- 3*u**2 + 9*u + u**2 - 2. Let c(v) = 6*b(v) + 5*f(v). Let c(a) = 0. What is a?
-2, 1/2
Let l = -8 + 10. Let k = -8 - -12. Let l*y**k - 2*y**4 - 2*y**4 = 0. What is y?
0
Let i be -2*(18/(-4))/3. Suppose -a = 4*o - 9*o - 13, -i*o = -a + 9. Find k, given that k**4 - 2*k**4 + 0*k**4 - k**a = 0.
-1, 0
Let 12/5*z**3 + 0 + 24/5*z**2 + 16/5*z + 2/5*z**4 = 0. What is z?
-2, 0
Let q(l) = l**2 - 5*l + 6. Let o be q(4). Let u = -458/5 + 92. Suppose -2/5*s**3 + 2/5*s**o - 2/5*s**4 + 0 + u*s**5 + 0*s = 0. Calculate s.
-1, 0, 1
Suppose -18*z**2 + 2*z + 0*z + 0*z + 22*z**3 - 8*z**4 - 9 + 11 = 0. What is z?
-1/4, 1
Let t(a) be the third derivative of 1/150*a**5 + 0 - 4/15*a**3 + 2*a**2 + 0*a**4 + 0*a. Factor t(k).
2*(k - 2)*(k + 2)/5
Let z = 80 + -239/3. Factor b**2 - b - z*b**3 + 1/3.
-(b - 1)**3/3
Let n(j) be the third derivative of j**6/40 - j**5/20 - j**4/4 - 12*j**2. Suppose n(t) = 0. What is t?
-1, 0, 2
Let r(t) be the second derivative of t**7/147 - t**6/105 - t**5/70 + t**4/42 - 8*t. Let r(g) = 0. Calculate g.
-1, 0, 1
Let a(x) = -x - 3. Let i be a(-5). Suppose 10*z**2 + z - 8 + 8*z + i*z + 5*z = 0. Calculate z.
-2, 2/5
Suppose 3*q + 2*q - 65 = 0. Let u = q - 11. Factor -1/3*m**u + 0 + 0*m + 5/3*m**3.
m**2*(5*m - 1)/3
Let u be (3 + (-116)/36)*(0 - 9). Factor -1/2*f + 0 + f**u + 0*f**3 - f**4 + 1/2*f**5.
f*(f - 1)**3*(f + 1)/2
Let h(i) be the third derivative of i**5/15 - 5*i**4/6 + 8*i**3/3 + 8*i**2. Find w such that h(w) = 0.
1, 4
Let j(z) be the first derivative of 1/2*z**4 + 2 - 2/5*z**5 + 0*z**2 + 0*z + 0*z**3. Determine h so that j(h) = 0.
0, 1
Factor 0*a - 2/3 + 2/3*a**2.
2*(a - 1)*(a + 1)/3
Let g = 17/4 + 19/12. Let i = g + -31/6. Find z, given that -4/3*z**2 + 0 - 2/3*z + i*z**5 + 4/3*z**4 + 0*z**3 = 0.
-1, 0, 1
Let q(i) be the first derivative of i**6/2 + 12*i**5/5 + 9*i**4/2 + 4*i**3 + 3*i**2/2 + 15. Factor q(u).
3*u*(u + 1)**4
Suppose 2*l = -3*l + 10. Find q, given that 2*q**l + 2*q**2 + 4*q - 7*q - q = 0.
0, 1
Let o = -679 + 4075/6. Factor 1/2*i**2 + o*i**4 + 0 + 1/2*i**3 + 1/6*i.
i*(i + 1)**3/6
Let d(c) be the third derivative of 2/15*c**4 - 1/175*c**7 + 4/15*c**3 + 0*c + 0 - 1/150*c**5 + c**2 - 2/75*c**6. Suppose d(h) = 0. What is h?
-2, -1, -2/3, 1
Suppose 0*p = -2*p + 6. Factor -2*a - 3*a**4 + 3 - 3 + 6*a**2 - a - p*a**5 + 6*a**3 - 3.
-3*(a - 1)**2*(a + 1)**3
Let t be (72/(-48))/((-2)/6). Suppose 3*s + t + 1/2*s**2 = 0. What is s?
-3
Let s(k) be the third derivative of k**9/22680 - k**7/1890 + k**5/180 - k**4/24 + k**2. Let v(z) be the second derivative of s(z). Factor v(a).
2*(a - 1)**2*(a + 1)**2/3
Let k be 8/140*(-20)/(-2). Suppose 5*u - 5*m + 18 = -2, -4*m + 16 = 2*u. Determine j so that -k*j + 2/7*j**2 + u = 0.
0, 2
Let x(c) be the second derivative of 0 - 3/20*c**4 + 1/5*c**3 - 7*c + 0*c**2 + 3/100*c**5. Factor x(l).
