*s**2
Suppose 7 = 2*m - 13. Suppose -11*c + 3 = -m*c. Factor 0 + 0*u - 2/7*u**2 + 2/7*u**c.
2*u**2*(u - 1)/7
Suppose 8*v**2 + 6*v + 7*v**2 + 12*v**3 + 7*v**4 + 4*v**4 - 8*v**4 = 0. What is v?
-2, -1, 0
Let t be 1 - ((-132)/(-18) - 7). Factor 0*x + t + 2/3*x**4 - 4/3*x**2 + 0*x**3.
2*(x - 1)**2*(x + 1)**2/3
Let z = 256 + -511/2. Let z*q**2 + 0*q - 1/2*q**4 + 0*q**3 + 0 = 0. What is q?
-1, 0, 1
What is z in 4/3*z + 1/3*z**4 - 2/3*z**3 + 4/3 - z**2 = 0?
-1, 2
Suppose -3*n - n = -4*x + 8, -3*n - 4*x = -22. Let k(s) be the second derivative of -4*s + 1/6*s**4 + 1/3*s**3 + 0 - n*s**2. Factor k(z).
2*(z - 1)*(z + 2)
Let a = 112/5 - 22. Factor -a*u**2 + 0*u**3 + 0 + 2/5*u**4 + 0*u.
2*u**2*(u - 1)*(u + 1)/5
Let a = 8321/80 - 104. Let v(j) be the second derivative of -a*j**5 + 0*j**2 + 0 - 3*j + 1/120*j**6 - 1/24*j**4 + 0*j**3. Factor v(i).
i**2*(i - 2)*(i + 1)/4
Solve -8/7*d**3 + 2/7*d**4 - 8/7 + 6/7*d**2 + 8/7*d = 0 for d.
-1, 1, 2
Let a(x) be the first derivative of -5*x**3/12 - x**2/8 - 30. Factor a(q).
-q*(5*q + 1)/4
Let k(v) be the third derivative of -v**8/112 + 3*v**7/56 - v**6/40 - 9*v**5/40 + v**4/4 + 3*v**3/8 - v**2. Let k(d) = 0. Calculate d.
-1, -1/4, 1, 3
Let q(v) be the third derivative of -v**7/120 - 19*v**6/480 - v**5/16 - v**4/96 + v**3/12 - 6*v**2. Solve q(f) = 0 for f.
-1, 2/7
Let v(k) = 20*k**2 + 40*k + 31. Let a(u) = 4*u**2 + 8*u + 6. Let r(l) = 11*a(l) - 2*v(l). Factor r(x).
4*(x + 1)**2
Let m(u) be the second derivative of 3*u**6/70 - 3*u**5/35 + 3*u + 2. Suppose m(r) = 0. What is r?
0, 4/3
Let q be 8/50*5 - -2. Factor 0 - q*j**2 - 2*j**3 - 4/5*j.
-2*j*(j + 1)*(5*j + 2)/5
Let r(l) = -21*l - 105. Let y be r(-5). Suppose y - 4*f**4 + 3*f**3 - 2/3*f**2 + 0*f + 5/3*f**5 = 0. Calculate f.
0, 2/5, 1
Factor -19/3*i**3 + 2/3 - 5*i**2 - 1/3*i - 7/3*i**4.
-(i + 1)**3*(7*i - 2)/3
Let k be (86/(-12))/((-1)/50). Let s = k - 355. What is o in 0*o - s*o**3 - 8/3*o**4 + 0 - 4/3*o**2 - 2/3*o**5 = 0?
-2, -1, 0
Let v = -361 - -2523/7. Let f = 15/14 + v. Determine i, given that -f*i**2 + 1/4*i + 0 + 1/4*i**3 = 0.
0, 1
Let m(j) be the first derivative of j**5/5 + 2*j**4 - 19*j**3/3 + 5*j**2 - 24. Solve m(x) = 0 for x.
-10, 0, 1
Let w(b) = -b**2 - 5*b - 1. Let i be w(-4). Let g be (i/5)/(3/30). What is h in -h**2 - h**2 - 2*h**3 - g*h**2 + 2*h**2 - 2 - 6*h = 0?
-1
Let m = -210 + 213. Suppose -4/5*t**m + 0 + 0*t + 2/5*t**4 + 2/5*t**2 = 0. Calculate t.
0, 1
Suppose 3*j + 98 = 5*j + 3*z, 0 = 5*j - 5*z - 245. Factor -j*x**2 + 4 - 5*x**3 - 36*x - 59*x**3 + 87*x**2 + 58*x**2.
-4*(x - 1)*(4*x - 1)**2
Let l(m) = m**4 + m**3 - m + 1. Let d(o) = -20*o**4 - 100*o**3 - 168*o**2 - 50*o + 26. Let v(k) = d(k) + 6*l(k). Find p, given that v(p) = 0.
