**3*(j + 1)/7
Let u(m) = 4*m**2 - 4*m - 4. Let h be u(-1). Let d(x) be the first derivative of -1/5*x**2 - 2/15*x**3 + 1/10*x**h + 0*x + 2/25*x**5 + 3. What is p in d(p) = 0?
-1, 0, 1
Let d = -115 - -577/5. Suppose -d*x**3 - 2/5*x**2 + 0 + 0*x = 0. What is x?
-1, 0
Let s(h) be the third derivative of h**7/28 + 11*h**6/240 - 7*h**5/120 - h**4/16 - 34*h**2. Find z, given that s(z) = 0.
-1, -1/3, 0, 3/5
Let m(u) be the third derivative of 1/84*u**8 + 0*u**3 + 1/12*u**5 + 0*u + 0 - 1/42*u**7 - u**2 - 1/24*u**4 - 1/40*u**6. Solve m(c) = 0 for c.
-1, 0, 1/4, 1
What is n in -24 - 4*n**2 - 17 - 59 + 40*n = 0?
5
Factor 1/3*f**3 - f**2 - 1/3*f + 1.
(f - 3)*(f - 1)*(f + 1)/3
Let x = 2 + -2. Suppose 5*u + x*u + 7 = -f, -4*f + 10 = u. Factor 4*l**2 + 0*l - 2*l**3 + 2*l + 4*l**f.
2*l*(l + 1)**2
Let v be (-4)/(-6)*(1 + 2). Solve 4*h + v*h**4 + 6*h**2 + 2*h**5 - 4*h**2 + h**4 - 6*h**3 - 5*h**4 = 0.
-1, 0, 1, 2
Let s = -1 - -4. Suppose 9 = -s*o + 36. Factor 5*i**3 - o*i**5 - i**5 - i**3 - 6*i**4.
-2*i**3*(i + 1)*(5*i - 2)
Let i be 2/(-3) + (-39)/9. Let f be 0/(i - (-1 - 2)). Suppose 2*v**4 - v - 3*v**4 - 3*v**3 + f*v - 3*v**2 = 0. Calculate v.
-1, 0
Let v(r) = -5*r + 14. Let p be v(10). Let o be (1/3)/((-3)/p). Solve 0 - 1/6*g + 56/3*g**o + 13/6*g**2 - 32/3*g**5 - 10*g**3 = 0 for g.
0, 1/4, 1
Let d(r) be the third derivative of -1/1344*r**8 + 0 + 0*r**6 + 1/420*r**7 + 0*r**3 - 1/120*r**5 - 6*r**2 + 1/96*r**4 + 0*r. Let d(h) = 0. Calculate h.
-1, 0, 1
Let k(u) be the second derivative of 0 + 1/24*u**4 + 0*u**3 - 1/168*u**7 + 1/80*u**5 - 1/60*u**6 + 0*u**2 - 7*u. Determine w so that k(w) = 0.
-2, -1, 0, 1
Let z = 8 - 6. Let -2*b + 4*b - b**z - b**2 = 0. What is b?
0, 1
Let b be (-15)/45 + 2/6. Factor 0 + b*g - 2/5*g**2.
-2*g**2/5
Let 0*x**2 - 5*x**2 + 2*x + 7*x**2 + 0*x**2 = 0. Calculate x.
-1, 0
Let n(h) = h**3 + 2*h**2 - 2*h - 1. Let d be n(-2). Suppose 0 = -d*m - 2*m + 15. Let 0*k - 2/7*k**m + 0 + 2/7*k**2 = 0. What is k?
0, 1
Let h(t) = -6*t - 72. Let g be h(-12). Let n(y) be the first derivative of -2/3*y**2 - 2/9*y**3 - 1 + g*y. Factor n(i).
-2*i*(i + 2)/3
Factor 19*j - 3*j**4 - 9*j**3 - 18 + 9*j**2 + 11*j - 9*j.
-3*(j - 1)**2*(j + 2)*(j + 3)
Let j(t) be the second derivative of -2/3*t**4 + 7*t + 0*t**3 + 0 - 1/5*t**5 + 0*t**2 + 2/15*t**6. Find m, given that j(m) = 0.
-1, 0, 2
Let j(z) be the second derivative of 3*z + 0 + 0*z**2 + 1/24*z**4 + 0*z**3. Factor j(b).
b**2/2
Suppose 8 - 2 = 3*t. Factor 1 - m**t - 10*m + 10*m.
-(m - 1)*(m + 1)
Suppose -3*h + 5*h = 6, -h = 4*c - 23. Let u = c + -3. Find g, given that -u - 2*g - 1/2*g**2 = 0.
-2
Factor 8*i**2 + 2*i + 4*i**3 - 35*i**4 - 6*i + 27*i**3.