3*l*(l - 2)*(l - 1)/5
Let a(p) be the third derivative of p**9/1512 - p**8/840 - p**7/420 + p**6/180 + p**3/6 - 6*p**2. Let n(y) be the first derivative of a(y). Factor n(v).
2*v**2*(v - 1)**2*(v + 1)
Suppose -102*j = -118*j + 48. Find b, given that -2/5*b**2 + 1/5*b**j + 0 + 1/5*b = 0.
0, 1
Let x(n) be the first derivative of 1/2*n**2 + 1/120*n**6 + 0*n**3 + 0*n + 1/60*n**5 + 0*n**4 - 2. Let h(u) be the second derivative of x(u). Factor h(f).
f**2*(f + 1)
Let -3*d + 1/3*d**3 + d**2 + 5/3 = 0. What is d?
-5, 1
Let n be (1 - 1)*(-1 - 0). Suppose 7*u - 11*u = n. What is x in -1/4*x**3 + 1/4*x - 1/4*x**4 + u + 1/4*x**2 = 0?
-1, 0, 1
Let i = 17 - 13. Suppose -i*z = -7*z + 9. Factor -h**z + 3/5*h**2 + 4/5 + 12/5*h.
-(h - 2)*(h + 1)*(5*h + 2)/5
Let p(u) be the third derivative of -u**7/420 - u**6/160 - u**5/240 + 16*u**2. Factor p(q).
-q**2*(q + 1)*(2*q + 1)/4
Let h(m) be the second derivative of 5*m - 1/4*m**7 - 33/40*m**5 + 1/4*m**4 + 0 + 0*m**2 + 4/5*m**6 + 0*m**3. What is o in h(o) = 0?
0, 2/7, 1
Let d(j) be the second derivative of j**7/147 - j**6/105 - j**5/70 + j**4/42 - 11*j. Solve d(k) = 0.
-1, 0, 1
Find h, given that 0 + 2/9*h + 2/9*h**2 = 0.
-1, 0
Let m(u) be the second derivative of u**4/18 - u**3/3 + 2*u**2/3 + 3*u. Find n, given that m(n) = 0.
1, 2
Suppose 3*q - 19 = -7. Let s(k) be the third derivative of 0*k + 0*k**3 + 0 - k**2 + 0*k**q + 1/30*k**5. Factor s(z).
2*z**2
Let x be 5/(-4) - (-68)/51. Let s(l) be the second derivative of 11/60*l**6 - 1/4*l**2 + 1/4*l**4 + 1/28*l**7 - x*l**3 + 7/20*l**5 + 0 + l. Factor s(p).
(p + 1)**4*(3*p - 1)/2
Suppose -6*o + 5*o = -3*o. Let 0 + 0*v - 2/5*v**5 + 2/5*v**3 + o*v**2 + 0*v**4 = 0. What is v?
-1, 0, 1
Let g(q) = -q**3 - 2*q**2 + 3*q + 4. Let x be g(-3). Let m(v) = -v - 4. Let w be m(-6). Let j**x + j**2 + j**w + 1 - 4*j**2 = 0. What is j?
-1, 1
Let n(r) = r**5 - 2*r**4 + 4*r**3 + 7*r**2 + r - 5. Let z(b) = b**5 - 4*b**4 + 8*b**3 + 13*b**2 + b - 9. Let m(c) = 5*n(c) - 3*z(c). Factor m(s).
2*(s - 1)**2*(s + 1)**3
Let p be (-13)/(-21) + (-2)/7. Let c = 3 - 1. Let 2/3*t + 1/3*t**c + p = 0. Calculate t.
-1
Let v(z) = -z**3 - 12*z**2 - 5*z - 16. Let r be v(-11). Let y = -244/3 - r. Solve 0*p + 2/3*p**5 + 0*p**3 + 0 - y*p**4 + 0*p**2 = 0 for p.
0, 1
Let z(n) be the second derivative of n**5/10 - 2*n**4/3 - 55*n. Factor z(x).
2*x**2*(x - 4)
Let g(p) be the second derivative of -p**5/10 + p**4/2 - 2*p**3/3 - 6*p. Factor g(c).
-2*c*(c - 2)*(c - 1)
Let r(m) be the first derivative of -1/2*m**3 - 4 - 6*m**2 + 3/10*m**5 - 1/4*m**6 - 6*m + 15/8*m**4. Find x, given that r(x) = 0.
-1, 2
Let y(b) = -2*b - 5. Let v be y(-3). Let p(a) = -6*a**3 + 3*a**2 + 3*a - 9. Let d(n) = -n**3 - n**2 - 1. Let l(o) = v*p(o) - 3*d(o). Factor l(j).
