- -13/7. Find n, given that s*n - 2/5*n**2 + h = 0.
0, 4
Let m(y) = y + 7. Let o be m(-5). Find j, given that -8 + 47*j**3 + 32*j + o*j**5 - 50*j**2 - 3*j**4 - 11*j**4 - 9*j**3 = 0.
1, 2
Suppose -5*w = -24*y + 27*y - 20, 8 = 2*w. Factor 2/5*u**2 - 2/5*u + y.
2*u*(u - 1)/5
Let u = 153 - 109. Let r be (-10)/35 + u/7. Factor -2*f**4 - 2 - 3*f**3 - r*f + 3*f**2 - 2*f - 15*f**2 - 5*f**3.
-2*(f + 1)**4
Determine d, given that 94/7 - 92/7*d - 2/7*d**2 = 0.
-47, 1
Let p(d) be the first derivative of -d**4/16 + 5*d**3/24 + d**2/4 - 6*d - 5. Let f(z) be the first derivative of p(z). Determine x, given that f(x) = 0.
-1/3, 2
Let d(u) be the second derivative of -u**7/42 - 23*u**6/15 - 307*u**5/10 - 494*u**4/3 - 763*u**3/2 - 441*u**2 + 35*u. Solve d(s) = 0 for s.
-21, -2, -1
Let s(q) be the first derivative of q**5/80 + q**4/24 - q**3/24 - q**2/4 + 22*q - 38. Let m(o) be the first derivative of s(o). Factor m(g).
(g - 1)*(g + 1)*(g + 2)/4
Let u = -1186 - -1188. Factor -8/5 - u*d**2 + 16/5*d + 2/5*d**3.
2*(d - 2)**2*(d - 1)/5
Let t(j) be the third derivative of -5*j**2 + 0*j**4 + 0 - 1/150*j**5 + 0*j + 1/15*j**3. Factor t(s).
-2*(s - 1)*(s + 1)/5
Let w(y) be the second derivative of 0 + 0*y**2 + 1/9*y**4 - 7/27*y**3 + 15*y + 1/90*y**5. Suppose w(d) = 0. Calculate d.
-7, 0, 1
Let c(a) = 6*a**2 - 10*a - 10. Let o(w) = -w**2 + w + 1. Let f(j) = c(j) + 10*o(j). Factor f(q).
-4*q**2
Factor 123 - 58*w**2 + 47 - 165*w + 28*w**2 + 25*w**2.
-5*(w - 1)*(w + 34)
Factor 0 + 2/3*r**2 - 20/9*r + 2/9*r**4 + 4/3*r**3.
2*r*(r - 1)*(r + 2)*(r + 5)/9
Let z(f) be the third derivative of 0*f + 3/32*f**4 + 0 - 1/480*f**6 + 37*f**2 + 1/80*f**5 + 5/24*f**3. What is s in z(s) = 0?
-1, 5
Let d be 2/6*1 - 0. Let a(l) = l**3 - 13*l**2 + l - 13. Let h be a(13). Factor d*i**2 - 1/3*i**3 + h*i + 0.
-i**2*(i - 1)/3
Let p(s) be the first derivative of s**6/2 - 6*s**5/5 - 33*s**4/4 + 12*s**3 + 54*s**2 - 290. Suppose p(i) = 0. Calculate i.
-2, 0, 3
Let g be (-2)/(0 - 4 - 26/(-13)). Let l be -1 + g/(2 - 22/14). Factor -2*y**2 + 2/3*y**4 + 0*y**3 + l*y + 0.
2*y*(y - 1)**2*(y + 2)/3
Suppose -4*c = 5*d - 28, -3*c + 15 = -2*d + 17. Determine g, given that 0*g**2 + 0 - 4/7*g**d + 0*g - 1/7*g**5 - 4/7*g**3 = 0.
-2, 0
Let v(n) be the second derivative of -n**4/48 - 5*n**3/12 - 2*n - 172. Factor v(b).
-b*(b + 10)/4
Let b(v) be the third derivative of -v**7/42 + 11*v**6/24 - 3*v**5/4 - 55*v**4/24 + 25*v**3/3 - 68*v**2 + 1. Factor b(y).
-5*(y - 10)*(y - 1)**2*(y + 1)
Let b(z) be the third derivative of z**7/1680 + 7*z**6/960 - z**5/60 + 552*z**2. What is c in b(c) = 0?
-8, 0, 1
Let u be 12/54 - (-7)/((-567)/(-225)). Factor 0*o + 0 - 8/7*o**2 - 4/7*o**u.
-4*o**2*(o + 2)/7
Let f = -3079 - -3079. Suppose 3*g + g - 12 = 0. Factor -8/5*i**2 + f*i**g + 1/5*i**4 + 0*i + 16/5.
