 + 2*t**4/3 - 10*t**3/3 + 35*t**2. Factor v(x).
4*(x - 1)*(x + 5)
Let z(l) be the second derivative of -2*l - 7/120*l**6 + 0 + 0*l**4 + 0*l**2 + 1/40*l**5 + 0*l**3. What is b in z(b) = 0?
0, 2/7
Let s(r) = r**3 + 3*r**2 - 6*r - 5. Let o be s(-4). What is v in -7/2*v**2 + 0 - 5/2*v**o - v = 0?
-1, -2/5, 0
Let r(n) be the third derivative of n**8/672 - n**7/140 + n**6/120 - 3*n**2 + 5. Find a such that r(a) = 0.
0, 1, 2
Let b(u) be the first derivative of -u**8/6720 - u**7/3360 - u**3/3 + 3. Let o(z) be the third derivative of b(z). Solve o(d) = 0.
-1, 0
Let n(o) be the first derivative of -8*o**5/25 + o**4/10 + 8*o**3/15 - o**2/5 - 6. Determine w so that n(w) = 0.
-1, 0, 1/4, 1
Let n(a) be the second derivative of 1/30*a**4 - 1/75*a**6 - 1/50*a**5 + 0 + 0*a**2 + 1/15*a**3 + a. What is k in n(k) = 0?
-1, 0, 1
Let d(u) = 3*u**2 + 3*u. Let a(r) be the first derivative of -10*r**3/3 - 5*r**2 - r + 2. Let q(x) = -2*a(x) - 7*d(x). Factor q(l).
-(l - 1)*(l + 2)
Let n(l) = -90*l + 542. Let v be n(6). Factor -2/3 - v*m**2 - 8/3*m.
-2*(m + 1)*(3*m + 1)/3
Let q(d) be the second derivative of d**8/16800 + d**7/6300 - d**6/900 + d**4/6 + 5*d. Let u(f) be the third derivative of q(f). Factor u(w).
2*w*(w - 1)*(w + 2)/5
Let w = 38701/60 + -645. Let c(q) be the third derivative of 1/525*q**7 - 2*q**2 + 0 + 0*q**3 + w*q**4 + 1/100*q**6 + 0*q + 1/50*q**5. Factor c(p).
2*p*(p + 1)**3/5
Let r(f) = -f + 1. Let i(p) = -p**3 - 2*p**2 - 4*p + 7. Let j(z) = -2*i(z) + 22*r(z). Find n such that j(n) = 0.
-4, 1
Let k(i) be the first derivative of -2*i**6/9 - 4*i**5/15 + i**4 + 20*i**3/9 + 4*i**2/3 + 8. Suppose k(j) = 0. Calculate j.
-1, 0, 2
Let y be (-2)/4 + 36/16. Let v = y - 3/2. Find s such that -1/4*s**3 + 0 + 1/4*s**5 + v*s**2 - 1/4*s**4 + 0*s = 0.
-1, 0, 1
Let x(a) be the second derivative of a**4/66 - 11*a. What is o in x(o) = 0?
0
Let j(b) = -2*b**3 - 2*b**2 - b. Let d be j(-1). Let x be -4*-1*(0 + d). Factor -4*z**3 + 2 + 13*z**2 + x*z - 13*z**2 - 2*z**4.
-2*(z - 1)*(z + 1)**3
Let m(n) be the first derivative of n**6/180 + 2*n**3 - 1. Let i(x) be the third derivative of m(x). Factor i(y).
2*y**2
Let u(s) = 3*s**3 - 2*s**2 - 3*s + 2. Let x(m) = -m**3 + m**2. Let g(i) = 5*u(i) + 10*x(i). Factor g(p).
5*(p - 1)**2*(p + 2)
Let r be (10/((-600)/(-12)))/(2/24). Let r*d**2 - 6/5*d**4 - 6/5 + 3*d + 3*d**5 - 6*d**3 = 0. What is d?
-1, 2/5, 1
Let k(a) be the second derivative of -a**8/6720 + a**6/1440 + a**3/2 - 2*a. Let q(u) be the second derivative of k(u). Suppose q(s) = 0. Calculate s.
-1, 0, 1
Suppose -7 = -o - 0*o. Suppose 3*z = -1 + o. Factor 3/2 + 1/6*q**z - q.
(q - 3)**2/6
Let i(x) be the third derivative of -x**9/151200 + x**8/16800 - x**7/6300 - x**5/20 + x**2. Let c(p) be the third derivative of i(p). Factor c(q).
