2 - 1834*i - 42592. Let g(h) = 2*h**2 + 167*h + 3872. Let t(d) = 6*a(d) + 68*g(d). Determine r so that t(r) = 0.
-44
Suppose -5*p**2 - 17*p**2 - 17*p**3 + 55 + 73 + 112*p + 2*p**2 + 13*p**3 = 0. Calculate p.
-8, -1, 4
Let j(w) = -3*w**3 + w**2 + w + 1. Let l be j(-1). Let d be ((-3)/2)/(2/l) + 3. Suppose -z**3 + 1/3*z**4 + d*z**2 + 0 + 4/3*z = 0. Calculate z.
-1, 0, 2
Suppose 5*v = v - 5*w - 10, 3*v - 4*w = 8. Let y(s) be the second derivative of 0*s**2 + 1/3*s**3 + v - 5*s + 1/10*s**5 + 1/3*s**4. Factor y(f).
2*f*(f + 1)**2
Suppose -6*s**3 - 36*s + 48 + 7*s**3 + 2*s**3 = 0. What is s?
-4, 2
Let b(m) = 3*m - 1. Let o be b(1). Let n be (o - 1)*0 - -3. Factor 12*i**3 + 5*i**4 + 6*i**2 + 2*i**2 + n*i**4 + 2*i**5 + 2*i.
2*i*(i + 1)**4
Suppose -3/7*a**4 + 0*a + 0 + 6/7*a**3 + 9/7*a**2 = 0. Calculate a.
-1, 0, 3
Factor -4*i**4 + 3*i**4 + 12*i + 36 - 2*i**4 + 0*i**4 - 18*i**3 - 27*i**2.
-3*(i - 1)*(i + 2)**2*(i + 3)
Let t(g) be the first derivative of 0*g**2 + 4/9*g**3 - 1/6*g**4 + 0*g - 1 - 2/15*g**5. Let t(b) = 0. What is b?
-2, 0, 1
Let z(a) be the second derivative of 0*a**2 + 3*a**4 - 3/10*a**6 - 4*a**3 + 14*a + 0 + 1/14*a**7 - 3/10*a**5. Solve z(k) = 0.
-2, 0, 1, 2
Let k(y) = 3*y**2 + 23*y + 10. Let x(l) = -l. Let a(c) = 7*c**2 + 51*c + 19. Let n(s) = a(s) + 5*x(s). Let r(o) = -7*k(o) + 4*n(o). Factor r(m).
(m + 3)*(7*m + 2)
Let b(w) = 21*w**2 + 9*w - 12. Let s = 71 + -69. Let o(n) = 5*n**2 + 2*n - 3. Let d(j) = s*b(j) - 9*o(j). Factor d(h).
-3*(h - 1)*(h + 1)
Let v(z) be the second derivative of z**5/60 - 5*z**4/18 + 2*z**3/3 + 12*z**2 - 3*z - 36. Factor v(d).
(d - 6)**2*(d + 2)/3
Let w(d) be the second derivative of d**6/10 + 6*d**5/5 + 23*d**4/4 + 14*d**3 + 18*d**2 - 441*d. Let w(c) = 0. Calculate c.
-3, -2, -1
Suppose -3*v + 0*v + 52 = -5*k, 2*v - k - 44 = 0. Let s be ((-50)/30)/((-10)/v). Determine t, given that 0 - 1/2*t**2 - 1/3*t + 0*t**3 + 1/6*t**s = 0.
-1, 0, 2
Suppose 3*d = -5*s + 31, -2*d - 4*s + 19 = -s. Factor -6*g**2 + d*g**2 - 12*g + 20*g.
-4*g*(g - 2)
Let y(w) be the first derivative of -6*w**2 + 7 - 1/4*w**4 - w + 2*w**3. Let a(f) be the first derivative of y(f). Suppose a(d) = 0. What is d?
2
Let f be (2/6)/(7/42). Factor -15*a**3 - 12*a + 24*a**f - 200*a**4 + 0*a**2 + 203*a**4.
3*a*(a - 2)**2*(a - 1)
Let k(q) be the third derivative of -q**5/30 + 29*q**4/3 - 3364*q**3/3 + 2*q**2 - 74. Find g, given that k(g) = 0.
58
Let r = -955 - -145. Let w be (r/24)/9 + 4. Let -w*u**2 + 1 + 0*u = 0. What is u?
-2, 2
Suppose 20 = 4*z, z = -2*f + 9 + 6. Suppose f*d - 2*i = 4, 3*d - 16 = -5*i + 5. Factor 0 + 1/4*m + 0*m**d - 1/4*m**3.
