r a(v).
v**4
Let l(d) = d**2 + 6*d - 1. Let t(s) = -s**2 - s - 1. Let g(p) = -l(p) - 2*t(p). Find w such that g(w) = 0.
1, 3
Let l(h) be the first derivative of -1/3*h**3 + 2*h - 3 + 1/2*h**2. Determine n so that l(n) = 0.
-1, 2
Solve -16/3*h**2 - 10/3*h + 4*h**3 - 2/3*h**5 + 4 + 4/3*h**4 = 0 for h.
-2, -1, 1, 3
Let f(k) be the third derivative of 6*k**2 - 1/2*k**3 + 0*k + 0 + 1/40*k**5 + 1/16*k**4. Let f(i) = 0. Calculate i.
-2, 1
Factor 6/5 + 2/5*w**2 - 8/5*w.
2*(w - 3)*(w - 1)/5
Let o = -10641 + 638483/60. Let r = o + -2/15. Let 1/2*m**2 + 0 - 1/4*m**3 - r*m = 0. Calculate m.
0, 1
Let k(v) = 5*v + 25. Let u be k(-4). Let 0*j - 4/3*j**u + 1/3*j**4 + 0 + 4/3*j**3 - 1/3*j**2 = 0. What is j?
-1, 0, 1/4, 1
Factor -12*j**3 - j**4 + 2*j + 7 - 5*j**2 + 3 + 4*j**5 - 10.
j*(j - 2)*(j + 1)**2*(4*j - 1)
Factor -3*n + n**3 + 5*n - 2*n + n**2.
n**2*(n + 1)
Let j(k) = -9*k**4 + 4*k**3 + 13*k**2. Let f be (-22)/(-8)*4*-1. Let t(q) = 5*q**4 - 2*q**3 - 7*q**2. Let h(m) = f*t(m) - 6*j(m). Factor h(b).
-b**2*(b + 1)**2
Let m be 9/10 - 6/12. Suppose 0*o = 5*k - 4*o - 11, -o = -5*k + 14. Factor 0 + 0*q**2 - m*q**k + 2/5*q.
-2*q*(q - 1)*(q + 1)/5
Let x(i) be the first derivative of -1/3*i**2 + 0*i + 3 + 1/9*i**6 + 4/15*i**5 - 4/9*i**3 + 0*i**4. Find h such that x(h) = 0.
-1, 0, 1
Let x(y) be the second derivative of -y**7/15 - 2*y**6/5 - 18*y**5/25 - 4*y**4/15 - 4*y. Find l such that x(l) = 0.
-2, -2/7, 0
Let x(o) be the second derivative of -o**5/25 - o**4/5 - 4*o**3/15 + 5*o. Factor x(t).
-4*t*(t + 1)*(t + 2)/5
Let m(f) = 5*f**4 + 6*f**3 - 4*f - 4. Let q(k) = 14*k**4 + 17*k**3 - 11*k - 11. Let v(j) = 11*m(j) - 4*q(j). Factor v(y).
-y**3*(y + 2)
Let f = 7 - 4. Solve -3 + 3 + 2*s - 5*s**3 + f*s**3 = 0 for s.
-1, 0, 1
Let m(j) be the third derivative of -j**5/450 - j**4/90 - j**3/45 + 4*j**2. Find q such that m(q) = 0.
-1
Let d(u) = -u**2 + 16*u - 16. Let i(x) = -x. Let b(v) = -3*d(v) - 24*i(v). Factor b(m).
3*(m - 4)**2
Let b = -12 + 12. Let g(t) be the second derivative of b - 1/18*t**3 - 1/36*t**4 + 0*t**2 + t. Suppose g(z) = 0. What is z?
-1, 0
Let z(m) be the first derivative of 3*m**5/5 - 3*m**4/2 + 3*m**2 - 3*m - 8. Factor z(b).
3*(b - 1)**3*(b + 1)
Let s(m) be the third derivative of -16*m**7/735 - 2*m**6/35 - 3*m**5/70 - m**4/84 + 3*m**2. What is x in s(x) = 0?
-1, -1/4, 0
Let o(a) be the third derivative of -1/210*a**5 - 1/21*a**3 + 7*a**2 + 0 + 0*a - 1/42*a**4. Factor o(r).
-2*(r + 1)**2/7
Let j(h) = -3*h**4 + 6*h**3 - 3*h**2 + 6*h. Let d(c) = 7*c**4 - 13*c**3 + 6*c**2 - 13*c. Let q(m) = -6*d(m) - 13*j(m). Determine f, given that q(f) = 0.
-1, 0, 1
Suppose 3*l + d - 20 = -3*d, -4*d - 16 = 0. Let x be ((-2)/4)/((-2)/l). Determine j so that -4*j**3 + 6*j**x + j**4 + j**2 + 0*j**4 = 0.
