 -3*h - 13. Let x be q(-5). Let o be 3 + x - (-2 + 3). What is f in -5*f**3 - f + f**2 + 3*f**3 - 8*f**o + 7*f**4 + 3*f**3 = 0?
-1, 0, 1
Let q = -20 - -27. Suppose -a = q - 12. Factor -2*d**3 + 0*d**2 + 3*d**a + 3*d**2 - 3*d**4 - 7*d**3 + 6*d.
3*d*(d - 2)*(d - 1)*(d + 1)**2
Determine b so that -12/13*b - 2/13*b**2 + 0 + 2/13*b**3 = 0.
-2, 0, 3
Let z(l) be the first derivative of -5*l**3/3 + 5*l**2/2 + 30*l + 16. Factor z(r).
-5*(r - 3)*(r + 2)
Let h = 186 - 371/2. Let b(q) be the first derivative of 0*q**3 - 2 - h*q**4 + 4*q**2 + 0*q. What is g in b(g) = 0?
-2, 0, 2
Suppose 0 = -6*p + 10*p - 16. Suppose 6 = p*h - 2. Factor 4*a**4 - 3*a + 3*a + 2*a + 0*a**2 - 4*a**h - 2*a**5.
-2*a*(a - 1)**3*(a + 1)
Let l(h) be the first derivative of h**4 - 76*h**3/3 - 82*h**2 - 84*h - 68. Factor l(o).
4*(o - 21)*(o + 1)**2
Let r(d) be the second derivative of 0*d**2 + 0 + 2/3*d**3 - 9*d + 0*d**4 - 1/20*d**5. Find y, given that r(y) = 0.
-2, 0, 2
Let s(o) be the first derivative of 0*o + 1/36*o**6 - 31 + 11/18*o**3 + 1/30*o**5 - 1/3*o**2 - 3/8*o**4. Factor s(k).
k*(k - 1)**3*(k + 4)/6
Suppose -21 = -0*v - v. Let s be (28/v)/(2/9). Factor 6 + 0 - 5*w + 2*w**2 - 9*w + s*w.
2*(w - 3)*(w - 1)
Let a = -290 + 295. Let w(i) be the third derivative of 1/90*i**a + 0 + 0*i + 16/9*i**3 + 2/9*i**4 + 7*i**2. Find j, given that w(j) = 0.
-4
Suppose -f + 13 = 9. Factor -f*o - 2 - 6 + 2 - 2*o**2 + 4.
-2*(o + 1)**2
Suppose -v = 4*l - 9, -6 + 8 = 2*l - 2*v. Factor x**2 - 7*x**l - 16 - 5*x + 2*x**3 + 11*x + 14.
2*(x - 1)**3
Let l(m) = m**2 + 8*m - 1. Let a be l(1). Let z(r) be the first derivative of 5/2*r**2 + r + 25/12*r**3 - a. Factor z(b).
(5*b + 2)**2/4
Let p(l) be the second derivative of l**6/9 + l**5/10 - l**4/9 + l - 8. Factor p(o).
2*o**2*(o + 1)*(5*o - 2)/3
Find d, given that -4*d**2 + 84*d - 132*d - 212*d + 264 = 0.
-66, 1
Let x be 127*2/(-20) + 13. Let z(a) be the first derivative of -a**2 + x*a**5 - 7/9*a**3 + 5/8*a**4 + 3 + 4/3*a. Factor z(s).
(s + 1)*(s + 2)*(3*s - 2)**2/6
Let u = -979 - -983. Factor -3/4*b + 15/8*b**2 + 0 + 3/8*b**u - 3/2*b**3.
3*b*(b - 2)*(b - 1)**2/8
Let k be ((-15)/(-20))/((-9)/(-24)). Factor 4/19*n**k - 4/19*n**4 + 2/19*n + 0 - 2/19*n**5 + 0*n**3.
-2*n*(n - 1)*(n + 1)**3/19
Let v(j) = -j**4 + 2*j**2 + 1. Let l(r) = 5*r**4 - 40*r**3 - 105*r**2 + 10*r + 110. Let h(g) = l(g) + 10*v(g). Find o such that h(o) = 0.
-4, -3, -2, 1
Let p be (-720)/231 + 3 - 3/7. Let f = 41/55 + p. Factor -f - 1/5*l**2 - 2/5*l.
-(l + 1)**2/5
Let r(t) = 0 - 11 + 4*t + 3*t + 0. Let w be r(8). Suppose -o**3 + w*o + 12*o**2 - 2 - 7*o**4 - 50*o + 3*o**4 = 0. What is o?
-2, -1/4, 1
Let h(o) be the first derivative of -25/2*o**4 + 7 + 25/3*o**3 - 5/3*o**6 + 15/2*o**5 - 5/2*o + 0*o**2. Factor h(t).
