h(k) = k**3 - k**2 - 2*k - 1. Suppose 3*p + 16 = -2. Let x = -4 - p. Let c(s) = s**2 + s + 1. Let a(f) = x*c(f) + 2*h(f). Factor a(b).
2*b*(b - 1)*(b + 1)
Suppose 2*p + 4 = 4*g, 6 = p + 2*p. Let k(h) be the first derivative of 0*h**g - 2/3*h**3 - 3 + 8*h. Let k(a) = 0. What is a?
-2, 2
Let w(r) be the second derivative of 0*r**2 + 0*r**5 + 0*r**3 - 1/120*r**6 - 22*r + 0 + 1/48*r**4. Solve w(f) = 0.
-1, 0, 1
Let l(u) be the third derivative of -u**8/20160 - u**7/7560 + u**4/24 + 6*u**2. Let w(j) be the second derivative of l(j). Factor w(m).
-m**2*(m + 1)/3
Suppose -2*a - 2*a + 16 = 0. Let w(d) be the first derivative of -1 + 1/16*d**a + 1/20*d**5 - 1/12*d**3 - 1/8*d**2 + 0*d. Determine k, given that w(k) = 0.
-1, 0, 1
Let x = -103 + 106. Let z = 22 + -17. Find k, given that 3/4*k**z - 9/4*k**4 - 9/4*k + 3/2*k**2 + 3/2*k**x + 3/4 = 0.
-1, 1
Suppose -4*l**3 - 2*l**3 + 349 - 349 - 12*l - 22*l**2 = 0. What is l?
-3, -2/3, 0
Let o(v) = -v**2 + 12*v + 1. Let s be o(12). Suppose 0 = -2*b + 4*r + 8, -2*b = 2*r + s - 3. Factor t + b*t + 8*t**2 - 9*t**2 - 2.
-(t - 2)*(t - 1)
Suppose 0 = 3*m, -3*n - 6*m + 36 = -4*m. Let k be (-2)/(-12)*(440/10 - -1). What is g in k*g**3 + 6 - 3/2*g**4 + 3/2*g**2 - n*g - 3/2*g**5 = 0?
-2, 1
Solve -3/5*h**3 + 0*h**2 + 0*h**4 + 0 + 3/5*h**5 + 0*h = 0.
-1, 0, 1
Let -52 - 59 + 54 - 90 + 798*p - 1083*p**2 = 0. Calculate p.
7/19
Let b(o) be the first derivative of -o**4 + 10*o**2 + 4*o**3 + 21 + 8*o - 4/5*o**5. Factor b(m).
-4*(m - 2)*(m + 1)**3
Let f be 3 - (-3 - -1 - -1). Let j = 0 + f. Solve -5*c**2 + 3*c - c**2 - j + 8*c - c = 0 for c.
2/3, 1
Let n(t) = 4*t - 7. Suppose 0 = -2*f + 4*f - 20. Let x be n(f). Factor -60*c**2 + 146*c - 21*c - 63 - 35*c**3 + x.
-5*(c - 1)*(c + 3)*(7*c - 2)
Suppose -6*x - 20*x**2 - 3*x + 4*x**5 - 8*x**4 + 5*x + 28*x**2 = 0. Calculate x.
-1, 0, 1
Let z = -9 - -6. Let p = 7 + z. Let 2 + w**5 + w**2 + 3*w**4 - 2 - w**3 - p*w**4 = 0. What is w?
-1, 0, 1
Let q(i) be the third derivative of -i**7/210 + 7*i**6/60 - 61*i**5/60 + 7*i**4/2 - 6*i**3 + 13*i**2. What is a in q(a) = 0?
1, 6
Let o(b) = -9*b**2 + 65*b + 82. Let n(r) = r**2 - 3*r + 2. Let a(k) = -14*n(k) - 2*o(k). Let a(g) = 0. What is g?
-2, 24
Factor -13/3*y - 16/3*y**2 - 1/3*y**3 + 10.
-(y - 1)*(y + 2)*(y + 15)/3
Let s(o) be the third derivative of -o**7/105 + o**6/60 + o**5/30 - o**4/12 - 86*o**2. Find t, given that s(t) = 0.
-1, 0, 1
Let y(m) be the first derivative of 8/5*m**5 - 30 - 2/3*m**6 + 2*m**2 + 0*m**4 - 8/3*m**3 + 0*m. Find s such that y(s) = 0.
-1, 0, 1
Let r(d) be the first derivative of -d**5/10 + d**3/3 + 5*d + 10. Let p(i) be the first derivative of r(i). Factor p(f).
-2*f*(f - 1)*(f + 1)
Let -6/7*s**2 + 18/7 + 12/7*s = 0. What is s?
