= 0.
-2, 1, 4
Let k(d) = -d**3 - 2*d**2 - d - 2. Let v be k(-2). Let w be -1 - (-8 - (-450)/66). Factor v*g + 2/11 - w*g**2.
-2*(g - 1)*(g + 1)/11
Suppose -3*d + 17 - 36 = -5*o, 4*o = -2*d + 24. Let c(z) be the first derivative of 1/2*z - 9/8*z**d + 7/12*z**3 - 10. Factor c(q).
(q - 1)*(7*q - 2)/4
Let o be -455 + 431 + 194/8. Suppose -11/4*f**3 - 1/4 + 9/4*f**2 + f**4 - o*f = 0. What is f?
-1/4, 1
Let u(d) be the second derivative of -d**7/315 - 2*d**6/225 + 4*d**5/75 + 8*d**4/45 - 16*d**3/45 - 32*d**2/15 - 138*d. What is y in u(y) = 0?
-2, 2
Factor 11/4*d**3 + 9/2*d**2 + 1/2*d**4 - 2 + d.
(d + 2)**3*(2*d - 1)/4
Suppose -5*z + 11*z - 12 = 0. Suppose -2*n = -4*k + n + 21, 0 = z*k - 2*n - 12. What is f in 0 + 2/7*f + 0*f**2 - 2/7*f**k = 0?
-1, 0, 1
Find k, given that 10/7*k - 6*k**3 + 0 + 6*k**2 - 10/7*k**4 = 0.
-5, -1/5, 0, 1
Let k(y) be the second derivative of -y**6/285 - y**5/190 + 2*y**4/19 + 28*y**3/57 + 16*y**2/19 + 60*y. Let k(l) = 0. What is l?
-2, -1, 4
Let n(c) = -c**3 - 5*c**2 + 5*c - 4. Let y be n(-6). Let o = -203 + 1829/9. Factor o*s**y + 2/9 + 4/9*s.
2*(s + 1)**2/9
Let t be (-58)/5 + (-2)/5. Let p be t + 4/(-4) - 2. Let y(h) = h**2 + 3*h + 2. Let s(f) = 3*f**2 + 7*f + 4. Let a(k) = p*y(k) + 6*s(k). Factor a(u).
3*(u - 2)*(u + 1)
Suppose 0 = 190*a - 178*a - 24. Let r(w) be the second derivative of 5/6*w**3 + 0 - 1/12*w**4 - a*w - 3*w**2. Factor r(m).
-(m - 3)*(m - 2)
Let f(c) be the third derivative of c**7/1680 - c**6/45 + 77*c**5/240 - 49*c**4/24 - 9*c**3/2 + 7*c**2. Let v(a) be the first derivative of f(a). Factor v(d).
(d - 7)**2*(d - 2)/2
Let b(q) be the second derivative of -q**5/80 + q**3/8 - q**2/4 - q - 40. Factor b(x).
-(x - 1)**2*(x + 2)/4
Let v(u) = -2*u - 10. Let x be v(-9). Let r(m) be the second derivative of 0 - 3/4*m**3 - 3/2*m**2 - x*m - 1/8*m**4. Factor r(h).
-3*(h + 1)*(h + 2)/2
What is s in 166 - 84 + 80*s + 3 - 5*s**2 = 0?
-1, 17
Suppose 3*l + 3*l = -336. Let d be (-133)/l + 3/(-8). Factor 10*u**2 - 15*u**d + u**2 - 32*u - 41 - 23.
-4*(u + 4)**2
Let a(j) = 6*j**2 + 5*j + 3. Let b(c) = 1 + 19*c**2 + 0 - 18*c**2. Let u(w) = -a(w) + 2*b(w). Let u(r) = 0. Calculate r.
-1, -1/4
Let v(m) = -m**3 + 37*m**2 - 272*m + 57. Let w be v(27). Let d(b) be the second derivative of -1/24*b**4 + 0 + 0*b**2 - 1/4*b**w + b. Factor d(z).
-z*(z + 3)/2
Let m be ((-6)/4)/(14/28) - (-31)/10. Factor m*a**2 - 1/5*a + 0 + 1/10*a**3.
a*(a - 1)*(a + 2)/10
Let z(n) = -n + 1. Let i(p) = 2*p**3 + 28*p**2 + 46*p + 28. Let l(b) = i(b) - 4*z(b). Factor l(g).
2*(g + 1)**2*(g + 12)
Let r = -25360 - -25362. Factor -2/3*o**r - 4 - 14/3*o.
-2*(o + 1)*(o + 6)/3
Let q(p) be the second derivative of -p**4/30 - 7*p**3/15 - 6*p**2/5 - 26*p + 2. Factor q(n).