-m*(m - 1)*(m + 1)/4
Let b(p) be the first derivative of p**4 - 176*p**3/3 + 170*p**2 - 168*p + 47. Factor b(r).
4*(r - 42)*(r - 1)**2
Suppose 4 = 2*l - 6. Let c(x) = -x**2 - 8*x + 22. Let z be c(-10). Factor -z*t**2 + 2*t**l + 0*t**4 - 4*t**4 - 2*t**4 + 6*t**3.
2*t**2*(t - 1)**3
Let y = 31189/327705 - -1/15605. Determine z so that -2/21*z**2 - y*z + 4/21 = 0.
-2, 1
Let a be (((-56)/140)/((-9)/(-70)))/(4/(-20)). Find u such that a*u**3 + 16/3 - 272/9*u + 36*u**2 = 0.
-3, 2/7, 2/5
Solve -32/5*c - 64/5 - 4/5*c**2 = 0 for c.
-4
Let o(b) = -b**2 + 15*b - 24. Let n be o(13). Let v(f) be the third derivative of 0 - 5*f**n + 3/16*f**4 + 9/8*f**3 + 1/80*f**5 + 0*f. Solve v(h) = 0 for h.
-3
Let r(y) be the first derivative of 4*y**6/27 - 8*y**5/9 - y**4/6 + 8*y**3 - 3*y**2 - 36*y - 734. Solve r(f) = 0 for f.
-3/2, 2, 3
Let z(a) be the first derivative of a**6/90 - a**5/30 + a**4/36 - 12*a + 7. Let k(g) be the first derivative of z(g). Factor k(t).
t**2*(t - 1)**2/3
Let r(z) be the first derivative of 1/25*z**5 + 39/10*z**2 + 29/15*z**3 - 21 + 9/20*z**4 + 18/5*z. Suppose r(o) = 0. Calculate o.
-3, -2, -1
Let h be ((-14)/(-10) - 1)/((-9)/(-90)). Factor l**2 + 5*l**2 + 5*l**3 + h*l**3 + 3*l**4.
3*l**2*(l + 1)*(l + 2)
Let f(a) = -11*a**2 + 1212*a + 68. Let t(d) = -2*d**2 + 202*d + 12. Let w(l) = 6*f(l) - 34*t(l). Factor w(h).
2*h*(h + 202)
Let a(o) be the first derivative of 2*o**5/15 - 17*o**4/12 + 4*o**3/3 - 21*o**2/2 + 2*o + 6. Let q(j) be the second derivative of a(j). Let q(l) = 0. What is l?
1/4, 4
Let l(j) be the first derivative of 24 + 0*j**3 + 1/28*j**4 + 0*j**2 + 0*j. Suppose l(n) = 0. What is n?
0
Let q be (2/7)/((-102)/21 - -5). Let f(s) be the second derivative of -1/45*s**6 + 0*s**5 + 1/9*s**4 + 2*s - 1/3*s**q + 0*s**3 + 0. Factor f(t).
-2*(t - 1)**2*(t + 1)**2/3
Let n = -916/7 - -13754/105. What is g in 2/15*g + 2/5*g**3 + 0 + n*g**4 + 2/5*g**2 = 0?
-1, 0
Let q be -1 + ((-56)/24 - (5 - 9)). Determine m so that -1 + 1/3*m**2 - q*m = 0.
-1, 3
Suppose 3*r + 5 = 3*v + 23, 4*v = -4*r + 64. Factor 6*n**5 - 18*n**2 + 2*n**5 - r*n**3 + 10*n**4 - 10*n**5 + 5*n**3.
-2*n**2*(n - 3)**2*(n + 1)
Let o(b) be the first derivative of b**3/3 + 69*b**2 - 139*b - 363. Factor o(y).
(y - 1)*(y + 139)
Suppose -5*d = -3*q + 27, -4*q + 28 = -3*d + 3. Let l(b) be the second derivative of -1/2*b**4 - 4/3*b**3 + q*b + 0 + 4*b**2. Determine o so that l(o) = 0.
-2, 2/3
Let c(o) be the third derivative of -o**8/3360 - o**7/140 - o**6/20 + 2*o**3/3 - 16*o**2. Let h(x) be the first derivative of c(x). Let h(k) = 0. Calculate k.
-6, 0
Suppose 0 = 3*w - d + 431, -2*w - 2*d - 211 = 87. Let v = -141 - w. Solve 6 - v*m + 2/3*m**2 = 0 for m.