-i*(i - 1)*(5*i + 2)*(7*i - 2)
Let j = -355 + 355. Suppose 2/7*y**3 + j + 4/7*y**2 + 2/7*y = 0. Calculate y.
-1, 0
Let w be 28/12 - 1/(-3). Let q be (1 - -7)*3/6. Factor -1/3*i**2 - w*i**5 + 0 + 0*i - 2*i**3 - 4*i**q.
-i**2*(2*i + 1)**3/3
Factor 2/11*i**4 + 0 + 4/11*i**3 - 2/11*i**2 - 4/11*i.
2*i*(i - 1)*(i + 1)*(i + 2)/11
Let j = -65/3 + 133/6. Find c such that j*c**2 + 1/2 + c = 0.
-1
Let l be (-4)/(-3) + -1 + (-10)/(-6). Factor -2/3*z - 1/3*z**l - 1/3.
-(z + 1)**2/3
Let d(w) be the second derivative of -w**6/90 - w**5/30 + w**4/12 - 3*w. Solve d(p) = 0 for p.
-3, 0, 1
Let z(t) be the second derivative of -8/35*t**5 - 3*t - 2/21*t**4 - 3/49*t**7 + 0*t**3 + 0*t**2 + 0 - 1/5*t**6. Factor z(q).
-2*q**2*(q + 1)*(3*q + 2)**2/7
Suppose 2 + 2 = 2*b. Let t(j) be the first derivative of -2/3*j**3 + 0*j + j**4 - 1 - 2/5*j**5 + 0*j**b. Factor t(z).
-2*z**2*(z - 1)**2
Let b be 39/18 - 2/12. Let n(x) be the second derivative of 0 + 0*x**3 + 0*x**b - 1/15*x**6 + 0*x**4 + 2/63*x**7 + 1/30*x**5 - x. Find s, given that n(s) = 0.
0, 1/2, 1
Let f = 8 - 6. Factor -1 - a + 0*a - 7 + 9*a - 2*a**f.
-2*(a - 2)**2
Solve -6*q + 3/2*q**2 + 9/2 = 0 for q.
1, 3
Let m(n) = -n**2 + 2*n + 24. Let q be m(6). Factor 2/7*j**2 - 2/7 + q*j.
2*(j - 1)*(j + 1)/7
Let q(u) be the third derivative of 2*u**2 + 0*u - 1/90*u**5 + 0 + 1/36*u**4 + 0*u**3. Factor q(y).
-2*y*(y - 1)/3
Suppose 0 + 3/2*p**4 - 3/2*p + 9/2*p**2 - 9/2*p**3 = 0. Calculate p.
0, 1
Determine j so that 0*j - 3/5*j**2 + 3/5 = 0.
-1, 1
Suppose 0 = -5*r + 11 + 4. Solve 3*f**5 - r*f**3 + 3*f**5 - 3*f**5 = 0.
-1, 0, 1
Let c(r) be the second derivative of -r**7/840 + r**6/30 - 2*r**5/5 + 7*r**4/12 - 5*r. Let k(b) be the third derivative of c(b). What is n in k(n) = 0?
4
Let u(j) = j**2 - j - 7. Let f be u(4). Factor 2*c - 4*c**2 - 3*c + f*c**2.
c*(c - 1)
Let l(k) be the first derivative of -k**7/756 + 7*k**6/1620 - k**5/270 - k**3/3 + 2. Let j(c) be the third derivative of l(c). Find p, given that j(p) = 0.
0, 2/5, 1
Let 2/3 + z + 1/3*z**2 = 0. Calculate z.
-2, -1
Let l(n) be the first derivative of n**6/3 - 9*n**5/10 + n**4/4 + 4*n**3/3 - 3*n**2/2 + n/2 - 14. Determine a, given that l(a) = 0.
-1, 1/4, 1
Let v(o) = 7*o**3 + 3*o**2 - 32*o. Let q(x) = -x**3 + x**2 + x. Let z(t) = 2*q(t) + v(t). Determine h, given that z(h) = 0.
-3, 0, 2
Let d(h) be the first derivative of h**4/4 + 2*h**3 + 6*h**2 + 4*h - 7. Let j(f) be the first derivative of d(f). Factor j(a).
3*(a + 2)**2
Let k(a) be the first derivative of a**4/8 + a**3/2 + a**2/2 + 5. Factor k(x).
x*(x + 1)*(x + 2)/2
Let w be 3/(-6)*6 + 6. Suppose w*b = -3*p + 21, -3*b + 0*b - 4 = -2*p. Find l such that -8/3*l**2 + 2/3*l - b*l**5 + 4/3*l**3 + 8/3*l**4 + 0 = 0.
-1, 0, 1/3, 1
Let p be -3*(-4)/(-36)*-9. Factor -1/2*t**p + 0*t**2 + 3/2*t + 1.