-2*(n + 1)*(n + 6)/5
Let i(s) be the first derivative of 0*s**3 + 0*s**2 - 1/21*s**6 + 0*s - 1/14*s**4 + 4/35*s**5 - 29. Factor i(j).
-2*j**3*(j - 1)**2/7
Let z = -29 + 32. Suppose -5*d + z*i + 13 = 0, -d + 10 = 2*d - 4*i. Factor 0*c + 3/5*c**d + 0.
3*c**2/5
Let x(m) be the third derivative of -m**11/1995840 - m**10/907200 - m**5/12 - 2*m**2. Let r(z) be the third derivative of x(z). Factor r(a).
-a**4*(a + 1)/6
Let z(k) be the third derivative of k**7/14 - k**6/20 - 3*k**5/4 + 2*k**4 - 2*k**3 + 129*k**2. Factor z(u).
3*(u - 1)**2*(u + 2)*(5*u - 2)
Let l(o) = 12*o**5 + 69*o**4 + 81*o**3 - 39*o**2 - 81*o - 12. Let y(b) = -b**4 - b**3 - b**2 - b - 1. Let v(h) = -l(h) - 6*y(h). Find d, given that v(d) = 0.
-3, -2, -1, -1/4, 1
Let k(a) be the third derivative of 0*a**3 + 0*a + 0 + 3*a**5 + 7/10*a**7 + 26*a**2 - a**4 - 63/20*a**6. Factor k(c).
3*c*(c - 2)*(7*c - 2)**2
Suppose 7*k**3 + 0 - 8/3*k**4 + 8/3*k - 22/3*k**2 + 1/3*k**5 = 0. What is k?
0, 1, 2, 4
Let q(j) be the second derivative of 1/54*j**4 + 1 + 13*j - 2/9*j**3 + 8/9*j**2. Factor q(y).
2*(y - 4)*(y - 2)/9
Suppose 21*p**3 + 266*p**4 - 140*p**4 - 42*p**2 + 24*p - 129*p**4 = 0. Calculate p.
0, 1, 2, 4
Let a(f) be the first derivative of 10/9*f**2 + 2/27*f**3 - 22/9*f + 35. Factor a(b).
2*(b - 1)*(b + 11)/9
Let k = -2875 - -2875. Determine t, given that 0*t**3 - 8/9*t**2 + 0*t + k - 2/9*t**5 + 2/3*t**4 = 0.
-1, 0, 2
Let x = 211 - 53. Suppose -2*d = x - 624. Factor 2*l**3 + 232*l - l**3 - d*l.
l*(l - 1)*(l + 1)
Let m(j) be the second derivative of 0 + 0*j**2 + 5/12*j**4 + 25/6*j**3 + 19*j. Determine v so that m(v) = 0.
-5, 0
Determine p, given that 21/5*p + 0 + 3*p**3 - 39/5*p**2 + 3/5*p**4 = 0.
-7, 0, 1
Let z(l) be the second derivative of l**7/595 - l**6/510 - 29*l**2/2 + 32*l. Let x(d) be the first derivative of z(d). Let x(v) = 0. Calculate v.
0, 2/3
Let a be (-3)/(195/(78/(-6))). Find f such that a*f**2 - 2/5*f + 1/5 = 0.
1
Suppose 0*g - 4*g - 3 = -3*o, -4*g = 2*o - 22. Factor 4*n + g*n**3 + 9/2*n**4 + 0 - 10*n**2.
n*(n + 2)*(3*n - 2)**2/2
Find u such that 32/9*u**3 - 16/9 - 34/9*u + 20/9*u**4 - 4/9*u**2 + 2/9*u**5 = 0.
-8, -1, 1
Suppose 3*l + 4 - 10 = 0. Suppose l*n + 5*o = -6, -3*n - 3*o + 4 = 2*n. Factor -3*j**4 - 1 + 7*j**3 + 9/2*j + 1/2*j**5 - 8*j**n.
(j - 2)*(j - 1)**4/2
Let a(p) be the second derivative of 1/40*p**5 - 3*p + 0*p**3 - 1/24*p**4 - 2*p**2 + 0. Let n(k) be the first derivative of a(k). Factor n(v).
v*(3*v - 2)/2
Let o = 72 - -30. Determine m, given that 102 - 4*m**4 - 4*m**5 - o = 0.
-1, 0
Suppose -13*f = 7*f - 14*f. Let h(d) be the second derivative of f*d**2 + 1/30*d**5 + 0 - 5*d + 0*d**3 - 1/18*d**4. Let h(g) = 0. Calculate g.
0, 1
Let j(y) = -6*y**3 - 3*y**2 - 3*y - 2. Let m be j(-2). Suppose -38*z - 10 = -m*z. Factor 3*k**z + 3/5*k**2 - 6/5*k + 0 + 27/5*k**3 - 39/5*k**4.
