
5*v*(v - 2)
Solve 16*f**5 + f**4 - 15*f**5 - 3*f**4 + f**3 = 0.
0, 1
Factor 2/3*i**2 + 4/3 + 2*i.
2*(i + 1)*(i + 2)/3
Let r(c) be the second derivative of -c**6/360 - c**5/180 - 2*c**2 - c. Let v(l) be the first derivative of r(l). Solve v(y) = 0.
-1, 0
Let f(h) = 2*h**4 - h**3 - 3*h**2 + 7*h - 7. Let t(m) = -m**4 + m**2 - 3*m + 3. Let g(b) = 6*f(b) + 14*t(b). Factor g(r).
-2*r**2*(r + 1)*(r + 2)
Let w(i) be the first derivative of i**3/5 + 12*i**2/5 + 48*i/5 - 10. Determine d, given that w(d) = 0.
-4
Suppose -m + 3*m - 4*q = 12, -3*m + 12 = -3*q. Factor 2/3*w**3 + 0*w + 0 + 2/3*w**m.
2*w**2*(w + 1)/3
Let s be 3*(1 + 0 - 0). Suppose n + s = -5*h, -4*n - 4*h = -n - 2. Factor 0*z**n - 4/3*z**3 - 2*z**4 + 0*z + 0.
-2*z**3*(3*z + 2)/3
Let b(d) be the second derivative of -1/6*d**3 - 1/60*d**5 + 1/12*d**4 + 0 - 1/2*d**2 - 2*d. Let u(h) be the first derivative of b(h). Let u(t) = 0. What is t?
1
Let g = -4 + 6. Suppose 6 = -3*x + 2*j, -2*x - 3 = g*x - j. Factor l**2 + 6 + 0*l**2 - 4*l**2 + 3*l + x*l**2.
-3*(l - 2)*(l + 1)
Let z(c) be the first derivative of 2*c**3/21 - 2*c**2/7 - 6*c/7 + 9. Find p such that z(p) = 0.
-1, 3
Let a(i) be the third derivative of 0 + 4*i**2 + 0*i**4 - 2/165*i**6 + 0*i + 5/1848*i**8 - 1/165*i**7 + 0*i**3 + 2/165*i**5. Determine t, given that a(t) = 0.
-1, 0, 2/5, 2
Let r(x) be the second derivative of 12*x**5/5 + 10*x**4 - 23*x**3/2 + 9*x**2/2 - 13*x. Factor r(l).
3*(l + 3)*(4*l - 1)**2
Let k(a) be the second derivative of 0 + 3*a - 1/10*a**5 - 5/42*a**4 + 0*a**2 - 1/35*a**6 - 1/21*a**3. Factor k(s).
-2*s*(s + 1)**2*(3*s + 1)/7
Suppose -3*t + 3 + 6 = 0. Factor p**4 + 6*p**t - 2*p**4 - p**3 - 3*p**3.
-p**3*(p - 2)
Let s(f) be the third derivative of -f**6/120 - f**5/60 + 27*f**2. Factor s(g).
-g**2*(g + 1)
Suppose -17 = 2*b - 21. Suppose b*o**3 + 0 + 10/9*o**5 - 4/9*o + 2/9*o**2 - 26/9*o**4 = 0. What is o?
-2/5, 0, 1
Let b(y) be the third derivative of y**6/60 - y**5/30 + 5*y**2. Factor b(n).
2*n**2*(n - 1)
Let t(q) be the second derivative of -q**4/72 + q**2/3 + 19*q. Suppose t(l) = 0. What is l?
-2, 2
Let x(m) be the second derivative of 0 - 1/15*m**5 - m + 0*m**2 - 1/45*m**6 + 1/18*m**4 + 2/9*m**3. Solve x(n) = 0.
-2, -1, 0, 1
Let h(z) be the second derivative of -21*z**5/160 + z**4/12 + z**3/12 + 13*z. Let h(y) = 0. Calculate y.
-2/7, 0, 2/3
Let u(v) be the first derivative of v**5/240 - v**4/48 + v**3/24 - v**2 - 4. Let s(t) be the second derivative of u(t). Let s(f) = 0. What is f?
1
Factor 10*c + 5*c**4 + 5*c**5 - 46*c**3 - 47*c**3 + 78*c**3 - 5*c**2 + 0*c**5.
5*c*(c - 1)**2*(c + 1)*(c + 2)
Let q(r) = 6*r. Let x be q(1). Suppose x = 2*j - z, 2*j - 3*j - 3 = -2*z. Determine p so that 8*p**2 + 2*p + 6*p**3 + 1 - j - 4*p = 0.
-1, 2/3
Let y(z) = -3*z**2 + 7*z + 2. Let b(p) = -7*p**2 + 15*p + 4. Let q(s) = 4*b(s) - 9*y(s). What is l in q(l) = 0?
