 0. What is h?
-2, -1, 0
Let t = 11 + -109/10. Let b(x) be the first derivative of t*x**4 - 2 + 1/5*x**2 + 0*x + 4/15*x**3. Factor b(j).
2*j*(j + 1)**2/5
Let n(x) be the third derivative of 1/240*x**6 + 1/60*x**5 + 0*x + 1/48*x**4 - 3*x**2 + 0*x**3 + 0. Find d, given that n(d) = 0.
-1, 0
Suppose 0 = -t + 83 - 28. Suppose 5*v - t = -2*s, -3*v + s + 21 + 1 = 0. Factor -5*l**3 - 4 + 3 + 2*l**4 + 5*l + 9*l**2 - 1 - v*l**4.
-(l - 1)*(l + 1)**2*(7*l - 2)
Let p(r) be the first derivative of -3*r**6/5 - 48*r**5/25 - 11*r**4/5 - 16*r**3/15 - r**2/5 - 4. Factor p(x).
-2*x*(x + 1)**2*(3*x + 1)**2/5
Let g(f) be the first derivative of 1/2*f**2 + 1/60*f**5 + 0*f**4 + 0*f - 1/6*f**3 + 1. Let h(b) be the second derivative of g(b). Factor h(x).
(x - 1)*(x + 1)
Let y = 6 + 2. Let v be -2 + (y - (-3)/(-1)). Find j such that -3/2 - 3/2*j**4 - 3/2*j**5 - 3/2*j + 3*j**2 + v*j**3 = 0.
-1, 1
Let k(n) = 2*n**2 + 2*n + 5. Let y = 12 + -9. Let c(h) = h**2 + 1. Let x(f) = y*k(f) - 15*c(f). Determine z so that x(z) = 0.
0, 2/3
Determine o so that 8/7 + 2*o + 6/7*o**2 = 0.
-4/3, -1
Let u(p) be the third derivative of 49*p**6/24 - 7*p**5/4 - 5*p**4 - 10*p**3/3 - p**2 + 14. Factor u(n).
5*(n - 1)*(7*n + 2)**2
Let w(k) = -k + 5 + 7*k**2 - 6*k**2 - 1. Let x(i) = -2*i**2 + i - 5. Let q be 3*3*(-8)/(-18). Let l(m) = q*x(m) + 5*w(m). Suppose l(d) = 0. Calculate d.
-1/3, 0
Let j be -4 - (22/4)/(-16 - -15). Let u(d) be the first derivative of 0*d + 4 - j*d**2 + d**3. Determine z, given that u(z) = 0.
0, 1
Let y be (3 - 2)/(2/4). What is z in 6*z**3 - 1 + 3*z - 21*z + 27*z**4 - 22*z**2 + 12*z**5 - y*z**2 - 2 = 0?
-1, -1/4, 1
Suppose 8 = 8*y - 16. Determine v, given that 6/7*v**2 + 0 + 2/7*v**y + 4/7*v = 0.
-2, -1, 0
Let r(y) be the second derivative of -y**4/18 - 2*y**3/9 - y**2/3 + 7*y. Factor r(p).
-2*(p + 1)**2/3
Let t(x) be the first derivative of -x**5/20 + 3*x**4/8 - x**3 + x**2 + 1. Let a(v) be the second derivative of t(v). Factor a(n).
-3*(n - 2)*(n - 1)
Suppose -r + 6 = 2*r. Let m = r + 0. Solve -3*v**3 - 1/2*v**5 + 0 - m*v**4 - 1/2*v - 2*v**2 = 0.
-1, 0
Let h(c) be the second derivative of 0*c**4 - 1/10*c**5 + 1/3*c**3 + 2*c + 0 - 1/2*c**2 + 1/30*c**6. Factor h(w).
(w - 1)**3*(w + 1)
Let a(d) be the second derivative of -d**7/105 - d**6/20 - d**5/15 + d**2/2 - 2*d. Let w(r) be the first derivative of a(r). Suppose w(k) = 0. Calculate k.
-2, -1, 0
Let k(m) be the first derivative of -m**6/2 - 9*m**5/5 - 9*m**4/4 - m**3 + 5. Determine v so that k(v) = 0.
-1, 0
Let i(u) be the third derivative of u**8/560 - u**7/70 + u**6/25 - u**5/25 + 29*u**2. Factor i(v).
3*v**2*(v - 2)**2*(v - 1)/5
Let j(f) be the third derivative of 7*f**5/15 + 13*f**4/3 - 16*f**3/3 + 13*f**2. Factor j(s).
4*(s + 4)*(7*s - 2)
Suppose 2*c + z - 3 = 0, 4*c + 5*z = 7*z + 18. Factor -2/11*r**4 + 8/11*r**c - 10/11*r**2 + 4/11*r + 0.