-2*q*(q - 2)*(q - 1)/5
Let t(h) be the third derivative of 0*h**7 + 0*h + 1/180*h**6 + 0*h**3 + 0*h**5 - 1/72*h**4 + 3*h**2 - 1/1008*h**8 + 0. Find a such that t(a) = 0.
-1, 0, 1
Determine w, given that 0*w + 0 - 2/7*w**2 = 0.
0
Suppose 4/11 + 14/11*g + 8/11*g**4 - 12/11*g**2 - 14/11*g**3 = 0. What is g?
-1, -1/4, 1, 2
Let -1/5*w**5 + 0*w**2 + 0*w + 0 - 1/5*w**3 - 2/5*w**4 = 0. Calculate w.
-1, 0
Let h(z) be the third derivative of -z**8/10080 + z**7/7560 - z**5/20 - 2*z**2. Let t(v) be the third derivative of h(v). What is r in t(r) = 0?
0, 1/3
Let m(f) = -2*f**2 + 33*f + 20. Let w be m(17). Let 3/2*i**4 + 6*i**w + 0 + 3*i + 15/2*i**2 = 0. Calculate i.
-2, -1, 0
Let z(s) be the first derivative of -2 - 1/2*s**2 + 4/5*s**5 + 2/3*s**3 + 7/4*s**4 + 0*s. Let z(k) = 0. Calculate k.
-1, 0, 1/4
Let s(w) be the third derivative of w**6/420 - w**5/210 - 5*w**4/84 - w**3/7 + 5*w**2. Find v such that s(v) = 0.
-1, 3
Let q(s) = -5*s**2 + 21*s - 12. Let r(f) = -f**2 - f + 1. Let y(x) = q(x) - 2*r(x). Factor y(t).
-(t - 7)*(3*t - 2)
Let l(q) be the third derivative of q**7/140 + q**6/80 - 3*q**5/40 - q**4/16 + q**3/2 + 37*q**2. Determine o, given that l(o) = 0.
-2, -1, 1
Let v(h) be the third derivative of -h**6/20 + 23*h**5/90 - 8*h**4/27 + 4*h**3/27 - 12*h**2. Determine r so that v(r) = 0.
2/9, 1/3, 2
Let t(k) = 3*k**2 - 8*k - 5. Suppose 5*o = w - 10, o = -4*w + 8 + 11. Let b(j) = 3*j**2 - 9*j - 6. Let r(g) = w*b(g) - 6*t(g). Solve r(d) = 0.
0, 1
Let y = -14 + 26. Let q = y + -10. Factor -2*p + p**3 + p**q + 2*p**2 + 4*p.
p*(p + 1)*(p + 2)
Let y(p) = p**2 + p - 1. Let o(t) = -6*t**2 - 18*t + 9. Let s(g) = o(g) + 9*y(g). Factor s(c).
3*c*(c - 3)
Let x(t) be the second derivative of t**5/35 - 2*t**3/21 - 25*t. Suppose x(z) = 0. What is z?
-1, 0, 1
Let y(v) be the second derivative of 11*v**5/5 - 20*v**4/3 + 14*v**3/3 + 4*v**2 + 7*v. Find z such that y(z) = 0.
-2/11, 1
Let 0*j**2 - 10*j**2 - 25*j**3 + 0*j**2 + 10*j**5 - 5*j**4 = 0. Calculate j.
-1, -1/2, 0, 2
Let r(g) be the third derivative of g**8/168 - g**7/105 - g**6/30 + g**5/15 + g**4/12 - g**3/3 + 3*g**2. Factor r(y).
2*(y - 1)**3*(y + 1)**2
Suppose f - 3 = 2. Let 4/3*l**2 - f*l**3 + 3*l + 2/3 = 0. What is l?
-2/5, -1/3, 1
Let s be 2/(-6) + (-12)/(-9). Let r be (3/6 + 0)*s. Find p, given that 0 + 1/2*p**3 - p**2 + r*p = 0.
0, 1
Let f(d) be the third derivative of -d**6/600 - d**5/150 - 9*d**2. Solve f(o) = 0 for o.
-2, 0
Let f(m) be the first derivative of -m**5/15 - m**4/6 + m**3/9 + m**2/3 - 22. Factor f(s).
-s*(s - 1)*(s + 1)*(s + 2)/3
Solve -3/2*v**3 + 3*v + 0 + 3/2*v**2 = 0.
-1, 0, 2
Suppose -23 = -5*i - 2*o, 2*i + 3*o = 7*i - 3. Find d such that -3 + i - 2*d**4 - d**2 + 3*d**2 = 0.
-1, 0, 1
Let t(n) be the first derivative of -3 - 1/2*n**4 - 8*n + 2*n**3 + 0*n**2. Determine v so that t(v) = 0.