-5*(t - 1)**4*(4*t + 1)/2
Let o(z) be the second derivative of 10/3*z**4 + 0 - 2*z**2 + 3*z + z**3. Determine w so that o(w) = 0.
-2/5, 1/4
Suppose 2*h + 4*h = 78. Suppose 2*u + 4*z = 26, -5*z + 0*z + h = -4*u. Suppose -5 - 2*v + 2 + 11*v - 9*v**2 + u*v**3 = 0. Calculate v.
1
Suppose 0 = 95*a - 355 + 33 + 37. Factor -2/13*x**a + 14/13*x - 4/13*x**2 - 8/13.
-2*(x - 1)**2*(x + 4)/13
Let f(y) = -3*y**2 + 8*y - 11. Let o(t) = t**2 + t + 1. Let v(w) = 2*f(w) + 4*o(w). Factor v(a).
-2*(a - 9)*(a - 1)
Let s(i) be the first derivative of -35*i**4/8 - 11*i**3/6 + 5*i**2 - 2*i - 75. Solve s(j) = 0.
-1, 2/7, 2/5
Suppose -16 = 4*b, -2*t + 5*b - 2 = -60. Suppose 5 = -8*s + 3*s - 5*r, -5*s + r = -t. Factor -s*l**2 + 2*l**2 - 2 + 3.
-(l - 1)*(l + 1)
Let g(v) be the first derivative of 5*v**3 + 57*v**2 - 48*v + 86. Suppose g(h) = 0. What is h?
-8, 2/5
Let a(m) be the third derivative of -m**7/5040 + m**6/2160 + m**5/360 - 2*m**3 + 35*m**2. Let b(v) be the first derivative of a(v). Suppose b(u) = 0. What is u?
-1, 0, 2
Let p(i) = -97*i**2 - 125*i - 28. Let a(z) = -2*z**2 + 2. Let v(j) = -9*a(j) - p(j). Factor v(f).
5*(f + 1)*(23*f + 2)
Let w(n) = n**3 - 39*n**2 - 82*n. Let s be w(41). Let g(o) be the second derivative of -1/42*o**4 + 8/21*o**3 - 16/7*o**2 + s - 10*o. Factor g(c).
-2*(c - 4)**2/7
Suppose 8*h - 5*h = 3, -c - 2*h = -12. Factor -c*q - 5*q + 4*q**2 - 7*q - 121 - 5*q**2.
-(q + 11)**2
Let d(h) be the first derivative of 9/2*h**2 + 1/2*h**3 + 15/2*h + 7. Determine g, given that d(g) = 0.
-5, -1
Let g(x) be the second derivative of 1/4*x**4 + 3*x**2 + 1/20*x**5 - 3/2*x**3 + 0 + 4*x. Let h(o) be the first derivative of g(o). Factor h(r).
3*(r - 1)*(r + 3)
Let f(o) = -13*o**3 + 21*o**2 + 4*o - 3. Let l be -20 + (3 - 4/4). Let p(s) = -3*s**3 + 5*s**2 + s - 1. Let r(h) = l*p(h) + 4*f(h). What is v in r(v) = 0?
-1, 1, 3
Let w(b) be the second derivative of -2*b**2 + 0 - 5*b - 1/390*b**5 - 1/156*b**4 + 2/39*b**3. Let k(l) be the first derivative of w(l). Factor k(y).
-2*(y - 1)*(y + 2)/13
Let t(r) be the second derivative of 0 - 17*r - 47/70*r**5 - 16/35*r**6 + 1/7*r**3 + 1/7*r**2 - 13/42*r**4 - 16/147*r**7. Solve t(a) = 0 for a.
-1, -1/4, 1/4
Let g(p) = -p**2 - 22*p + 32. Let f be g(-21). Factor f + 33*h**3 + 81*h**2 - 29 - 2*h**4 + 5*h**4 + 75*h.
3*(h + 1)**3*(h + 8)
Let i be (-491)/(-880) - (-8 + 846/99). Let d(u) be the second derivative of 5*u + 0*u**2 + 1/48*u**4 + 0 + i*u**5 + 0*u**3. What is l in d(l) = 0?
-1, 0
Let s(y) = 10*y**2 - 5. Let z(k) = -k**2 - k + 1. Let n(o) = -s(o) - 5*z(o). Factor n(b).
-5*b*(b - 1)
Factor -2/9*u**3 + 36 - 32/9*u**2 - 10*u.
-2*(u - 2)*(u + 9)**2/9
Let t = 96 + -76. Factor t*k**3 + 24*k**4 - 5*k**4 - 3*k**4 + 8*k**2 + 4*k**5.