-1, 0
Let f be 27 + (-3 - -3 - -1). Factor -62*g + f*g**3 - 4*g**2 + 8 - 4*g**2 + 34*g.
4*(g - 1)*(g + 1)*(7*g - 2)
Let j(a) be the third derivative of a**7/14 + a**6/24 - 7*a**5/4 + 55*a**4/24 + 5*a**3 - 4*a**2. Solve j(t) = 0.
-3, -1/3, 1, 2
Let l(t) be the first derivative of t**5/20 + t**4/8 - t**2/4 - t/4 + 6. Solve l(w) = 0 for w.
-1, 1
Factor -b**2 + 5*b - 4*b + 0*b - 4*b + 10.
-(b - 2)*(b + 5)
Suppose -21 - 4 = -5*w, 0 = 2*y - 5*w + 11. Factor o + 6 + 3*o**2 + y*o - 2*o + 3*o.
3*(o + 1)*(o + 2)
Let t = -1 + -35. Let b be (-2)/t - 4/(-24). Factor 0 + 2/9*o + b*o**2.
2*o*(o + 1)/9
Solve 0 + 3/4*i**2 + 3/4*i = 0 for i.
-1, 0
Let z(u) be the second derivative of -u**4/12 - 10*u**3/3 - 19*u**2/2 - 12*u. Let d be z(-19). Factor 6/11*j**2 + d + 4/11*j + 2/11*j**3.
2*j*(j + 1)*(j + 2)/11
Let r(c) be the third derivative of -c**5/30 + c**4/12 + 11*c**2. Find g, given that r(g) = 0.
0, 1
Let a(k) be the second derivative of k**5/100 + k**4/60 - k**3/30 - k**2/10 + 10*k + 1. Factor a(o).
(o - 1)*(o + 1)**2/5
Factor 0 - 1/4*t + 1/4*t**2.
t*(t - 1)/4
Solve 0 + r - 1/2*r**2 + 1/2*r**4 - r**3 = 0.
-1, 0, 1, 2
Let u be (-22)/(-30) - 14/35. Find x such that -2/3*x**3 + u*x + 1/3*x**5 - 2/3*x**2 + 1/3 + 1/3*x**4 = 0.
-1, 1
Let t(d) be the third derivative of 3*d**6/40 - 19*d**5/100 + 2*d**3/5 - 19*d**2. Let t(h) = 0. Calculate h.
-2/5, 2/3, 1
Let y(f) be the second derivative of f**6/60 - 3*f**5/40 + f**3/3 - f. Determine o, given that y(o) = 0.
-1, 0, 2
Let k be (-20)/(-8) - 1/2. Suppose m + 0*m + 2*s = 2, -k = -m - 3*s. Factor 2*t**2 - 4*t**2 - 2*t + 4*t**m.
2*t*(t - 1)
Suppose -2*c - 13 = -3*c. Determine k, given that -k**3 + 13*k - k**2 - c*k = 0.
-1, 0
Let r(c) = -c**3 + c**2 - 1. Suppose 3*t + t = 4. Let g(n) = -6*n**3 + n**2 - n - 4. Let j(s) = t*g(s) - 4*r(s). Suppose j(d) = 0. Calculate d.
-1, -1/2, 0
Let b(d) = 5*d**2 - d + 1. Let f be b(1). Suppose -12*o + 2*o**2 - f*o**2 - 12 + 0*o = 0. Calculate o.
-2
Let w = 195 + -190. Suppose -4/3*m**2 + 4/3*m**4 + 2/3*m**w + 0*m**3 + 0 - 2/3*m = 0. What is m?
-1, 0, 1
Let h(l) be the second derivative of l**6/5 + l**5/10 - 7*l. Let h(j) = 0. Calculate j.
-1/3, 0
Let h(v) be the third derivative of -v**7/210 + 7*v**6/120 - 3*v**5/10 + 5*v**4/6 - 4*v**3/3 - 14*v**2. Find g such that h(g) = 0.
1, 2
What is f in -4/5*f**2 + 4/5 + 0*f = 0?
-1, 1
Let n(x) = x**2 - 7*x + 9. Let g be n(3). Let p be 0/((-4 - g)*-2). Determine f so that 0*f - 2/5*f**2 + p + 2/5*f**3 + 2/5*f**4 - 2/5*f**5 = 0.
-1, 0, 1
Let w = 111 - 111. Factor 0 + 0*t - 1/4*t**4 + w*t**2 + 1/4*t**3.
-t**3*(t - 1)/4
What is z in -3/4*z**3 + 11/4*z**2 - 5/2 + 3/4*z - 1/4*z**4 = 0?
-5, -1, 1, 2
Let p(f) = 7*f**5 - 7*f**3 + 11*f**2 + 11. Let b(g) = 4*g**5 - 4*g**3 + 6*g**2 + 6. Let h(c) = -11*b(c) + 6*p(c). Determine w so that h(w) = 0.
