 h(r) = -6*f(r) + 15*z(r). Determine c, given that h(c) = 0.
-1/4, 1/3, 1
Let -10*l + 38*l + 13*l + 14*l**2 + 5*l + 12 = 0. What is l?
-3, -2/7
Find w, given that 8/13*w - 16/13*w**2 - 2/13*w**4 + 10/13*w**3 + 0 = 0.
0, 1, 2
Let l be -5*152/171*(-3)/10. What is a in 2*a + l + 2/3*a**2 = 0?
-2, -1
Let v(s) = s. Let b(o) = -4*o**5 + 4*o**4 + 4*o**3 - 4*o**2 - 3*o. Let i(n) = n + 5. Let d be i(-4). Let g(w) = d*b(w) + 3*v(w). Factor g(p).
-4*p**2*(p - 1)**2*(p + 1)
Let m(q) be the second derivative of 3/7*q**2 - 1/42*q**4 + 2/21*q**3 + 3*q + 0. Factor m(p).
-2*(p - 3)*(p + 1)/7
Let i(y) = 3*y**4 + 3*y**3 - 8*y**2 + 4*y - 6. Let d(r) = -r**2 + 2*r - 3. Let a be d(3). Let p(n) = n**4 - n**3 + 1. Let l(q) = a*p(q) - i(q). Factor l(k).
-k*(k + 1)*(3*k - 2)**2
Let n be -3 - 1/((-4)/18). Let h(y) be the first derivative of 3/4*y**4 + 9/10*y**5 + 1 + n*y**2 + 0*y - 7/2*y**3. Let h(k) = 0. Calculate k.
-2, 0, 1/3, 1
Let k(f) be the second derivative of f**6/80 + f**5/10 + f**4/4 + f**2 + 4*f. Let j(r) be the first derivative of k(r). Factor j(m).
3*m*(m + 2)**2/2
Let i(p) be the third derivative of p**7/210 - p**6/120 - 7*p**5/60 + p**4/24 + p**3 - 32*p**2. Solve i(f) = 0.
-2, -1, 1, 3
Let t(x) be the first derivative of -x**7/105 + x**5/30 + x**2/2 - 1. Let w(u) be the second derivative of t(u). Factor w(d).
-2*d**2*(d - 1)*(d + 1)
Let y = 132 + -129. Find b such that 4/9*b + 2/3*b**y + 0 - 10/9*b**2 = 0.
0, 2/3, 1
Let j = 2 + 8. Suppose j*r**2 + 3*r + r**3 + 0 - 7*r**2 + 1 = 0. What is r?
-1
Let k(d) be the first derivative of -2*d**5/15 + d**4/6 + 4*d**3/9 - 11. What is w in k(w) = 0?
-1, 0, 2
Let i(k) = -k**3 - k**2 - 1. Suppose -1 = 4*w + 3. Let l(v) = -3*v**5 + v**4 - 2*v**3 - 6*v**2 - 5. Let a(r) = w*l(r) + 5*i(r). Factor a(n).
n**2*(n - 1)*(n + 1)*(3*n - 1)
Let f be 2 + ((-5)/(-2))/(-5). Let c be 5 - ((7 - 2) + -3). Factor 3/2*y**c - f*y**2 + 0 - 1/2*y**4 + 1/2*y.
-y*(y - 1)**3/2
Let w(b) be the first derivative of b**6/12 + b**5/5 - b**4/4 - 4*b**3/3 - 7*b**2/4 - b - 7. Suppose w(t) = 0. What is t?
-1, 2
Suppose -1/3*f - 1/2*f**2 + 1/6 = 0. Calculate f.
-1, 1/3
Suppose -2/11*u**2 + 30/11*u**4 + 0 + 32/11*u**3 - 4/11*u = 0. Calculate u.
-1, -2/5, 0, 1/3
Factor 0*d - 135/2 - 20*d**3 + 45*d**2 + 5/2*d**4.
5*(d - 3)**3*(d + 1)/2
Suppose -4 = -2*n - 0*h - 2*h, 0 = -n - 4*h - 1. Factor 1 + 2 + 12*m**2 + 5 + 15*m + 3*m**n - 2.
3*(m + 1)**2*(m + 2)
Factor f**5 + f**5 + 2*f**2 + 4*f**4 - 2*f - f**2 - 5*f**2.
2*f*(f - 1)*(f + 1)**3
Let t(c) be the second derivative of -c**10/12096 - c**9/15120 + c**4/3 - c. Let x(u) be the third derivative of t(u). Factor x(g).
-g**4*(5*g + 2)/2
Let 9/5*f + 3/5*f**2 + 6/5 = 0. Calculate f.
