- s. Suppose 2/3*j**3 - 1/3*j**4 + 1/3 + 0*j**2 - k*j = 0. What is j?
-1, 1
Let t = 11 + -6. Let d be (-6)/(-2) + (-5)/t. Find y, given that -1/4*y**d + 0 - 1/4*y = 0.
-1, 0
Let c(n) = n**3 - 1. Let j(q) = 4*q**5 + 12*q**4 + 2*q**3 - 28*q**2 + 10. Let a(g) = -6*c(g) + j(g). Determine p, given that a(p) = 0.
-2, -1, 1
Suppose -6 - 6 = -4*p. Let 2*j**p + 0*j**4 - 2*j**4 + 3*j**4 + j**2 = 0. What is j?
-1, 0
Let r be (2 + (0 - 5))*(-18)/81. Factor 0*x + 4/3*x**2 + 0 + r*x**3.
2*x**2*(x + 2)/3
Let h(z) = z**5 + z**4 - z. Let n(b) = 4*b**5 + 4*b**4 - b**3 - b**2 - 3*b. Let v(w) = -3*h(w) + n(w). Factor v(q).
q**2*(q - 1)*(q + 1)**2
Factor 95*i**3 - 8*i - 5*i**2 - 90*i**3 + 5 + 3*i.
5*(i - 1)**2*(i + 1)
Let a(r) be the first derivative of -r**5 + 25*r**4/2 - 60*r**3 + 140*r**2 - 160*r - 3. Factor a(i).
-5*(i - 4)*(i - 2)**3
Suppose -7*i = -3*i - 20. Let c = i - 3. Determine v, given that 5*v**2 - v + 3*v**3 - 4*v**3 - 1 - c*v**3 = 0.
-1/3, 1
Let a(s) be the third derivative of -s**5/20 + 3*s**4 - 72*s**3 - 2*s**2 + 23*s. Solve a(v) = 0.
12
Let m(g) = -3*g**3 + g**2 + 7*g + 5. Let r be 2*(16/(-4) - -6). Let f(z) = z**3 - 3*z - 2. Let c(d) = r*m(d) + 10*f(d). Suppose c(o) = 0. Calculate o.
0, 1
Let b(f) be the first derivative of f**6/5 + 9*f**5/25 - 3*f**4/20 - 3*f**3/5 - 3*f**2/10 + 2. Suppose b(p) = 0. What is p?
-1, -1/2, 0, 1
Let k = 2138/105 + -136/7. Let a(q) be the first derivative of 0*q + 9/10*q**4 - 1 - k*q**3 - 2/5*q**2. Factor a(b).
2*b*(b - 1)*(9*b + 2)/5
Let i(t) be the first derivative of 2*t**7/21 - 2*t**6/15 - 2*t**5/5 - t + 1. Let b(d) be the first derivative of i(d). Factor b(a).
4*a**3*(a - 2)*(a + 1)
Let w(x) = x - 3. Let r be (20/16)/((-4)/(-16)). Let g be w(r). Let -12/5*z**g + 3/5 + 9/5*z = 0. What is z?
-1/4, 1
Suppose -s + 4*g + 23 = 0, 6*s = 2*s - g + 7. Factor 0 - 4/9*d - 2/9*d**s + 2/3*d**2.
-2*d*(d - 2)*(d - 1)/9
Suppose 0 = -3*g + 4*s - 30, -s = 5*g - g + 40. Let j be (g/(-15))/((-2)/(-27)). Factor -4*h**4 - 7*h**4 - 2*h**5 + h - j*h**3 - h**2 + 0*h - 2*h**5.
-h*(h + 1)**3*(4*h - 1)
Let t(f) be the first derivative of -f**5/15 - f**4/6 + 9*f**2/2 + 2. Let g(y) be the second derivative of t(y). Factor g(n).
-4*n*(n + 1)
Let z(t) be the second derivative of 7*t + 0 + 1/4*t**3 - 1/12*t**4 - 1/4*t**2. Suppose z(r) = 0. Calculate r.
1/2, 1
Suppose 2*o - 3*b = -o - 9, 2*b = o + 6. What is l in 4/11*l**2 - 2/11 + o*l**3 + 0*l - 2/11*l**4 = 0?
-1, 1
Let p = -379/4 + 95. Let h(l) be the second derivative of -2*l + 0 - 1/2*l**3 + 0*l**2 - p*l**4. Let h(m) = 0. What is m?
-1, 0
Let r = 95 - 95. Factor 20/3*v**3 + r + 7/3*v**5 + 26/3*v**4 + 0*v - 8/3*v**2.
v**2*(v + 2)**2*(7*v - 2)/3
Let j(q) be the third derivative of -q**5/15 - q**4/3 + 2*q**3 - 26*q**2. Factor j(c).