-1, 3
Suppose 22*s + 8 = 20*s. Let x be (18/15)/((-6)/20) - s. Factor 1/5*v**2 + x + 1/5*v.
v*(v + 1)/5
Let r(j) = -3*j**3 - j**2 - j - 1. Let n be r(-1). Suppose 5*g + 7285*c = 7288*c - 3, -27 = g - 5*c. Let 3/5*a**g - 9/5*a**n - 3/5 + 9/5*a = 0. Calculate a.
1
Let w(d) = 24*d + 240. Let m be w(-10). Let q(b) be the second derivative of -1/48*b**4 + 0 - 7*b + m*b**2 + 1/24*b**3. What is r in q(r) = 0?
0, 1
Let t = 335/226 - -2/113. Factor -1/6*u**2 + u - t.
-(u - 3)**2/6
Let q(s) be the first derivative of -343*s**6/18 + 490*s**5/3 + 189*s**4 + 664*s**3/9 + 32*s**2/3 + 98. Find x, given that q(x) = 0.
-2/7, 0, 8
Let z(n) be the first derivative of 0*n**4 + 0*n**2 - 1/10*n**5 - 1/15*n**6 + 0*n**3 - 8*n - 1. Let b(a) be the first derivative of z(a). Factor b(f).
-2*f**3*(f + 1)
Let c(l) be the second derivative of -l**6/150 - 7*l**5/100 + 3*l**4/10 + 51*l + 3. Factor c(g).
-g**2*(g - 2)*(g + 9)/5
Let x(n) = -n**4 - n**3 - 1. Suppose 6*p + 51 = 23*p. Let j(r) = 2*r**4 - 23*r**3 + 15*r**2 + 20*r - 23. Let c(h) = p*x(h) - j(h). Find l such that c(l) = 0.
-1, 1, 2
Let y(p) = p**3 - p**2 - p. Let u(x) = -2*x**3 + 6*x - 1. Let l = -3 + 6. Let d(m) = l*y(m) + u(m). Factor d(g).
(g - 1)**3
Let p(n) be the third derivative of n**6/210 - 8*n**5/105 + n**4/2 - 12*n**3/7 - 466*n**2. What is y in p(y) = 0?
2, 3
Let k(y) be the second derivative of y**5/10 + 13*y**4/6 - 34*y. Factor k(s).
2*s**2*(s + 13)
Suppose 0 = -5*u, u = -r - 4*u - 3. Let c = r - -7. Factor -2*s**4 + 8*s**2 + 3*s**4 + 13*s**4 - 2 + 22*s**3 + 4*s**c + 5*s**5 - 3*s.
(s + 1)**4*(5*s - 2)
Let 5445*b + 330*b**2 + 8*b**3 + 5*b**3 - 11*b**3 + 3*b**3 = 0. What is b?
-33, 0
Suppose c - 160 = -4. Suppose 6*t - 195 = t + 4*i, 4*t = 3*i + c. Solve 100 - 12*n + 11*n - t*n - 2*n**2 + 6*n**2 = 0 for n.
5
Let q(l) be the first derivative of l**4/2 + 13*l**3/3 - 7*l**2/2 - 761. Suppose q(a) = 0. Calculate a.
-7, 0, 1/2
Let y(b) = -b**3 + 16*b**2 - 79*b + 117. Let p(g) = 6*g**3 - 96*g**2 + 474*g - 703. Let s(f) = -6*p(f) - 34*y(f). Factor s(z).
-2*(z - 8)*(z - 5)*(z - 3)
Find a, given that -726 - 2/3*a**2 - 44*a = 0.
-33
Let z(y) = 9*y + 3. Let j(k) = 5 - 11*k**2 - 2*k - 3*k + 0*k. Let q(w) = 4*w**2 + 2*w - 2. Let c(h) = -3*j(h) - 8*q(h). Let n(o) = -3*c(o) + z(o). Factor n(a).
-3*a*(a - 4)
Factor 4*y**2 + 6*y**2 - 8*y**2 - 18*y.
2*y*(y - 9)
Let d(h) = -h**2 - 3*h - 1. Let g(j) = -3*j**3 - 9*j**2 + 24*j - 12. Let m(t) = -12*d(t) + g(t). Factor m(q).
-3*q*(q - 5)*(q + 4)
Let j be -13 + 31 - 16 - -3. Let -4/7*d**3 - 4/7*d**2 + 6/7*d - 2/7 + 6/7*d**4 - 2/7*d**j = 0. Calculate d.
-1, 1
Let z(i) be the second derivative of 0 + 2/3*i**4 - 1/10*i**5 + 37*i + 11/3*i**3 + 6*i**2. Factor z(x).
-2*(x - 6)*(x + 1)**2
Let -6 - 4*r - 1/2*r**2 = 0. Calculate r.