-2, -1
Let n(s) = 28*s**4 - 8*s**3 - 36*s**2 + 20*s + 20. Let b(y) = 4*y**4 - y**3 - 5*y**2 + 3*y + 3. Let g(j) = 20*b(j) - 3*n(j). Solve g(u) = 0 for u.
-1, 0, 2
Let i(h) be the first derivative of -h**6/40 + h**4/16 - 4*h + 3. Let o(b) be the first derivative of i(b). Solve o(r) = 0 for r.
-1, 0, 1
Let l be 5/3*(-162)/(-90). What is m in -3*m + 3/2*m**2 + 3/2*m**l + 0 = 0?
-2, 0, 1
Let o(v) = -16*v**3 + 5*v**2 + 7*v - 5. Let f(q) = -8*q**3 + 2*q**2 + 4*q - 2. Let z(u) = 9*f(u) - 4*o(u). Factor z(c).
-2*(c - 1)*(c + 1)*(4*c + 1)
Suppose -c + 5*c + 84 = 0. Let t be (-2)/(-4) - c/(-70). Let 1/5*l**4 + 3/5*l**2 - 3/5*l**3 - t*l + 0 = 0. What is l?
0, 1
Let l be 24/80 - (-51)/30. Let -7/2*g**4 + 9/2*g**l + 5/2*g**3 - 5/2*g - 1 = 0. What is g?
-1, -2/7, 1
Let y(l) be the first derivative of -5*l**3/12 + 5*l**2 - 20*l + 16. Factor y(z).
-5*(z - 4)**2/4
Let x(g) be the third derivative of 5*g**8/1344 - g**7/420 - g**6/96 + g**5/120 - 26*g**2. Determine w, given that x(w) = 0.
-1, 0, 2/5, 1
Let r(y) be the first derivative of 6 + 2/15*y**3 + 0*y**2 - 2/5*y. Factor r(k).
2*(k - 1)*(k + 1)/5
Let u = -6 - -8. Suppose s + z - 1 = 2, -z + 5 = u*s. Factor 1/3*n**s + 2/3 - n.
(n - 2)*(n - 1)/3
Factor 1/7*s**3 + 0*s**2 + 0*s - 1/7*s**5 + 0*s**4 + 0.
-s**3*(s - 1)*(s + 1)/7
Let j(r) be the first derivative of -r**5/240 - r**4/48 + 3*r**2/2 + 2. Let i(p) be the second derivative of j(p). Let i(z) = 0. Calculate z.
-2, 0
Suppose 0 - 1/2*t - 3/2*t**2 = 0. Calculate t.
-1/3, 0
Suppose -3*k = -6*k - 12. Let z be (6/(-4))/(6/k). Let f**2 - z - 6*f**2 + 4*f**2 - 2*f = 0. What is f?
-1
Suppose d - 15 = -2*d. Let i(s) be the third derivative of 0*s + 0*s**3 + 0*s**4 + 0 + 0*s**6 + 0*s**d - 2*s**2 - 1/672*s**8 - 1/420*s**7. Factor i(l).
-l**4*(l + 1)/2
Suppose 0 = 4*d + 29 - 9. Let r be 6/15*d/(-1). Let t**2 - 3*t**2 - 3*t**3 - t - 3*t**r + 9*t**4 = 0. Calculate t.
-1/3, 0, 1
Factor 0 + 1/3*s - 4/3*s**2.
-s*(4*s - 1)/3
Let j(i) be the third derivative of 9*i**7/70 + 5*i**6/8 + 21*i**5/20 + 3*i**4/8 - i**3 - 13*i**2. Solve j(r) = 0.
-1, 2/9
Let a(l) = l**3 - 12*l**2 - 11*l + 12. Let i(o) = -6*o**2 - 6*o + 6. Let z(g) = -3*a(g) + 5*i(g). Factor z(y).
-3*(y - 2)*(y - 1)*(y + 1)
Let g = -59 - -185/3. Let l(y) be the first derivative of -4/3*y - 2 - 5/9*y**3 - 25/12*y**4 + g*y**2. Determine w, given that l(w) = 0.
-1, 2/5
Suppose -4 = -o - 1. Let w = 7 - o. What is i in -1/2*i**w + 0 + 1/2*i**2 + 0*i + 0*i**3 = 0?
-1, 0, 1
Let n(f) be the third derivative of 9*f**6/40 + 3*f**5/20 - 5*f**4/8 + f**3/2 + 7*f**2. Factor n(q).
3*(q + 1)*(3*q - 1)**2
Let j(h) = -5 - 3*h - 5*h**2 + 2*h**3 - 2*h + 0*h**2 - 5*h**3. Let z(y) = -5*y**3 - 8*y**2 - 8*y - 8. Let d(g) = -8*j(g) + 5*z(g). Find c such that d(c) = 0.