-4*(c - 1)*(c + 3)
Let v(p) = -p**3 - p**3 - 32 + 26 + 6*p**2. Let g(n) = -2*n**3 + 5*n**2 - 5. Let b(h) = -6*g(h) + 5*v(h). Let b(j) = 0. Calculate j.
0
Let a(w) be the first derivative of w**4/48 + w**3/8 + w**2/4 + 3*w + 1. Let c(u) be the first derivative of a(u). Factor c(j).
(j + 1)*(j + 2)/4
Factor 2/5*m**3 + 2*m**2 + 8/5 + 16/5*m.
2*(m + 1)*(m + 2)**2/5
Suppose 14/11*k**5 - 14/11*k**2 + 78/11*k**3 - 12/11*k - 6*k**4 + 0 = 0. What is k?
-2/7, 0, 1, 3
Let i(f) be the second derivative of 5*f**7/14 - 4*f**6/5 + 3*f**5/20 + f**4/2 - 6*f. Factor i(o).
3*o**2*(o - 1)**2*(5*o + 2)
Let z be (-52)/(-14) + 0 + (-14)/(-49). Let w be ((-2)/3)/(-2)*15. Let 0 + 2/7*c**2 - 2/7*c**z + 2/7*c**3 + 0*c - 2/7*c**w = 0. What is c?
-1, 0, 1
Let l(w) be the third derivative of 0*w - 3*w**2 - 1/180*w**6 - 1/36*w**4 - 1/45*w**5 + 0*w**3 + 0. Factor l(s).
-2*s*(s + 1)**2/3
Let m(v) be the first derivative of -v**3/6 + v/2 + 2. Factor m(z).
-(z - 1)*(z + 1)/2
Suppose 0 = 4*d - 3*d - 1. Let j(h) be the first derivative of -d + h + 9/4*h**2 + 7/6*h**3. Determine r so that j(r) = 0.
-1, -2/7
Let i(y) be the second derivative of -y**4/54 + 8*y**3/27 - 16*y**2/9 + 27*y. Determine h, given that i(h) = 0.
4
Let f(l) be the third derivative of -l**8/168 - l**7/35 - l**6/30 + 5*l**2. Determine w, given that f(w) = 0.
-2, -1, 0
Let m(v) = -4*v**3 + 8*v - 4. Let t(z) = 4*z**3 - 9*z + 5. Let q(c) = -5*m(c) - 4*t(c). Find h, given that q(h) = 0.
-1, 0, 1
Let m(i) be the first derivative of i**6/360 + i**5/60 + i**4/24 + i**3/18 + 3*i**2/2 + 3. Let x(k) be the second derivative of m(k). Factor x(b).
(b + 1)**3/3
Factor -4/3*s**3 + 7*s**2 - 7*s + 4/3.
-(s - 4)*(s - 1)*(4*s - 1)/3
Suppose -2*w - 7 = 7. Let s(g) = -5*g**3 - 7*g**2 + 2*g + 4. Let i(d) = 9*d**3 + 13*d**2 - 3*d - 7. Let f(r) = w*s(r) - 4*i(r). What is x in f(x) = 0?
-2, -1, 0
Factor -2*d - 2/7*d**3 - 6/7 - 10/7*d**2.
-2*(d + 1)**2*(d + 3)/7
Factor -5/2*s - 1 - 2*s**2 - 1/2*s**3.
-(s + 1)**2*(s + 2)/2
Let a(z) = z**3 - 9*z**2 + 6*z + 8. Let l be a(8). Let s be (1/2)/((-2)/l). Suppose -2/7*g**4 + 0 - 8/7*g**3 - 8/7*g**s + 0*g = 0. What is g?
-2, 0
Let h = 134 - 668/5. Let 0 - 2/5*t**3 + 0*t - h*t**2 = 0. What is t?
-1, 0
Let z(s) be the first derivative of -s**3/12 - 3*s**2/4 - 9*s/4 - 7. Factor z(y).
-(y + 3)**2/4
Suppose 0*n**3 + 0 + 2/3*n**4 + 0*n - 2/3*n**2 = 0. Calculate n.
-1, 0, 1
Solve -9/2*v - 3/2*v**2 + 0 = 0.
-3, 0
Suppose 0 = 2*k + 5*z - 17, 3*k - 1 = z + 16. Suppose k = 6*h - 3*h. Factor q**5 - h*q**5 - 3*q**5 + 3*q**5.
-q**5
Suppose 0 = o + 6. Let p(c) = -5*c**2 + 8*c - 5. Let y(v) = -11*v**2 + 17*v - 11. Let x(h) = o*y(h) + 13*p(h). Suppose x(s) = 0. Calculate s.
-1
Factor 0*n + 2/9*n**3 + 0*n**2 + 0.
2*n**3/9
Let u(o) = -o**4 - 3*o**3 - 5*o**2 + 3*o - 3. Let q(s) = -s**3 + s - 4 + 0*s**4 - s**2 + 3 - s**4. Let v(h) = 3*q(h) - u(h). Solve v(f) = 0 for f.