3*k*(k - 1)**3*(5*k + 2)/5
Let q(s) be the third derivative of -s**7/1680 - s**6/320 - s**5/160 - 2*s**4/3 - 11*s**2. Let p(t) be the second derivative of q(t). Let p(j) = 0. What is j?
-1, -1/2
Let g(m) be the first derivative of m**5 + 25*m**4/2 + 85*m**3/3 + 20*m**2 - 122. Factor g(i).
5*i*(i + 1)**2*(i + 8)
Let m(t) be the second derivative of 0*t**2 - 2/9*t**4 - 1/18*t**7 + 0*t**3 - 18*t - 1/3*t**6 + 0 - 3/5*t**5. Suppose m(p) = 0. What is p?
-2, -2/7, 0
Suppose 0*a - 4*a - 2*b + 36 = 0, 5*a = 3*b + 34. Determine x, given that -7*x**2 - 16 + a*x**2 + 3*x**2 = 0.
-2, 2
Let y(i) = i**4 + i**3 - i. Suppose 4*l = 4*a - 2 + 18, 2*l - 4*a = 18. Let v(p) = 12*p**4 - 27*p**3 + 108*p**2 - 9*p. Let h(o) = l*v(o) + 9*y(o). Factor h(s).
-3*s**2*(s - 6)**2
Find l, given that -2/3*l**3 - 16*l + 24 - 22/3*l**2 = 0.
-6, 1
Suppose 38 = 225*r - 206*r. Determine c so that -2*c + 0 + 2/3*c**4 + r*c**3 - 2/3*c**2 = 0.
-3, -1, 0, 1
Let y(i) be the second derivative of i**6/1800 + i**5/150 + i**4/40 + 23*i**3/6 + 13*i. Let c(r) be the second derivative of y(r). Factor c(p).
(p + 1)*(p + 3)/5
Let a be (-48)/(-16) + 5/1. Suppose -v - 11 = -4*z, v - 5 - 8 = -4*z. Determine g, given that -6*g**2 - 7*g + 5 + 6*g**2 - a*g + 20*g**z = 0.
-1, 1/2
Suppose d = 5*a + 4*d - 16, 2*a - 19 = 3*d. Suppose -5*o + a = 0, -5*o + 3 + 2 = -f. What is v in 2*v**4 - 1/2*v - 2*v**2 + f + 1/2*v**3 = 0?
-1, -1/4, 0, 1
Let c(u) be the third derivative of 0 + 0*u - 11*u**2 - 1/15*u**5 + 7/48*u**4 - 1/12*u**3 - 1/15*u**6. Determine o so that c(o) = 0.
-1, 1/4
Factor 4/9*r**3 - 4/9*r - 1/9*r**4 - 2/9*r**2 + 1/3.
-(r - 3)*(r - 1)**2*(r + 1)/9
Let p = 6089/12 + -1520/3. Determine c, given that -1/2 + 1/4*c**4 - 3/4*c**3 + 1/4*c**2 + p*c = 0.
-1, 1, 2
Let n = -33 - -47. Factor -4 - 14*p**5 + 12*p + 12*p**4 + 5*p**5 + 6*p**2 - 8*p**3 - n*p**2 + 5*p**5.
-4*(p - 1)**4*(p + 1)
Suppose -3*m + 21 = -63. Let a be (34/m - 1)/((-6)/(-7)). Let 1/2*j + 0 - a*j**3 + 1/4*j**2 = 0. What is j?
-1, 0, 2
Let x be (72/15 - 5)/(1/(-10)). Factor -17 + 20*y**x - 21 + 18 - 4*y**3 + 4*y.
-4*(y - 5)*(y - 1)*(y + 1)
Suppose -333 - 129 = 6*t. Let v = t - -233/3. Factor 2/3*a**2 - 4/3 - v*a.
2*(a - 2)*(a + 1)/3
Let i(n) be the third derivative of n**6/72 + n**5/3 + 10*n**4/3 + 13*n**3/6 - 4*n**2. Let h(t) be the first derivative of i(t). Solve h(d) = 0.
-4
Find x such that 36*x - 4*x**4 - 17*x**3 - x**4 + 3*x**3 + 5*x**5 - x**4 - 3*x**5 + 30*x**2 = 0.
-2, -1, 0, 3
Let c(n) be the second derivative of 0*n**5 - 1/15*n**4 + 0*n**2 + 0 + 2/75*n**6 + 1/15*n**3 - 1/105*n**7 - 20*n. Factor c(r).
-2*r*(r - 1)**3*(r + 1)/5
Let x = -31 - -76. Suppose 6*s = 5*l + s - x, -5*s = -3*l + 35. Let -n**4 + 11*n**2 + 11*n**4 - 29*n**2 - 6*n**l +