(i - 2)**2*(i + 2)**2/5
Let q(x) be the first derivative of 9 + 2/27*x**3 - 2/3*x - 2/9*x**2. Factor q(k).
2*(k - 3)*(k + 1)/9
Let v(y) be the third derivative of -y**7/5040 - y**6/1440 + 5*y**4/8 - 17*y**2. Let f(h) be the second derivative of v(h). Suppose f(j) = 0. Calculate j.
-1, 0
Let b(i) be the first derivative of i**7/420 + 11*i**6/180 + i**5/6 + 3*i**3 + 2*i - 50. Let z(s) be the third derivative of b(s). Let z(w) = 0. What is w?
-10, -1, 0
Let u(z) = -69*z - 1031. Let r be u(-15). Suppose 0*y + 0 + 0*y**2 + 0*y**3 + 2/15*y**r = 0. What is y?
0
Factor 37/5*y**2 + 4/5 + 4/5*y**4 + 21/5*y**3 + 24/5*y.
(y + 1)*(y + 2)**2*(4*y + 1)/5
Let z(c) be the third derivative of -c**7/420 + c**5/60 - c**3/12 + 2*c**2 - 74. Determine h so that z(h) = 0.
-1, 1
Let w(h) be the first derivative of -5*h**4/12 + 35*h**3/6 - 15*h**2 - 28*h + 36. Let d(p) be the first derivative of w(p). Factor d(i).
-5*(i - 6)*(i - 1)
Let w be (-223)/(-2)*9/(-45). Let p = w - -419/10. Factor 56/5*g + p*g**2 + 8/5.
2*(7*g + 2)**2/5
Find x such that 2/15*x**3 - 8/5*x**2 - 56/15*x - 32/15 + 2/15*x**4 = 0.
-2, -1, 4
Suppose 4*u + 4 = 3*v - 6, -4*u + 8 = 0. Factor 4*q**3 + 0*q**2 - 13*q**3 - v + 15*q + 12*q**2.
-3*(q - 2)*(q + 1)*(3*q - 1)
Let w(d) be the third derivative of d**6/720 - d**5/120 + d**3 - 8*d**2. Let u(s) be the first derivative of w(s). Solve u(g) = 0.
0, 2
Let o(i) be the second derivative of i**7/2880 + i**6/640 + i**5/480 + 7*i**4/12 - 5*i. Let h(q) be the third derivative of o(q). Solve h(u) = 0.
-1, -2/7
Let -528/5*l + 242/5*l**2 + 288/5 = 0. Calculate l.
12/11
Let p(u) be the second derivative of u**4/54 - u**3/3 + 14*u**2/9 + 341*u. Suppose p(b) = 0. What is b?
2, 7
Let j = -3217 - -19397/6. Let y = j + -439/30. Suppose -4/5*l - 2/15*l**2 - y = 0. What is l?
-3
Let w be 1*3/(-6)*-12. Let j(k) = k**2 - 9*k + 22. Let c be j(7). Determine v so that c*v**2 + w*v + v - 3*v = 0.
-1/2, 0
Suppose -2*l - 2*p = -4, -4*p - 5 = -l - 2*p. Factor 7/3*j + 0 - 1/3*j**l + 2*j**2.
-j*(j - 7)*(j + 1)/3
Let y(s) be the second derivative of s**4/30 - 37*s**3/15 + 36*s**2/5 + 222*s. Let y(z) = 0. Calculate z.
1, 36
Let g(x) be the third derivative of 2*x**6/15 + 37*x**5/15 - 31*x**4/6 - 20*x**3/3 + 81*x**2 + 2. Factor g(y).
4*(y - 1)*(y + 10)*(4*y + 1)
Let j(a) = -a**2 - a + 7. Let m be j(0). Suppose -5*z + 3 = -m. Find t, given that 39*t**5 - 1 + 32*t**3 + 12*t - 1 - 35*t**5 - 28*t**z - 18*t**4 = 0.
1/2, 1
Suppose 8 = 4*l - 12. Suppose -l*m = 4*r + 3, -2*r + 0*r - 4*m - 6 = 0. Factor -r*i**3 + 2*i**3 + 5*i**4 + 4*i**2 + i**2 - 9*i**3.
5*i**2*(i - 1)**2
Factor 1/3*q**3 + 4/3 + 0*q - q**2.
(q - 2)**2*(q + 1)/3
Suppose 4*p - 2*p - o - 65 = 0, 4*p - 4*o - 120 = 0. Suppose -p = -23*f + 18*f. Find h, given that -51*h**3 + 47*h**3 + f*h + h - 4*h**2 = 0.