-1, 0, 1
Factor -3/5*v + 0 - 18/5*v**3 - 12/5*v**2 - 3/5*v**5 - 12/5*v**4.
-3*v*(v + 1)**4/5
Find x such that -2*x + 0 + 1/3*x**3 + 1/3*x**2 = 0.
-3, 0, 2
Factor 0 - 25/3*d**2 - 10/3*d.
-5*d*(5*d + 2)/3
Let o(r) = r**2 + 5*r + 4. Let s be o(-5). Let a**2 + 4*a**3 + s*a + 0*a**3 - 3*a**2 - 6*a**2 = 0. What is a?
0, 1
Suppose -3*u = -27 + 21. Let -2*m**u + 10/3*m**3 - 2/3*m + 2/3 - 4/3*m**4 = 0. What is m?
-1/2, 1
Suppose -3*z = 2*a - 5*a - 18, 0 = a - 2*z + 8. Let d be (a/7)/(24/(-84)). Suppose -2/5*m + 0 + 2/5*m**d = 0. Calculate m.
0, 1
Let r = 288 + -288. Find s such that 2/7*s**2 + 0*s**3 + 0*s - 2/7*s**4 + r = 0.
-1, 0, 1
Determine b so that 3*b**3 - 2*b**2 + 5*b**2 - 5*b + 9 - 10*b = 0.
-3, 1
Determine w, given that -27*w**2 + 24*w - 11 - w**2 + 15 = 0.
-1/7, 1
Let o = 5 - 1. Factor -n**5 - n**o + 0*n**2 + 4*n**2 + 0*n**5 - 6*n**3 + 5*n**4 - n.
-n*(n - 1)**4
Let g(w) be the first derivative of 5 - 8/25*w**5 + 1/10*w**4 + 0*w**3 + 0*w + 0*w**2. Factor g(m).
-2*m**3*(4*m - 1)/5
Let k = -82 + 54. Let x be -10*(k/24 - -1). Factor 7/3*i**4 + 0 + x*i**3 + i**5 + 0*i + 1/3*i**2.
i**2*(i + 1)**2*(3*i + 1)/3
Let s(n) = n**2 + n - 2. Let u be s(2). Let w(k) be the first derivative of -46/3*k**3 - 3 + 16*k**2 + 7*k**u - 6/5*k**5 - 8*k. Find q, given that w(q) = 0.
2/3, 1, 2
Factor 14/3*m**2 + 2*m**3 + 2/3 + 10/3*m.
2*(m + 1)**2*(3*m + 1)/3
Factor -1/7 + 5/7*m**2 - 4/7*m.
(m - 1)*(5*m + 1)/7
What is f in -1/3*f**3 - 1/3*f**4 + f**2 - 2/3 + 1/3*f = 0?
-2, -1, 1
Let l(a) = -2*a**2 + 6*a - 2. Let p(r) = 3*r + 2. Let k(b) = 16*b + 11. Let o(q) = 2*k(q) - 11*p(q). Let y(w) = l(w) + 2*o(w). Factor y(z).
-2*(z - 1)**2
Let v(p) = 4*p**4 - 7*p**3 + 6*p**2 - p + 2. Let s(z) = z**4 - z**3 + z**2 + 1. Let c(w) = 2*s(w) - v(w). Solve c(a) = 0 for a.
0, 1/2, 1
Find l such that l**3 + l**4 - 20 + 20 = 0.
-1, 0
Let i = 7 + -4. What is j in -4*j**4 + 0*j**4 + 0*j**4 + 2*j**2 - 5*j**3 - i*j**4 = 0?
-1, 0, 2/7
Let w(a) be the third derivative of 0*a**4 + 1/80*a**5 + 0 + 0*a + 1/80*a**6 - 4*a**2 + 0*a**3 + 1/280*a**7. Solve w(n) = 0.
-1, 0
Let z(p) be the first derivative of -p**5/150 + p**4/15 - 4*p**3/15 - 2*p**2 - 4. Let y(q) be the second derivative of z(q). What is v in y(v) = 0?
2
Let y(d) = -d**2 - d - 1. Let j(w) = -2*w**2 - 2*w - 5. Let h(c) = j(c) - 5*y(c). Factor h(u).
3*u*(u + 1)
Let h(r) = r**2 - 3*r + 3. Let s be h(2). Suppose -s = 3*a - 13. Factor 8*z**3 + 0*z - 2*z**4 - 2*z**2 + a*z + 0*z**4 - 8*z**2.
-2*z*(z - 2)*(z - 1)**2
Factor 2/11 - 2/11*x - 4/11*x**4 + 10/11*x**3 - 6/11*x**2.
-2*(x - 1)**3*(2*x + 1)/11
Let y(i) be the second derivative of i**6/135 - i**4/18 - 2*i**3/27 - 16*