-1, 0, 1
Let b be -3*(-3)/7*4/6. Let 0 - 2/7*n**3 - b*n**2 - 4/7*n = 0. What is n?
-2, -1, 0
Let g(c) be the first derivative of 4*c**3/3 + 2*c**2 - 8*c - 6. Determine f so that g(f) = 0.
-2, 1
Let p be 2/(-7) + 137/455. Let u = 197/130 - p. Suppose -3/2*z**2 + 0 - 1/2*z**4 + u*z**3 + 1/2*z = 0. Calculate z.
0, 1
Factor 2/3*n**2 + 0 - 2/3*n.
2*n*(n - 1)/3
Let k(q) be the first derivative of q**5/60 - q**4/18 - 4*q + 1. Let u(v) be the first derivative of k(v). Factor u(a).
a**2*(a - 2)/3
Let m(d) be the first derivative of -d**2 + 2 - 4/3*d**3 - 1/2*d**4 + 0*d. Find t such that m(t) = 0.
-1, 0
Suppose 3*r - 2*l - 10 = 2*l, -5*r - 4*l + 6 = 0. Factor -4*c + c**r - 2*c**2 + 4*c**2 + 5*c.
c*(3*c + 1)
Suppose 2*w + 17 = 5*m, -3*w + 2 = -5*w. Find a such that a + m*a**2 - 4*a + 0*a**2 = 0.
0, 1
Suppose 2/9*f**4 + 4/3*f**5 + 4/9 - 2/3*f**2 - 22/9*f**3 + 10/9*f = 0. Calculate f.
-1, -2/3, -1/2, 1
Factor 0 + 2/5*x**4 - 2/5*x + 2/5*x**3 - 2/5*x**2.
2*x*(x - 1)*(x + 1)**2/5
Let f(j) = 3*j**2 + 5*j + 2. Let i(t) = -t - 1. Let l(d) = -f(d) - 4*i(d). Let y(a) = 4*a**2 + 2*a - 2. Let m(q) = 6*l(q) + 4*y(q). Find v, given that m(v) = 0.
-1, 2
Let i(g) be the second derivative of -g**8/112 + g**7/35 - 3*g**2/2 + 8*g. Let z(o) be the first derivative of i(o). Determine h, given that z(h) = 0.
0, 2
Let q(n) = -n**3 + 2*n**2 + 2*n - 1. Let o(b) = 44*b**2 - 20*b**2 - b - 25*b**2. Let l(s) = o(s) + q(s). Factor l(a).
-(a - 1)**2*(a + 1)
Suppose -6*p + 2*p = 72. Let x be (2/p)/((-2)/20). Factor 2/9 + 20/9*w**2 + 2/9*w**5 + x*w**4 + 10/9*w + 20/9*w**3.
2*(w + 1)**5/9
Factor 4*j**3 - 162 - 5*j**2 + 162 - 10*j + j**3.
5*j*(j - 2)*(j + 1)
Factor -5*t - 6 + 0*t**2 + 2*t + 3*t**2.
3*(t - 2)*(t + 1)
Let g be 8*(-3 - 21/(-6)). Factor -4*x + g*x + 2*x**2 - 2.
2*(x - 1)*(x + 1)
Let h = -713/10 + 6439/30. Let k = h + -2980/21. Factor 0 + 0*r + 2/7*r**2 + 8/7*r**4 + k*r**3.
2*r**2*(r + 1)*(4*r + 1)/7
Suppose 11*v - 8*v = 15, 3*t - 2*v + 10 = 0. Solve -2/5*z**5 + 2/5*z + 4/5*z**4 + 0*z**3 - 4/5*z**2 + t = 0.
-1, 0, 1
Let x(t) be the first derivative of t**6/30 + t**5/10 + t**4/12 - 4*t + 2. Let n(u) be the first derivative of x(u). Solve n(v) = 0.
-1, 0
Suppose 0*u = u. Let x = 5 + -3. What is z in u*z + z**x - z + z - 2*z = 0?
0, 2
What is n in 0*n + 2/9*n**2 - 2/9 = 0?
-1, 1
Let r(x) be the third derivative of x**6/40 + x**5/5 + 3*x**4/8 + 7*x**2. Factor r(j).
3*j*(j + 1)*(j + 3)
Let q(x) = x**2 - 10*x + 13. Let v be q(9). Factor 25*s**v - 186 + 24*s**2 - 4*s - 45*s**3 + 186.
s*(s - 1)*(5*s - 2)**2
Let f(j) be the first derivative of -j**6/3 - 26*j**5/5 - 21*j**4 - 116*j**3/3 - 37*j**2 - 18*j + 61. Factor f(o).
-2*(o + 1)**4*(o + 9)
Let y(c) be the third derivative of -2*c**2 