-2*r*(r - 2)*(r - 1)**2/11
Determine j, given that 34/9*j**2 + 10/9*j**3 + 32/9*j + 8/9 = 0.
-2, -1, -2/5
Suppose -2*u**2 + 20*u**3 - 48*u**5 + 6*u**2 + 60*u**5 + 28*u**4 = 0. What is u?
-1, -1/3, 0
Let i(u) be the first derivative of u**7/84 - u**6/60 - u**5/40 + u**4/24 + u - 2. Let w(z) be the first derivative of i(z). Factor w(o).
o**2*(o - 1)**2*(o + 1)/2
Let y(f) be the third derivative of -f**5/300 + f**4/30 - 2*f**3/15 + 6*f**2. Factor y(b).
-(b - 2)**2/5
Suppose 3*i**5 + 4*i**2 - 4*i**4 - i**3 - 3*i**3 + i**5 = 0. What is i?
-1, 0, 1
Let f be (-8)/36 - (-52)/(-9). Let i = -3 - f. Determine k so that -2/5*k**4 - 2/5*k**i + 0*k + 2/5*k**2 + 2/5*k**5 + 0 = 0.
-1, 0, 1
Suppose 14*o - 58*o + 88 = 0. Factor -4/7*s**o - 2/7 + 6/7*s**4 + 2/7*s**5 + 4/7*s**3 - 6/7*s.
2*(s - 1)*(s + 1)**4/7
Factor -8/9*n + 4/9*n**2 - 2/3 + 2/9*n**4 + 8/9*n**3.
2*(n - 1)*(n + 1)**2*(n + 3)/9
Let g be (-102)/10*(8 + -13). Let q = 461/9 - g. Find w, given that 0 - 2/3*w**2 - q*w**3 + 2/3*w**4 - 2/9*w + 4/9*w**5 = 0.
-1, -1/2, 0, 1
Find w, given that -19*w**2 - w**3 - 6*w**3 - 8*w + 4 + 0*w**2 = 0.
-2, -1, 2/7
Let p = -14 + 30. Suppose 2*u + p = 6. Let c(l) = 5*l**2 + 5*l. Let i(q) = 6*q**2 + 6*q. Let j(t) = u*c(t) + 4*i(t). Factor j(b).
-b*(b + 1)
Let n(y) = y**2 - 3*y - 3. Let t(z) = 4*z + 4. Let d(j) = 4*n(j) + 3*t(j). Factor d(f).
4*f**2
Factor -1 - 5/6*x + 1/6*x**2.
(x - 6)*(x + 1)/6
Factor -a**5 + 280 - 280 - 2*a**3 + 3*a**4.
-a**3*(a - 2)*(a - 1)
Let -1/6*g**2 - 1/6*g + 1/6*g**4 + 1/6*g**3 + 0 = 0. What is g?
-1, 0, 1
Let t(d) = -d**2 - 2*d - 6. Let i(w) = -w + 1. Let k(y) = -2*i(y) - t(y). Factor k(s).
(s + 2)**2
Let g(y) be the third derivative of y**7/3360 + y**6/960 - y**5/80 - y**4/6 - 5*y**2. Let t(i) be the second derivative of g(i). Find c such that t(c) = 0.
-2, 1
Let v(b) be the first derivative of b**7/210 - b**6/45 - b**5/30 + b**4/3 + 2*b**3/3 + 2. Let r(l) be the third derivative of v(l). Factor r(s).
4*(s - 2)*(s - 1)*(s + 1)
Let o(h) be the second derivative of -1/10*h**5 + 0 + h**2 - 1/6*h**4 - h + 1/3*h**3. Factor o(i).
-2*(i - 1)*(i + 1)**2
Suppose 0 = 6*r - r + 5, 2*r = -4*j - 18. Let i be 2/j*4/(-1). Factor 0 - 2/7*u**i + 0*u + 2/7*u**3.
2*u**2*(u - 1)/7
Let c = -333 - -1667/5. Determine d so that 2/5*d**2 + 0 - c*d = 0.
0, 1
Let q(s) = 11*s**2 + 16*s - 12. Let t(n) = 12*n**2 + 15*n - 12. Let r(c) = 6*q(c) - 5*t(c). Suppose r(v) = 0. Calculate v.
-4, 1/2
Let z(p) be the third derivative of -4*p**2 - 3/448*p**8 + 0*p + 0*p**5 + 1/32*p**4 + 0 + 0*p**3 - 3/80*p**6 + 1/35*p**7. Factor z(q).
-3*q*(q - 1)**3*(3*q + 1)/4
Let v(j) = -j**2 + j + 3. Let r be v(0). Factor -16*m**2 + 13*m**3 - 6*m**r + 3*m**3 - 8*m.
