). Let k be 6 + -2 - (b/15)/(-3). Find f, given that 8/5*f**4 + 0 - k*f**5 - 2*f**3 + 0*f + 4/5*f**2 = 0.
0, 1, 2
Find v, given that -4/9*v - 2/9*v**2 + 16/3 = 0.
-6, 4
Let o(d) be the third derivative of 11*d**5/10 + 101*d**4/36 + 2*d**3/9 + 145*d**2. Solve o(k) = 0.
-1, -2/99
Let u(y) be the third derivative of y**6/420 + 13*y**5/105 - 29*y**4/21 + 40*y**3/7 - 9*y**2 + 6. Factor u(g).
2*(g - 2)**2*(g + 30)/7
Let i(k) = k. Let w be i(5). Suppose l + u = -5, 8*l - 3*l = -u - w. Find x, given that 12*x**2 - 2*x**5 - x**5 - 9*x**4 + l*x + 0*x = 0.
-2, 0, 1
Let t(g) be the third derivative of g**8/147 + 10*g**7/147 + 5*g**6/21 + g**5/3 + g**4/7 - 115*g**2. Let t(d) = 0. Calculate d.
-3, -2, -1, -1/4, 0
Let f(b) = -b + 12. Let s be f(-8). Factor -s*k**2 + 4 + 21*k + 2 + 29*k**2.
3*(k + 2)*(3*k + 1)
Let t = 119237/30 + -3974. Let q = t + -1/6. Let -2/5*d + q*d**2 + 2/5*d**3 - 2/5*d**4 + 0 = 0. Calculate d.
-1, 0, 1
Let z(o) = -3*o**3 + 8*o**2 + 36*o. Let l(n) = -n**3 + n**2 + 2*n. Let a(t) = 2*l(t) + z(t). Let a(g) = 0. Calculate g.
-2, 0, 4
Suppose v + 4*n = 23, -2*n + 13 = -0*v + v. Factor 74*f + 4*f**v + 16*f + 400 + 230*f - 76*f**2.
4*(f - 10)**2*(f + 1)
Factor 18/5*j**3 + 14/5*j**2 + 2/5*j**5 + 4/5*j + 2*j**4 + 0.
2*j*(j + 1)**3*(j + 2)/5
Let l(g) be the third derivative of -g**7/70 + g**6/20 - g**5/20 - 15*g**2. Find s such that l(s) = 0.
0, 1
Let w(k) be the first derivative of k**7/630 + 7*k**6/1080 + k**5/180 - k**4/72 - 11*k**3/3 + 1. Let f(v) be the third derivative of w(v). Factor f(h).
(h + 1)**2*(4*h - 1)/3
Let v(f) be the second derivative of 0 + 1/90*f**5 + 0*f**2 - 1/18*f**4 + 4*f + 2/27*f**3. Factor v(h).
2*h*(h - 2)*(h - 1)/9
Suppose -100/7 + 254/7*j + 6/7*j**3 - 160/7*j**2 = 0. Calculate j.
2/3, 1, 25
Let a(i) be the third derivative of -i**7/42 + 5*i**6/24 - 2*i**5/3 + 5*i**4/6 + 50*i**2. Factor a(y).
-5*y*(y - 2)**2*(y - 1)
Let j(q) = 12*q**5 - 130*q**4 + 284*q**3 + 52*q**2 - 161*q - 11. Let u(o) = -o**4 - 3*o**2 - o - 1. Let l(m) = -2*j(m) + 22*u(m). Solve l(w) = 0 for w.
-3/4, 0, 2/3, 5
Let 15*v**5 - 6 - 195/4*v**3 - 45*v - 195/2*v**2 + 99/4*v**4 = 0. What is v?
-2, -1, -2/5, -1/4, 2
Find b such that -14*b**3 - 6*b**2 + 11*b**3 + 0*b**2 - 12 - 6*b + 27*b = 0.
-4, 1
Let t(i) be the third derivative of i**6/3 - 21*i**5 + 6175*i**4/16 + 21125*i**3/12 - 7*i**2. Suppose t(o) = 0. What is o?
-1, 65/4
Let d(n) be the third derivative of -n**7/6720 + n**6/480 - 3*n**5/320 - 13*n**4/24 - 11*n**2. Let j(r) be the second derivative of d(r). Factor j(x).
-3*(x - 3)*(x - 1)/8
Determine x so that 2*x + 3 - 7/4*x**2 - 1/2*x**3 + 1/4*x**4 = 0.
-2, -1, 2, 3
Let m = -32558/27 - -1206. Let i(l) be the first derivative of 0*l**5 - 1/6*l**4 + m*l**6 + 0*l - 2/27*l**3 + 0*l**2 + 3. Factor i(s).
2*s**2*(s - 1)*(2*s + 1)**2/9
Let p(u) = -33*u**3 - 72*u**2 - 37*u - 6. Let h = -104 + 112. Let a(k) = -22*k**3 - 48*k**2 - 25*k - 4. Let s(q) = h*a(q) - 5*p(q). Let s(c) = 0. Calculate c.
-1, -2/11
Suppose 2*c = 4, 2*j + 0*c = c + 104. Factor -h**3 + 61*h**2 - j*h**2 + 0*h**3 - 3*h**3.
-4*h**2*(h - 2)
Suppose 19 = -15*d - 11. Let s be ((-5)/45)/(d/3). Suppose s*h**5 + 0*h + 0*h**2 + 0*h**4 - 1/6*h**3 + 0 = 0. What is h?
-1, 0, 1
Factor 7/2*j**3 - 18 - 47/2*j**2 - 70*j.
(j - 9)*(j + 2)*(7*j + 2)/2
Factor 0*y**2 + 12*y**2 - 3*y**2 + 46 - 10*y**2 + 44 - 9*y.
-(y - 6)*(y + 15)
Let t(j) be the second derivative of -7*j + 0*j**2 + 0 - 2/3*j**3 + 1/3*j**4. Let t(z) = 0. What is z?
0, 1
Let b be 97/(1/(-6)*(-16)/(-6)). Let y = -217 - b. Suppose -u**2 + y*u - 1/2 + 1/4*u**3 = 0. What is u?
1, 2
Let d(z) = -2*z**2 - 11*z + 66. Let s be d(-9). Factor -2/5*g**s - 2*g**2 - 8/5 - 16/5*g.
-2*(g + 1)*(g + 2)**2/5
Let o(j) = j - 1. Let b(r) = 2*r - 1. Let n(y) =