4*k**2*(k + 1)**2*(k + 2)
Let z(p) = -5*p**3 - 21*p**3 - 22*p**3 + 12*p**2 + 28*p**4 + 12*p. Let o(d) = -84*d**4 + 144*d**3 - 36*d**2 - 35*d. Let a(y) = 4*o(y) + 11*z(y). Factor a(w).
-4*w*(w - 1)**2*(7*w + 2)
Let r(f) be the first derivative of -f**6/12 - f**5 - 7*f**4/2 - 5*f**3/3 + 29*f**2/4 + 10*f - 334. Suppose r(k) = 0. What is k?
-5, -4, -1, 1
Let -236/3*v + 36*v**5 + 8 + 144*v**4 - 384*v**3 + 824/3*v**2 = 0. Calculate v.
-6, 1/3, 1
Let h(w) = w**3 + 6*w**2 + 7*w + 4. Let a be h(-4). Suppose a*v = 6*v. Find c such that v*c**3 + c**3 + 0*c**3 + 0*c**3 - c = 0.
-1, 0, 1
Let s be 219/15 + (-34)/(-85). Suppose 3*g + 6*j - 66 = j, 4*j = 0. Find d, given that -s - 5*d**4 - 31*d + 3*d - 60*d**2 - 42*d**3 - g*d + 12*d**3 = 0.
-3, -1
Let b(c) be the second derivative of -c**5/60 - 5*c**4/24 - 4*c**3/9 + c**2 + c + 52. Solve b(x) = 0 for x.
-6, -2, 1/2
Let y be 16/24 - 1540/(-66). Factor -8/5 - 554/5*z**2 - 338/5*z**4 + 156*z**3 + y*z.
-2*(z - 1)**2*(13*z - 2)**2/5
Factor -2/11*p**2 + 8 - 40/11*p.
-2*(p - 2)*(p + 22)/11
Let m(n) be the first derivative of 3*n**5/10 + 7*n**4/4 + 3*n**3/2 - 11*n + 16. Let k(g) be the first derivative of m(g). Factor k(o).
3*o*(o + 3)*(2*o + 1)
Let z(a) = -96*a + 192. Let q be z(2). Determine d, given that q - 6*d**4 + 4/7*d**3 + 16/7*d - 18/7*d**5 + 40/7*d**2 = 0.
-2, -2/3, 0, 1
Let d(u) = -10*u + 54. Let v be d(5). Let t(j) be the third derivative of 0*j - 4*j**2 + 0*j**v - 1/180*j**5 + 0 + 2/9*j**3. Factor t(z).
-(z - 2)*(z + 2)/3
Find v, given that 30/7*v**2 - 12/7 - 18/7*v**4 + 8/7*v**5 + 2/7*v - 10/7*v**3 = 0.
-1, -3/4, 1, 2
Let k(a) be the second derivative of a**6/15 - 3*a**5/10 - a**4 + 28*a**3/3 - 24*a**2 - 34*a - 1. Suppose k(t) = 0. Calculate t.
-3, 2
Factor -1/4*o**3 + 507/4 - 23/4*o**2 - 91/4*o.
-(o - 3)*(o + 13)**2/4
Let j(d) be the second derivative of -5*d**4/12 + 1360*d**3/3 - 184960*d**2 + 2*d + 387. What is a in j(a) = 0?
272
Suppose -5*p + 110 = 8*q - 11*q, 4*p = -3*q + 115. Let n = 25 - p. Factor 0*m + 4/7*m**5 + n*m**2 + 4/7*m**3 + 0 - 8/7*m**4.
4*m**3*(m - 1)**2/7
Let q(f) = -5*f**2 + 1744*f + 95061. Let l(x) = -x**2 + 436*x + 23765. Let r(a) = 26*l(a) - 6*q(a). Factor r(j).
4*(j + 109)**2
Let b(n) = 70*n**2 - 120*n + 630. Let g(w) = -11*w**2 + 20*w - 105. Let c(q) = -4*b(q) - 25*g(q). Solve c(d) = 0 for d.
-7, 3
Let r(f) be the second derivative of -f**7/21 + 2*f**6/15 + 9*f**5/10 - f**4/3 - 8*f**3/3 - 2*f + 60. Find n such that r(n) = 0.
-2, -1, 0, 1, 4
Let d(y) be the first derivative of y**6/21 + 4*y**5/35 - 27*y**4/14 + 104*y**3/21 - 4*y**2 + 299. Suppose d(p) = 0. Calculate p.
-7, 0, 1, 2
Let a(v) = -195*v + 2536. Let h be a(13). Determine z, given that h - 1/8*z**3 - 1/4*z**2 + 1/2*z = 0.
-2, 2
Let l(i) = -i**3 + 10*i**2 - 80*i - 2. Let a(d) = d**2 + d. Let c(g) = 5*a(g) + l