2*m*(m - 2)*(5*m + 2)
Determine t, given that 2*t**5 - 16/3*t**4 + 0*t + 0 + 14/3*t**3 - 4/3*t**2 = 0.
0, 2/3, 1
Factor -7/8*o**3 + 3/2*o - 1/2 + 9/8*o**2.
-(o - 2)*(o + 1)*(7*o - 2)/8
Find t, given that 1 - 25/4*t**2 + 2*t**3 + 21/4*t**4 - 2*t = 0.
-1, -2/3, 2/7, 1
Let f(d) be the second derivative of d**5/42 + 2*d**4/21 - 4*d**3/21 + 3*d**2/2 - d. Let s(n) be the first derivative of f(n). Factor s(p).
2*(p + 2)*(5*p - 2)/7
Let x(u) be the second derivative of -3*u**5/20 - u**4/2 + u**3/2 + 3*u**2 + 13*u. Factor x(n).
-3*(n - 1)*(n + 1)*(n + 2)
Find w such that 2/9*w**2 + 0 + 2/9*w = 0.
-1, 0
Let y(v) = v**2 - 3*v - 6. Let b be y(5). Suppose g = 5*g + 5*h + b, -4 = g + 2*h. Determine l, given that -g*l + 53*l**2 + 36*l + 4 + l**2 - 2*l = 0.
-1/3, -2/9
Let c(b) = -11*b**2 - 11*b + 8. Let u(j) = -7*j**2 - 7*j + 5. Suppose -3*w - 2 = -2*w. Let m be w + -6*(0 + 1). Let v(x) = m*u(x) + 5*c(x). Solve v(o) = 0.
-1, 0
What is g in -380*g**4 + 58*g**2 - 331*g**2 - 115*g**2 - 556*g**3 - 100*g**5 - 128*g - 16 = 0?
-1, -2/5
Let h be 2 - (-1 - -6) - (-75)/20. Let -1/4*o**5 - 1/2*o + 1/4*o**2 + 0 + h*o**3 - 1/4*o**4 = 0. What is o?
-2, -1, 0, 1
Let g be (-92)/(-15) - (-8)/(-60). Suppose 4*l**3 - g*l - 2 - 6*l**3 - l**2 - 5*l**2 + 0*l**3 = 0. What is l?
-1
Suppose -l = j + 1, -j + 2*l + 6 = -2*j. Suppose -7*h = -j*h. Suppose -2/3*f**3 + h*f + 0 + 0*f**2 = 0. Calculate f.
0
Let r(s) be the third derivative of s**5/15 - 2*s**4/3 - 23*s**2. Suppose r(z) = 0. What is z?
0, 4
Let z(x) = -x**4 + x**3 - x**2 - x. Let b(i) = i**5 + 5*i**4 - 5*i**3 + 3*i**2 + 4*i. Let u(l) = -b(l) - 4*z(l). Determine m, given that u(m) = 0.
-1, 0, 1
Let x(u) be the first derivative of -12/5*u**5 - 2*u**3 - 3/2*u**2 + 0*u - 2 + 21/4*u**4. Let x(t) = 0. Calculate t.
-1/4, 0, 1
Let n(f) = -f**3 + 6*f**2 - 18*f + 108. Let h be n(6). Suppose 0 + h*w + 1/5*w**2 = 0. Calculate w.
0
Find k such that -4/13*k**2 + 4/13 - 2/13*k + 2/13*k**3 = 0.
-1, 1, 2
Let t(a) be the third derivative of a**5/360 - a**4/72 - a**3/12 + 5*a**2. Factor t(n).
(n - 3)*(n + 1)/6
Let j(h) = -2*h - 32. Let u be j(-18). Suppose -u*w = -8*w. What is t in w*t + 0 - 2/5*t**2 = 0?
0
Factor 2/3*u - u**3 + 0 + 1/3*u**5 + 1/3*u**2 - 1/3*u**4.
u*(u - 2)*(u - 1)*(u + 1)**2/3
Let q(t) = t**2 + 12*t + 9. Let y be q(-11). Let o be -1 - ((-1)/(-2) + y). Factor 3/2*i**4 + 1/2*i + 1 - o*i**3 - 5/2*i**2.
(i - 1)**2*(i + 1)*(3*i + 2)/2
Let k(n) = -n**2 + 10*n - 33. Let d(l) = -1. Let z(y) = 24*d(y) - 3*k(y). Factor z(m).
3*(m - 5)**2
Let n(s) be the second derivative of s**5/100 + s**4/20 + s**3/15 - 2*s - 38. Let n(m) = 0. Calculate m.
-2, -1, 0
Suppose -2 = r + 2*r - 2*d, 5*r = -5*d + 30. Let g be 0 + 0 + 1 + 1. Solve 2*t - 5*t**g + 3*t**r - 4*t = 0 for t.