-4, -2, -1, 2/7
Let q(o) = 4 + 6*o + o**2 - 4 + 3 + 2. Let m be q(-5). Factor 0*w - 2/5*w**2 + m.
-2*w**2/5
Suppose b - 4 + 2 = 0. Factor 4*w**3 + 0*w**2 - 6*w**2 - b*w**3 - 4*w**3 - 6*w - 2.
-2*(w + 1)**3
Factor 4/9*g**4 - 14/9*g**5 + 0*g**3 + 0*g**2 + 0 + 0*g.
-2*g**4*(7*g - 2)/9
Let d(u) be the third derivative of u**8/1848 - u**7/1155 - u**6/660 + u**5/330 + 21*u**2. Solve d(x) = 0.
-1, 0, 1
Let -16*y**2 - 5*y - 50*y**5 + 16*y**3 + 46*y**5 + 4*y**4 + 5*y = 0. What is y?
-2, 0, 1, 2
Let r(z) be the first derivative of z**5/25 - z**4/10 + z**2/5 - z/5 - 1. Factor r(n).
(n - 1)**3*(n + 1)/5
Factor -1/4 - 1/4*t**3 - 3/4*t - 3/4*t**2.
-(t + 1)**3/4
Let m(g) be the third derivative of g**8/84 - 4*g**7/105 - g**6/10 + 4*g**5/15 + 2*g**4/3 + 8*g**2. Solve m(n) = 0 for n.
-1, 0, 2
Let j(x) be the third derivative of 0*x**3 + 0 - 4*x**2 + 1/15*x**5 + 0*x**4 + 0*x - 1/60*x**6. Determine a so that j(a) = 0.
0, 2
Let o(j) be the first derivative of 1/4*j**2 + 0*j - 5/12*j**3 + 1 - 7/16*j**4. Let o(r) = 0. Calculate r.
-1, 0, 2/7
Suppose -56 = -2*b + 14. Suppose b = 7*g - 2*g. Factor 2*l - 5*l + g*l + 2*l**2.
2*l*(l + 2)
Suppose 3*j - 2*m - 8 = -7*m, 5*j = 5*m. Let x be -4 + 3 + 4 - j. Let -45/2*c**x + 6 - 18*c - 6*c**3 = 0. What is c?
-2, 1/4
Let z(i) be the third derivative of -i**8/1512 - i**7/315 - i**6/180 - i**5/270 - 25*i**2. Factor z(p).
-2*p**2*(p + 1)**3/9
Let n(u) be the second derivative of -u**4/48 + u**3/24 + 4*u. Factor n(v).
-v*(v - 1)/4
Let w(d) = -d - 8. Let z be w(-10). Factor z*c - c - 2 - c + 2*c**2.
2*(c - 1)*(c + 1)
Let v(l) be the third derivative of 7/72*l**4 - 3*l**2 + 0*l + 1/126*l**7 - 11/360*l**6 - 7/180*l**5 + 0 + 1/252*l**8 + 1/9*l**3. Suppose v(h) = 0. Calculate h.
-2, -1, -1/4, 1
Find u such that -3/7*u**4 - 6/7 - 15/7*u**3 - 27/7*u**2 - 3*u = 0.
-2, -1
Suppose 42 - 2 + 110*s**2 - 106*s - 34*s - 25*s**3 = 0. Calculate s.
2/5, 2
Let j(c) be the third derivative of c**7/15 - 3*c**6/20 - c**5/6 + 3*c**4/4 - 2*c**3/3 - 5*c**2. Factor j(k).
2*(k - 1)**2*(k + 1)*(7*k - 2)
Let c(s) be the second derivative of -s**7/630 + s**5/60 + s**4/36 - s**2 + 2*s. Let g(o) be the first derivative of c(o). Suppose g(v) = 0. What is v?
-1, 0, 2
Let k(h) = 3*h**4 - 3*h**3 + 6*h. Let c(y) = -y**4 - 2*y**3 - 2*y**3 + 5*y**3 - y. Let n(d) = 6*c(d) + k(d). Factor n(u).
-3*u**3*(u - 1)
Let x(m) be the second derivative of m**5/20 - m**4/12 - m**3/6 + m**2/2 + 9*m. Solve x(d) = 0.
-1, 1
Solve 9/2 + 3/2*r**3 + 3/2*r**2 - 15/2*r = 0.
-3, 1
Let c(l) be the third derivative of -l**7/1155 + l**6/330 + 5*l**2. Factor c(j).
-2*j**3*(j - 2)/11
Suppose 20 = 4*m - 4*g, 3*g = -g - 8. Let i(z) be the first derivative of 1/3*z**2 + 1/9*z**3 - m + 1/3*z. Let i(o) = 0. What is o?
-1
Let b(z) = z**3 - 19*z**2 - 19*z - 18. Let i be b(20). Suppose 2*c = 3*c - i. Solve 2/9*x**c + 0 + 2/9*x = 0 for x.