0
Determine n, given that -5*n**2 - 2*n + 7*n - 77 + 97 + 10*n = 0.
-1, 4
Let j(f) be the third derivative of f**8/42 - f**7/105 - f**6/15 + f**5/30 - 12*f**2. Suppose j(w) = 0. Calculate w.
-1, 0, 1/4, 1
Determine f so that 0 - 3/4*f**3 + 0*f - 3/4*f**4 + 3/2*f**2 = 0.
-2, 0, 1
Let t(r) = r**3 + 5*r**2 + 8*r + 4. Let s be t(-2). Suppose 2/7*x**2 + s*x - 2/7 = 0. Calculate x.
-1, 1
Let h(z) be the second derivative of z**5/35 - 2*z**4/21 + 21*z. Factor h(b).
4*b**2*(b - 2)/7
Let y(k) be the second derivative of k**4/78 - 2*k**3/13 + 9*k**2/13 - 20*k. What is u in y(u) = 0?
3
Let f(n) be the third derivative of -n**7/900 - n**6/900 - n**4/8 - 2*n**2. Let b(l) be the second derivative of f(l). Factor b(a).
-2*a*(7*a + 2)/5
Let s(w) be the second derivative of w**6/150 + 3*w**5/100 - 2*w**3/15 - 36*w. Solve s(u) = 0 for u.
-2, 0, 1
Let m be (-5)/(-20) + (-27)/12 + 2. Solve 3/2*y**3 + 0*y**2 + m - 3/2*y = 0.
-1, 0, 1
Let i(w) be the second derivative of -w**5/80 - 5*w**4/48 - w**3/3 - w**2/2 - 27*w. Let i(f) = 0. What is f?
-2, -1
Suppose 3*b - 6 = 2*f - 2, -5*b + 8 = -2*f. Factor 6*r**2 + b*r + 2*r + 2*r**4 - 2*r**3 - 4*r**3 - 6*r.
2*r*(r - 1)**3
Suppose -4*k + 12 = -k. Let l = k - 2. Factor -4*q + 4*q**l - 5*q**2 + 3*q.
-q*(q + 1)
Factor 3*m + 5*m + 38*m**4 - 30*m**3 - 4*m - 14*m**5 + 2*m**2.
-2*m*(m - 1)**3*(7*m + 2)
Suppose 0*k - 31 = -4*i - 5*k, 0 = -5*i + k + 17. Let d = 4 - i. Find r such that 1/3*r**3 + 0 + d*r + 1/3*r**2 = 0.
-1, 0
What is g in -26/7*g**2 + 12/7*g**3 - 2/7*g**4 + 24/7*g - 8/7 = 0?
1, 2
Let k(a) be the second derivative of -a**9/18900 + a**8/3360 - a**7/1575 + a**6/1800 + 7*a**4/12 - 7*a. Let h(s) be the third derivative of k(s). Factor h(z).
-2*z*(z - 1)**2*(2*z - 1)/5
Let a(x) be the second derivative of -x**7/945 + x**6/270 - x**5/270 + 11*x**2/2 + 3*x. Let s(j) be the first derivative of a(j). Let s(z) = 0. What is z?
0, 1
Let u(i) be the second derivative of 2*i**7/21 + i**6/30 + 5*i**3/6 + i. Let b(n) = 5*n**5 + n**4 + 6*n. Let g(t) = -5*b(t) + 6*u(t). Factor g(k).
-k**4*(k - 1)
Find g such that -3*g - 5*g + 5*g**3 + 9*g**3 - 10*g**3 - 4*g**2 = 0.
-1, 0, 2
Let y(i) be the first derivative of -9/2*i**4 - 3/2*i**2 - 1/2*i**6 + 0*i - 2 + 4*i**3 + 12/5*i**5. Factor y(a).
-3*a*(a - 1)**4
Let f(c) = c**2 + 31*c - 2*c**2 - 26*c + 16. Let d be f(7). Factor 6/7*m + 0*m**d + 2/7 - 8/7*m**3.
-2*(m - 1)*(2*m + 1)**2/7
Suppose -4*d = -5*c - 5*d + 44, -3*c + 26 = d. Find t, given that 7*t**3 - 9*t**3 - c*t - 7*t + 7 + 1 + 10*t**2 = 0.
1, 2
Let b(w) = 2*w - 48. Let t be b(24). Let l(m) be the second derivative of -1/189*m**7 - 2/135*m**6 + 0*m**4 + t*m**5 + 0*m**3 + 0 + m + 0*m**2. Solve l(o) = 0.
-2, 0
Let l(o) be the first derivative of o**8/7560 + o**7/1890 - o**5/270 - o**4/108 + 2*o**3/3 + 3. Let x(f) be the third derivative of l(f). Factor x(k).
2*(