-3*(j - 2)*(j - 1)*(j + 1)
Let b be (-2991)/(-42) - (-3)/6. Let c = 72 - b. What is a in c*a**2 + 2/7 + 4/7*a = 0?
-1
Solve 16/3 + 3*n**2 - 8*n = 0 for n.
4/3
Let d(g) = g**4 - 3*g**3 - 4*g**2 + 3. Let h(q) = 3*q**3 + 3*q**2 - 2. Let m(y) = -2*d(y) - 3*h(y). Suppose m(z) = 0. Calculate z.
-1, -1/2, 0
Let n = 11 - 6. Suppose 4*o = -3*p + 25, 8 + n = -p + 4*o. Solve -2*s**5 + 3*s**3 - 18*s - 18*s**3 - 12*s**4 - 13*s**3 - p - 1 - 32*s**2 = 0 for s.
-2, -1
Factor -f**3 + 3*f**2 - f**3 + 6*f**4 - 7*f**2.
2*f**2*(f - 1)*(3*f + 2)
Let x(j) be the second derivative of j**4/12 + j**3/6 + 3*j**2 + 2*j. Let q be x(0). Solve 2 - q*g**2 - 2*g**3 + 1 - 4 - 1 - 6*g = 0 for g.
-1
Let n(r) be the second derivative of -r**5/120 + r**3/12 - r**2/2 + 3*r. Let q(k) be the first derivative of n(k). Factor q(y).
-(y - 1)*(y + 1)/2
Let s = 3 - 2. Let j = 4 - s. Determine t so that -7*t**5 + t - 5*t**2 + 9*t**j + 5*t**4 - 3*t + 0*t**5 = 0.
-1, -2/7, 0, 1
Let t = -5 + 6. Let k = -1 + t. Factor k*q - 1/3 + 1/3*q**2.
(q - 1)*(q + 1)/3
Let u(w) be the second derivative of w**7/63 - 2*w**6/45 + w**5/30 - 20*w. Factor u(z).
2*z**3*(z - 1)**2/3
Let s(l) be the third derivative of -1/9*l**4 + 0*l + 1/90*l**5 + 0 + 3*l**2 + 1/3*l**3. Factor s(r).
2*(r - 3)*(r - 1)/3
Suppose 0 = -3*f - 7 - 5. Let a be (15/(-6) - -2)*f. Factor -y**3 - y**3 + 2*y**a + 0*y + 2*y - 2.
-2*(y - 1)**2*(y + 1)
Let a be 4/(-21)*6/(-4). Let b(h) = 3*h - 2. Let i be b(2). Factor -4/7*c**2 + 4/7*c**i + 0 + 2/7*c**5 - a*c + 0*c**3.
2*c*(c - 1)*(c + 1)**3/7
Let k(y) be the third derivative of -y**6/180 - y**5/45 - y**4/36 + 71*y**2. Factor k(u).
-2*u*(u + 1)**2/3
Factor 0*p - 1/4*p**2 + 1/4.
-(p - 1)*(p + 1)/4
Determine r so that 1/2*r**5 - 1/2*r**4 + 0*r + 1/2*r**2 - 1/2*r**3 + 0 = 0.
-1, 0, 1
Let b(r) be the second derivative of r**9/3024 - r**7/420 + r**5/120 + 5*r**3/6 + 7*r. Let v(c) be the second derivative of b(c). What is l in v(l) = 0?
-1, 0, 1
Suppose -28*y**3 + 76*y**2 - 4*y - 28*y + 10 + 4 - 30 = 0. What is y?
-2/7, 1, 2
Let h = 10 - 10. Suppose 0 = -h*p - 2*p. Determine s, given that -2/5*s**2 + p + 2/5*s = 0.
0, 1
Let z = 14 - -1. Let m = -11 + z. Let 0*r - 2/9 + 4/9*r**2 + 0*r**3 - 2/9*r**m = 0. What is r?
-1, 1
Let v be 6/(-9)*63/(-14). Determine f so that 3/5*f**4 + 0 - 1/5*f**5 - 3/5*f**2 - 1/5*f**v + 2/5*f = 0.
-1, 0, 1, 2
Let m(w) be the third derivative of w**6/60 + 7*w**5/120 - 7*w**4/24 + w**3/4 - 4*w**2. Determine l, given that m(l) = 0.
-3, 1/4, 1
What is u in 0*u**2 + 8/5*u**4 + 0*u + 6/5*u**5 + 0 + 2/5*u**3 = 0?
-1, -1/3, 0
Let u(y) = 20*y**3 + 2*y**2 - 1. Let d be u(1). Suppose c = 3*n + d, -4*c + n - 5*n = -4. Factor c + z**5 - 6 + z**5.
2*z**5
What is r in -18*r**2 + 7*r**3 - 4 + 84*r*