-2, -1
Let f = -2 - 0. Let i(j) = j**2 + j. Let o(u) = -4*u**2 - 6*u - 2. Let m(s) = f*i(s) - o(s). Find p such that m(p) = 0.
-1
Let b be (8/6)/(36/54). Find u, given that -8 + 2*u**3 - u**2 + 0*u**2 - u**b + 16*u - 8*u**2 = 0.
1, 2
Factor m**4 - m**5 - 6*m - 9*m**3 + 2*m**4 - 15*m**2 + 4*m**5.
3*m*(m - 2)*(m + 1)**3
Let r = 47 + -43. Factor 0*k - k**3 + 1/2*k**2 + 1/2*k**r + 0.
k**2*(k - 1)**2/2
Let k(s) = 43*s - 28*s + 6 - 17*s. Let a be k(2). What is t in 12*t + 39/2*t**4 + a + 9/2*t**5 + 57/2*t**2 + 67/2*t**3 = 0?
-1, -2/3
Factor -5*l**2 + 4 + 3*l**2 + 0*l**2 - 2*l**2.
-4*(l - 1)*(l + 1)
Suppose 22*o = o + 42. Factor -1/2*m**o + m - 1/2.
-(m - 1)**2/2
Let s(z) be the second derivative of -z**4/12 + z**3/3 + 3*z. Suppose s(r) = 0. What is r?
0, 2
Let p = 268/7 + -262/7. Suppose 3/7*a - 3/7*a**2 + p = 0. What is a?
-1, 2
Let k(v) = -10*v + 5 + 2 + 8 + v**2. Let i be k(9). Find w such that i*w**2 + 15/2*w + 3/2 = 0.
-1, -1/4
Let l = -20 + 38. Determine w, given that -12*w**2 + l*w**3 + 0*w + 2*w + 0*w - 8*w**4 = 0.
0, 1/4, 1
Factor 4/5*b**2 + 2/5*b**3 - 4/5 - 2/5*b.
2*(b - 1)*(b + 1)*(b + 2)/5
Let m(y) be the third derivative of y**7/630 + y**6/360 - y**5/360 - y**3/6 - y**2. Let j(q) be the first derivative of m(q). Find c such that j(c) = 0.
-1, 0, 1/4
Let c(h) = -3*h**2 - 4*h**3 + 1 - 1 - 3*h**4 - 5*h. Let b(j) = -2*j**4 - 2*j**3 - 2*j**2 - 3*j. Let y(m) = 5*b(m) - 3*c(m). Factor y(w).
-w**2*(w - 1)**2
Let h(k) = -k**4 + 5 + 13*k**2 - 12*k**2 - 1 + k**3 - 3. Let m(p) = -12*p**4 + 9*p**3 + 21*p**2 + 9. Let j(u) = -9*h(u) + m(u). Let j(w) = 0. Calculate w.
-2, 0, 2
Let n be -2*1 - (-5 + 1). Let b = -1 - -4. Factor -1 + 2*c**3 + n*c - 2*c**2 - 4*c + b.
2*(c - 1)**2*(c + 1)
Let q = 26 - 14. Let y be 19/21 + (-4)/q. Determine p so that y*p**2 + 2/7*p**3 + 0 + 2/7*p = 0.
-1, 0
Let p(n) be the first derivative of -3*n**5/20 - 3*n**4/16 + 3*n**3/4 + 3*n**2/8 - 3*n/2 - 17. Suppose p(x) = 0. Calculate x.
-2, -1, 1
Let q(t) = -t**2 + 12*t + 4. Let y be q(12). Suppose 4*j = 2*j + y. Let 94*w**j + 225*w**4 + 240*w**3 + 16*w - 1 - 1 - 1 + 4 = 0. Calculate w.
-1/3, -1/5
Let a be ((-9)/(-6))/((-1)/10). Let d = 31/2 + a. Determine o, given that d*o**2 + 1/2 - o = 0.
1
Suppose 0 = 2*h - 2*q - 3*q + 13, 3*h - 4*q = -23. Let n(f) = 4*f. Let o(y) = -y**2 - 17*y. Let i(w) = h*n(w) - 2*o(w). Determine c, given that i(c) = 0.
0, 1
What is q in -18/11*q + 2/11*q**2 + 28/11 = 0?
2, 7
Let c(x) be the second derivative of -x**6/12 + 5*x**4/12 - 5*x**2/4 + 14*x. Solve c(q) = 0 for q.
-1, 1
Suppose 2*v = -2*v. Let k(h) be the second derivative of 0*h**4 + 1/42*h**7 + 1/6*h**3 + v*h**6 + 0 + 0*h**2 - 1/10*h**5 + h. Solve k(c) = 0 for c.