-1, 2
Let f(g) be the second derivative of -g**5/4 + 5*g**4/4 - 5*g**3/3 + 6*g. Let f(v) = 0. Calculate v.
0, 1, 2
Let j = 9 - 7. Let c(l) be the third derivative of -1/6*l**3 + 1/32*l**6 - 1/12*l**4 + 0*l - l**j + 11/240*l**5 + 0. Factor c(d).
(d + 1)*(3*d - 2)*(5*d + 2)/4
Let s(x) be the second derivative of -2*x + 1/12*x**4 + 1/3*x**3 + 0 + 1/2*x**2. Suppose s(a) = 0. What is a?
-1
Let q be -1*4/6*-6. Factor 0*x**4 + 4*x - 2*x**q - x**2 + 7*x**2.
-2*x*(x - 2)*(x + 1)**2
Let w(d) = -6*d**2 - 17*d + 5. Let s be w(-3). Suppose 0 + 1/4*h - h**s = 0. Calculate h.
0, 1/4
Let a(x) = 27*x - 31*x + x**2 + 1 - 6. Let u be a(5). Let -1/4*y**3 + 0*y**2 + 0*y + u = 0. Calculate y.
0
Suppose -3*j = -m + 15, 3*j + 28 = 3*m + 7. Suppose -13*k**m - k**2 - k**2 + 4*k**3 = 0. Calculate k.
-2/9, 0
Suppose -14 = 2*b + b + 5*q, -4*q - 24 = -4*b. Find k such that -k**3 + k**2 - 6 + 5*k**b + 4*k**3 - 3*k = 0.
-2, -1, 1
Let p(i) be the second derivative of -i**8/1680 - i**7/280 - i**6/120 - i**5/120 + i**3/6 - i. Let f(m) be the second derivative of p(m). Factor f(y).
-y*(y + 1)**3
Factor 2*h**3 + 2*h**2 - 14/3*h**4 + 0 + 2*h**5 - 4/3*h.
2*h*(h - 1)**3*(3*h + 2)/3
Factor -m**3 - 5/7*m**4 - 1/7*m**5 + 0 - 3/7*m**2 + 0*m.
-m**2*(m + 1)**2*(m + 3)/7
Suppose 2*m = -3*k + 13, 0 = -2*k - 0*k - 3*m + 12. Suppose 4*w + 3*n - 8 = 0, k*n = 3*w + 5*n - 6. Let -4*f - 4/3 + 21*f**w + 196/3*f**3 = 0. Calculate f.
-2/7, 1/4
Suppose 3*w + 1 = 22. Let c(k) = -k**3 + 8*k**2 - 5*k + 1. Let l be c(w). Determine n, given that 15*n - 2*n**4 - n**5 - l*n - n**3 = 0.
-1, 0
Suppose -2*p + 0*p = -4. Factor -2*o**2 - 3*o**p + 8*o**2.
3*o**2
Let y(d) be the first derivative of 5 - 1/8*d**2 + 1/2*d + 1/16*d**4 - 1/6*d**3. Factor y(m).
(m - 2)*(m - 1)*(m + 1)/4
Suppose -x + 2*i - 3 = -2*x, -3*x + 1 = -2*i. Let r be (-12)/(-4) + 0 + x. Factor -2/5*q**r + 0*q - 2/5 + 4/5*q**2 + 0*q**3.
-2*(q - 1)**2*(q + 1)**2/5
Let l(j) be the second derivative of -5*j**7/189 + 8*j**6/135 + j**5/10 - 4*j**4/27 - 4*j**3/27 + 3*j. Suppose l(i) = 0. Calculate i.
-1, -2/5, 0, 1, 2
Determine y, given that 1/4*y**2 - 1/2*y**3 + 0*y + 1/4*y**4 + 0 = 0.
0, 1
Let u(v) be the third derivative of -v**9/1512 + v**7/210 - v**5/60 + 2*v**3/3 - 2*v**2. Let b(i) be the first derivative of u(i). Suppose b(k) = 0. What is k?
-1, 0, 1
Let w(m) be the first derivative of -2/15*m**3 - 2/5*m - 2/5*m**2 - 1. Factor w(c).
-2*(c + 1)**2/5
Let t(c) = -c**2 - c. Let j(q) = -6*q**2 - 8*q - 2. Let a(k) = -j(k) + 5*t(k). Factor a(y).
(y + 1)*(y + 2)
Let f(n) = -n**3 + 6*n**2 + n - 4. Let i be f(6). Let s be 5/10*(0 + 0). Factor 0*k**2 + s*k + 6*k - 4*k**i - 2.
-2*(k - 1)*(2*k - 1)
Let f(d) be the first de