-(t - 2)*(t + 1)**2/2
Let i(w) be the second derivative of w**6/40 - 3*w**5/80 - 5*w**4/16 - 3*w**3/8 + 17*w. Factor i(x).
3*x*(x - 3)*(x + 1)**2/4
Let f(g) be the third derivative of g**5/120 - 5*g**4/96 + g**3/12 - 31*g**2. Suppose f(n) = 0. What is n?
1/2, 2
Let -3/7*b**3 + 0 - 6/7*b**2 + 0*b = 0. Calculate b.
-2, 0
Let y(a) = a - 4. Let u be y(6). Let l(r) = -r**2 + 2*r + 2. Let n be l(u). Solve -12*v**n - 1 + 8*v - 1 - v**4 + 8*v**3 - v**4 = 0 for v.
1
Suppose -20*w**3 - 13*w**4 - 37*w**4 + 8*w**2 + 80*w**5 - 18*w**4 = 0. Calculate w.
-2/5, 0, 1/4, 1
Let -5*t**4 - 4*t**2 + 13*t**4 - 2*t - 3*t**4 - t**4 + 2*t**5 = 0. What is t?
-1, 0, 1
Let f(y) = -y**2 + 11*y + 8. Let t(v) = v + 1. Let x(w) = -3*f(w) + 24*t(w). Factor x(p).
3*p*(p - 3)
Let b be (-4 + 2)/(-3 - -2). Let m be (b - 2)/(-3 - -1). Determine a so that -2*a**3 + 0 - 4/7*a**2 + m*a = 0.
-2/7, 0
Let u(m) = -m**4 - m**3 + m**2 - 1. Let a(v) = v**4 - 3*v**3 - v**2 - 3. Let f(y) = a(y) - 3*u(y). Factor f(t).
4*t**2*(t - 1)*(t + 1)
Let i(z) be the third derivative of z**8/168 + 5*z**7/84 + 7*z**6/40 + 5*z**5/24 + z**4/12 - 22*z**2. Determine b, given that i(b) = 0.
-4, -1, -1/4, 0
Let n be (-2 - 0)/(3/6). Let s be 0/n - -3*1. Factor 2/9*l**5 + 4/3*l**s + 0 + 10/9*l**4 - 16/9*l - 8/9*l**2.
2*l*(l - 1)*(l + 2)**3/9
Suppose 0*i + 21 = 5*q + 2*i, q + 5*i - 18 = 0. Factor 12*g**5 + 2*g**q + 2*g**3 - 21*g**5.
-g**3*(3*g - 2)*(3*g + 2)
Let s = 212 + -1057/5. Let m = 2 + 0. Factor 3/5*b + 0 + 0*b**m - s*b**3.
-3*b*(b - 1)*(b + 1)/5
Let m(n) be the second derivative of n**7/3780 - n**5/180 + n**4/3 + 6*n. Let w(r) be the third derivative of m(r). Suppose w(x) = 0. Calculate x.
-1, 1
Let a be (0 + 0 + -1)*2. Let s(j) = 17*j**3 + j**2. Suppose -27 = -2*l - l. Let c(y) = 4*y**3. Let f(m) = a*s(m) + l*c(m). Find g such that f(g) = 0.
0, 1
Let n(q) = 26*q**3 + 27*q**2 + 6*q + 5. Let a(x) = -25*x**3 - 27*x**2 - 6*x - 4. Let z(c) = 5*a(c) + 4*n(c). Find l, given that z(l) = 0.
-1, -2/7, 0
Let n(j) be the third derivative of -1/210*j**6 + 0 + 1/84*j**4 - 1/210*j**5 + j**2 + 0*j + 0*j**3. Suppose n(r) = 0. What is r?
-1, 0, 1/2
Let h be (-20)/(-2) - (3 - 3). Let o be 10/h + 3*1. Factor 0*p**2 + p**2 + o*p - 3*p**2.
-2*p*(p - 2)
Factor 4*b**4 + 2 - 5*b**4 - 5*b + 8*b - 5*b**3 + 2*b**3 - b**2.
-(b - 1)*(b + 1)**2*(b + 2)
Solve -6 - 21*y - 11*y - 44*y**2 - 22 + 40*y**2 = 0.
-7, -1
Let t(k) = 6*k**2 + 6*k - 7. Let n(f) be the second derivative of -f**4/12 - f**3/6 + f**2/2 - 2*f. Let h(l) = 10*n(l) + 2*t(l). Factor h(s).
2*(s - 1)*(s + 2)
Let y(n) be the second derivative of -n**8/840 + n**6/150 - n**4/60 + 9*n**2/2 + 3*n. Let u(p) be the first derivative of y(p). Find q such that u(q) = 0.
-1, 0, 1
Let y(w) = -w**3 - 6*w**2 + 8*w + 10. Let b(i) = i**2 + i - 7. Let k be b(0). Let r be y(k). Solve -r*j**2 - 2*j**4 + 5