-1, 0, 1
Factor 5*i**4 + 26*i - 36*i + 3*i**5 - 15*i**3 + 2*i**5 - 25*i**2.
5*i*(i - 2)*(i + 1)**3
Factor 1/2*p**5 - p**4 - 3/2*p**3 + 2*p + 2*p**2 + 0.
p*(p - 2)**2*(p + 1)**2/2
Suppose -4*p + p = -9. Let n = 11 + -6. Let 10/3*x**4 - 8/3*x**n + 2/3*x + 0 - 10/3*x**2 + 2*x**p = 0. Calculate x.
-1, 0, 1/4, 1
Let x(g) = g**5 - g**4 + g**3 + 1. Let q(t) = 4*t**5 - 6*t**4 + 4*t**3 + 3*t**2 - 2*t + 3. Let h(p) = 2*q(p) - 6*x(p). Factor h(u).
2*u*(u - 2)*(u - 1)**2*(u + 1)
Let c(n) = -3*n**5 - 9*n**4 - 11*n**3 + 3*n**2 + 8*n. Let a(d) = -2*d**5 - 8*d**4 - 10*d**3 + 4*d**2 + 8*d. Let m(y) = 5*a(y) - 4*c(y). Factor m(l).
2*l*(l - 2)**2*(l + 1)**2
Let g(x) = -x + 11. Let k be g(7). Let a(w) be the second derivative of 1/18*w**3 + 0*w**2 - 1/36*w**k - 1/60*w**5 + 3*w + 1/90*w**6 + 0. Factor a(i).
i*(i - 1)**2*(i + 1)/3
Suppose 0 = 2*o - 2*l + 7*l, -4*l = -3*o. Factor o*z + 3/4*z**2 + 1/4*z**3 + 0.
z**2*(z + 3)/4
Let k(n) be the second derivative of 8*n**6/15 - 17*n**5/5 + 16*n**4/3 - 2*n**3 + 5*n. Factor k(z).
4*z*(z - 3)*(z - 1)*(4*z - 1)
Let d(w) be the first derivative of 7/150*w**5 + 2/15*w**3 + 1 + 3/20*w**4 + 0*w + 1/2*w**2. Let p(l) be the second derivative of d(l). Solve p(h) = 0 for h.
-1, -2/7
Let h(c) be the third derivative of c**7/840 - c**6/240 + c**4/12 - c**2. Let a(u) be the second derivative of h(u). Solve a(k) = 0.
0, 1
Let x be (-2)/(-2) - -3*2/(-6). Find v such that 8/11*v**4 + 8/11*v**3 + x + 0*v + 2/11*v**2 = 0.
-1/2, 0
Let r be 0 + 2 + -2 - -3. Suppose 0 = -r*y + 4 + 2. Factor -3*a + a**y + 3*a + a.
a*(a + 1)
Suppose 3*f + 5 = 7*f + 3*u, f - 5*u - 7 = 0. Factor -33*t**4 + 2*t + 2*t**3 - 4*t - f*t**2 + 35*t**4.
2*t*(t - 1)*(t + 1)**2
Let y be (-2*2)/(1/(-2)). Suppose 0*z + 4*z = -4*s + y, -5*z + 10 = -5*s. Determine c so that -2*c**z - 2/3*c**3 - 2*c - 2/3 = 0.
-1
Let q = 0 - -2. Let o(a) = 2*a - 18. Let y be o(10). Factor -4*c + 4*c**2 - 2*c**q + 7*c + c**y.
3*c*(c + 1)
Let v = 4858/5 + -968. Factor -8/5 + 8*h - v*h**2.
-2*(h - 2)*(9*h - 2)/5
Let p(m) = -3*m + m**2 - 4*m + 11 - m. Let i be p(7). Find c such that -4/9*c**3 + 0 + 2/9*c**2 + 0*c + 2/9*c**i = 0.
0, 1
Let t(l) be the first derivative of -2*l**6/15 - 4*l**5/5 - 2*l**4 - 8*l**3/3 - 2*l**2 - 8*l + 9. Let u(h) be the first derivative of t(h). Factor u(m).
-4*(m + 1)**4
Let a(u) be the first derivative of -4*u**3/3 - 6*u**2 - 8*u - 34. Let a(q) = 0. What is q?
-2, -1
Let b(m) = -m**2 + 1. Let g(l) = -l - 1. Suppose 2*d = -d + 3. Let f(v) = d*g(v) - b(v). What is x in f(x) = 0?
-1, 2
Suppose -3*g = -10 + 4. Factor 0 + 3/2*l**3 + 1/2*l + 3/2*l**g + 1/2*l**4.
l*(l + 1)**3/2
Let o(b) be the first derivative of -b**4/12 + b**3/3 - b**2/3 + 12. Let o(y) = 0. Calculate y.
0, 1, 2
Factor -10*l**2 - 4*l +