-6, -2
Suppose -372*h + 366*h = -30. Let v(t) be the second derivative of 3/50*t**5 + 0*t**2 - 1/20*t**4 - 1/50*t**6 + h*t + 0*t**3 + 0. Let v(k) = 0. Calculate k.
0, 1
Let t(c) be the first derivative of c**4/3 - 8*c**3/3 - 14*c**2/3 + 39. Suppose t(a) = 0. Calculate a.
-1, 0, 7
Factor 92*s**2 - 13*s**4 + 51*s**3 - 6*s**4 + 53*s**3 - s**4 + 24*s**3 - 56*s.
-4*s*(s - 7)*(s + 1)*(5*s - 2)
Suppose 4*f = -0*f - 56. Let d = f + 16. Factor -21*h**d + 19*h**2 - 6*h + h + h.
-2*h*(h + 2)
Let c(v) = v**3 - 5*v**2 + 12*v - 617. Let a be c(10). Factor -2*l + 1/2*l**a + 0 + 3/2*l**2.
l*(l - 1)*(l + 4)/2
Let p(b) = 3*b + 2. Let m be p(-2). Let s = -2 - m. Factor 96*i**4 + s*i**2 + 64*i**5 - 52*i**5 + 24*i**3 + 82*i**5 + 34*i**5.
2*i**2*(4*i + 1)**3
Factor 3 + 16*r**3 - 12*r - 14 + 62*r**2 + 3 - 54*r**2 - 4*r**5.
-4*(r - 2)*(r - 1)*(r + 1)**3
Factor -36/5*k**2 + 36/5 + 2/5*k**3 - 2/5*k.
2*(k - 18)*(k - 1)*(k + 1)/5
Factor 10/3*p + 2/9*p**3 + 0 + 32/9*p**2.
2*p*(p + 1)*(p + 15)/9
Let t = 3212/7 - 5084/35. Find v, given that -8/5*v + 8/5 + t*v**4 + 112/5*v**3 - 222/5*v**2 = 0.
-2/7, 1/4
Suppose f - 4 = -f. Factor 150*u - 3*u**2 + 4*u**f - 6 - 155*u.
(u - 6)*(u + 1)
Suppose l - 1 = m, 5*l - 15 = -m + 2*l. Suppose -p + 2*u = -6, -m*u = 4*p - 6*u - 14. What is h in 5*h**4 - h**3 - h**4 - p*h**3 - h**4 = 0?
0, 1
Let z(h) be the third derivative of -7/360*h**6 + 0 + 1/105*h**7 - 1/30*h**5 - 1/72*h**4 + 0*h**3 - 8*h**2 + 0*h + 1/126*h**8. Determine t, given that z(t) = 0.
-1, -1/2, -1/4, 0, 1
Suppose 4*x = -0*r + r + 20, -5*x + 25 = 5*r. Factor r - 9/2*o + 3/2*o**2.
3*o*(o - 3)/2
Let k(l) be the first derivative of 5*l**4/4 + 10*l**3 + 55*l**2/2 + 30*l - 328. Determine t so that k(t) = 0.
-3, -2, -1
Let o(i) = 22*i + i**3 - 22*i + 6*i**2 + 3. Let x(k) = 2*k**3 + 11*k**2 + 5. Let a(u) = 5*o(u) - 3*x(u). Factor a(q).
-q**2*(q + 3)
Let n(p) be the first derivative of p**6/11 - 2*p**5/5 - 2*p**4/11 + 32*p**3/11 - 32*p**2/11 - 32*p/11 + 246. Determine r, given that n(r) = 0.
-2, -1/3, 2
Suppose 37 - 9 = 7*k. Factor g**2 + 3*g**k - 2*g - 4*g**4 - 248*g**3 + 250*g**3.
-g*(g - 2)*(g - 1)*(g + 1)
Find z, given that 30/7*z - 6/7*z**3 + 36/7 - 12/7*z**2 = 0.
-3, -1, 2
Let b(p) be the first derivative of p**6/3 + 17*p**5/5 + 5*p**4 - 10*p**3/3 - 11*p**2 - 7*p - 67. Let b(d) = 0. What is d?
-7, -1, -1/2, 1
Let t(j) be the first derivative of j**4/10 + 4*j**3/9 - 3*j**2/5 - 8*j/15 - 344. Determine z so that t(z) = 0.
-4, -1/3, 1
Let z(n) = -48*n**3 - 2684*n**2 + 3496*n - 716. Let o(v) = -10*v**3 - 537*v**2 + 699*v - 143. Let g(h) = -16*o(h) + 3*z(h). Factor g(c).
4*(c - 1)*(c + 35)*(4*c - 1)
Let k(t) = t**2 - 11*t + 34. Let n(o) = -5*o**2 + 43*o - 138. Let m(s) = -9*k(s) - 2*n(s). Let m(i) = 0. What is i?
-15, 2
Let t(n) = -n**3 + 43*n**2 - 37*n 