-2, 0, 1
Suppose 12*n**2 + 6*n**4 - 2/3*n**5 - 52/3*n**3 - 18 + 18*n = 0. Calculate n.
-1, 1, 3
Solve 4/13*v**4 - 2/13*v**5 + 0 + 14/13*v**3 + 24/13*v - 40/13*v**2 = 0.
-3, 0, 1, 2
Let h be 2/(-8) + (-710)/(-200) - 3. Let n(b) be the second derivative of -1/4*b**4 - 1/10*b**6 + h*b**5 + b + 0*b**3 + 0 + 0*b**2. What is i in n(i) = 0?
0, 1
Let n(c) be the second derivative of 2*c**7/21 - 4*c**6/5 + 13*c**5/5 - 4*c**4 + 8*c**3/3 - 135*c. Suppose n(s) = 0. Calculate s.
0, 1, 2
Suppose 0*x = 4*l - 4*x - 12, 0 = 3*l + 4*x - 9. Suppose 0*p = -l*y - 2*p + 12, p - 1 = y. Factor 1 + 2*f + y*f**2 + 3 - f - 7*f.
2*(f - 2)*(f - 1)
Let x(j) be the first derivative of 2*j**3/9 - 8*j**2/3 + 14*j/3 + 342. Factor x(u).
2*(u - 7)*(u - 1)/3
Let l(j) = 4*j**5 + 32*j**4 - 116*j**3 - 10*j**2 - 5*j. Let c(r) = -5*r**5 - 34*r**4 + 115*r**3 + 12*r**2 + 6*r. Let n(m) = 5*c(m) + 6*l(m). Factor n(d).
-d**3*(d - 11)**2
Let u = -14 + 30. Suppose -u*q + 13*q = -6. Factor 1/2*y**3 - q*y - 1/2*y**2 + 2.
(y - 2)*(y - 1)*(y + 2)/2
Let m(q) be the first derivative of -2/27*q**3 + 25 + 1/9*q**2 - 1/18*q**4 + 2/9*q. Factor m(k).
-2*(k - 1)*(k + 1)**2/9
Let n(h) = -27*h**3 - 33*h**2 + 12*h. Let m(l) = -l**3 - l**2 + l. Let w(q) = -18*m(q) + n(q). Find y such that w(y) = 0.
-1, -2/3, 0
Let w be (2/(-5) + 1)/(26/130). Find c such that -4*c**2 - 4/5*c**5 + 16/5 - 16/5*c + 4/5*c**4 + 4*c**w = 0.
-2, -1, 1, 2
Let m(t) be the third derivative of -t**6/480 + 23*t**5/60 + 187*t**4/96 + 47*t**3/12 + 180*t**2. Factor m(c).
-(c - 94)*(c + 1)**2/4
Let l(y) = 10*y**4 + 163*y**3 + 300*y**2 - 7*y + 7. Let c(k) = -5*k**4 - 81*k**3 - 150*k**2 + 4*k - 4. Let g(p) = 7*c(p) + 4*l(p). Factor g(b).
5*b**2*(b + 2)*(b + 15)
Let i be ((-1)/(-12))/(-2 - 90/(-40)). Let w(x) be the first derivative of 1/3*x**3 + 0*x - i*x**2 - 6. Factor w(j).
j*(3*j - 2)/3
Let d(c) = 59 + 4*c - 59 - 4*c**3 - 5*c**2 + 0*c**2. Let q(n) = -2*n**3 - 2*n**2 + 2*n. Let x(g) = -2*d(g) + 5*q(g). Factor x(w).
-2*w*(w - 1)*(w + 1)
Suppose 0 = 3*l + 2*l + 2*f - 200, -3*f = 5*l - 200. Factor -i**2 - 4*i**2 + 32 + 48*i - l*i + i**2.
-4*(i - 4)*(i + 2)
Let l(v) = 4*v**2 + 530*v + 35378. Let u(h) = 5*h**2 + 529*h + 35378. Let w(f) = -3*l(f) + 2*u(f). Let w(a) = 0. Calculate a.
-133
Let d(h) be the second derivative of h**8/336 + h**7/168 - h**6/36 + 11*h**3/3 + 10*h. Let j(m) be the second derivative of d(m). Factor j(t).
5*t**2*(t - 1)*(t + 2)
Let r = -132 - -261. Let w = 790 - 661. Factor -r - f**3 + w.
-f**3
Let s be -1*27/(-576)*4. Let u(o) be the second derivative of 0 - 1/8*o**3 - s*o**4 + 5*o + 3/80*o**5 + 9/8*o**2. Solve u(c) = 0 for c.
-1, 1, 3
Let 44*a**4 + 10*a**5 + 100*a**3 + a**4 + 34*a - 2*a**2 - 2 + 6