-1, 0
Suppose 28 = -0*k - 4*k. Let c = -5 - k. Factor -19*j**2 + 0 + 7*j**2 - c + 3*j**3 - 4 + 15*j.
3*(j - 2)*(j - 1)**2
Suppose 9*l = 5*l. Let w(k) be the second derivative of -1/9*k**2 + 0*k**3 - k + 1/54*k**4 + l. Find z, given that w(z) = 0.
-1, 1
Let t be (-6)/15 + (-334)/(-10). Let r = t + -31. Suppose 3/7*g + 3/7*g**r - 3/7*g**4 - 3/7*g**3 + 0 = 0. What is g?
-1, 0, 1
Let a(l) be the second derivative of -l**8/16800 + l**6/600 - l**5/150 + 7*l**4/12 - 8*l. Let y(g) be the third derivative of a(g). Solve y(m) = 0.
-2, 1
Let x(m) = -2*m + 13. Let n be x(5). Let g(v) be the first derivative of 0*v - 4/27*v**3 - n - 1/18*v**4 - 1/9*v**2. Factor g(w).
-2*w*(w + 1)**2/9
Suppose 72 = 6*c - 0*c. Suppose o - c = -5*o. Solve -3/2*y**3 + y**5 + 1/2*y**4 + 0 - 1/2*y**o + 1/2*y = 0.
-1, 0, 1/2, 1
Let i(n) = -8*n**2 + n. Let h(g) = 23*g**2 - 2*g - 1. Let w(p) = -3*h(p) - 8*i(p). Let y(o) = 2*o**2 + o - 1. Let u(a) = 3*w(a) + 8*y(a). Factor u(z).
(z + 1)**2
Suppose 792*a + 484/3 + 620*a**2 + 400/3*a**3 = 0. Calculate a.
-11/5, -1/4
Let n = -590 + 593. Factor 3/2*l**4 + 0*l + 3/2*l**2 + 0 - n*l**3.
3*l**2*(l - 1)**2/2
Let c(m) be the first derivative of -m**6/1260 - m**5/420 + m**4/42 + 4*m**3/3 - 3. Let i(l) be the third derivative of c(l). Let i(u) = 0. Calculate u.
-2, 1
Let s = -13/28 - -251/420. Let 4/15*g - s*g**2 + 0 = 0. What is g?
0, 2
Suppose 12 = -0*h - 3*h. Let s be 6/8 - 9/h. Solve 2/3 + 2*y + 4/3*y**2 - 4/3*y**s - 2/3*y**5 - 2*y**4 = 0.
-1, 1
Let j(d) be the third derivative of 2*d**7/105 - d**6/60 - d**5/6 - d**4/6 - 21*d**2. Determine h, given that j(h) = 0.
-1, -1/2, 0, 2
Factor 6*n**3 - 5 + 7*n**2 - 3*n**4 + 8 - 7*n**2 - 6*n.
-3*(n - 1)**3*(n + 1)
Let j be (0/1)/(-1 + 0). Let z(x) be the second derivative of 0*x**2 - 1/20*x**5 - 2*x + 0 - 1/12*x**4 + j*x**3. Factor z(c).
-c**2*(c + 1)
Let n = -1/334 - -673/1670. Let 0*m - 2/5*m**2 + 0 - n*m**3 = 0. What is m?
-1, 0
Suppose -3*d - 8 + 8 = 0. Let w(r) be the third derivative of 1/12*r**4 + 1/20*r**5 + 3*r**2 + d + 0*r + 0*r**3 + 1/120*r**6. Factor w(s).
s*(s + 1)*(s + 2)
Let d = 56/25 - 443/200. Let o(m) be the second derivative of -2*m + 0 - d*m**5 + 0*m**2 + 1/12*m**3 + 0*m**4. Suppose o(y) = 0. What is y?
-1, 0, 1
Let x(q) = q - 5. Let z be x(-6). Let k(d) = d**3 + 11*d**2 - d - 9. Let y be k(z). Solve 9/2*f**4 + 3/2*f**3 - 4*f**y - 2*f + 0 = 0.
-2/3, 0, 1
Let g(i) be the first derivative of i**6/6 + i**5/5 - 3*i**4/4 - i**3/3 + i**2 - 4. Factor g(l).
l*(l - 1)**2*(l + 1)*(l + 2)
Factor -2 + 12*o**3 - 12*o - 155*o**2 + 2 + 151*o**2 + 4.
4*(o - 1)*(o + 1)*(3*o - 1)
Let 1/5*t**2 + 4/5*t**5 - 1/5*t**4 - 4/5*t**3 + 0*t + 0 = 0. Calculate t.
-1, 0, 1/4, 1
Factor -l**4 - l**3 - 2*l**4 - 2*l