3
Suppose -13*j + 9 = -30. Suppose 0*l = -j*l + 5*z - 10, 4*z = 2*l + 8. Factor -4/17*s**2 + 0 + 2/17*s**3 + l*s.
2*s**2*(s - 2)/17
Let b = 55 - 53. Suppose b*u + 16 = -5*c, 2*c + 12 + 4 = 4*u. Suppose 1/2 + u*i**3 + 9/2*i**2 + 3*i = 0. What is i?
-1, -1/4
Let c(y) = 2*y**2 - 18*y - 3. Let d(w) be the second derivative of w**4/12 + w**3/6 + w**2/2 - 9*w. Let j(m) = c(m) + 3*d(m). Factor j(f).
5*f*(f - 3)
Let v = 1488/11 - 34070/253. Let -2/23*u**3 + 2/23*u + 14/23*u**2 - v = 0. Calculate u.
-1, 1, 7
Factor -16/3*i + 16/3*i**2 + 0 + 4/3*i**3 - 4/3*i**4.
-4*i*(i - 2)*(i - 1)*(i + 2)/3
Let i(o) be the second derivative of 35*o**4/12 + 155*o**3/6 + 60*o**2 + 3*o - 36. Let i(d) = 0. Calculate d.
-24/7, -1
Let h = 2 + 3. Factor h*c + 3*c - 4 - 6*c + 0*c + 2*c**2.
2*(c - 1)*(c + 2)
Suppose -w = 2*w, -2*i = -3*w - 6. Let x = 75077/2 + -37537. Factor 0 + 0*y + y**2 - x*y**i + 1/2*y**4.
y**2*(y - 2)*(y - 1)/2
Let c = -3/22 + 81/110. Let k = c - 1/10. Find h, given that 1/3 - k*h + 1/6*h**2 = 0.
1, 2
Let c = -3069 + 76727/25. Factor -2/25*a + 2/25 - c*a**2 + 2/25*a**3.
2*(a - 1)**2*(a + 1)/25
Let c(b) be the second derivative of 1/10*b**5 + 4/15*b**4 + 0*b**2 + 34*b + 4/15*b**3 + 0 + 1/75*b**6. Factor c(q).
2*q*(q + 1)*(q + 2)**2/5
Factor 2*u**3 + 1165*u**4 - 587*u**4 - u**5 - 577*u**4.
-u**3*(u - 2)*(u + 1)
Find t, given that -12*t - 6*t - 16*t**2 - 12*t**3 - 11*t**2 - 3 = 0.
-1, -1/4
Let x(m) be the third derivative of -m**7/168 - m**6/24 - m**5/12 + 5*m**3/3 + 12*m**2. Let r(d) be the first derivative of x(d). Factor r(i).
-5*i*(i + 1)*(i + 2)
Let n(d) be the second derivative of 4/105*d**6 - 1/14*d**5 + 1/21*d**4 - 1/147*d**7 + 0 - 33*d + 0*d**3 + 0*d**2. Solve n(m) = 0 for m.
0, 1, 2
Let i(r) be the first derivative of 2/39*r**3 + 6/13*r**2 - 14/13*r + 11. Solve i(n) = 0.
-7, 1
Let d be -85*(-10)/375 - (42/9 + -4). Factor -2/5*c**4 + 6/5*c**2 - 4/5*c**3 - 8/5 + d*c.
-2*(c - 1)**2*(c + 2)**2/5
Let n(k) = 4*k**2 + 3. Let h(p) = 19*p**2 + 8*p + 24. Let m(q) = h(q) - 5*n(q). Factor m(s).
-(s - 9)*(s + 1)
Let l(h) be the third derivative of -h**7/42 + 13*h**6/24 - 35*h**5/12 - 245*h**4/24 - 66*h**2. Factor l(f).
-5*f*(f - 7)**2*(f + 1)
Let x(v) be the first derivative of v**7/126 + v**6/36 + v**5/36 + 6*v**2 - 12. Let d(f) be the second derivative of x(f). Find o such that d(o) = 0.
-1, 0
Let f(y) be the second derivative of -1/160*y**6 + 1/120*y**5 - 13*y + 0 + 3*y**2 + 1/8*y**4 - 1/3*y**3. Let x(k) be the first derivative of f(k). Factor x(h).
-(h - 2)*(h + 2)*(3*h - 2)/4
Let m(g) = -g**5 + 4*g**4 + 7*g**3 - 8*g + 2. Let i(u) = 4*u**5 - 17*u**4 - 27*u**3 - u**2 + 32*u - 9. Let k(o) = -2*i(o) - 9*m(o). Suppose k(b) = 0. What is b?
-2, -1, 0, 1, 4
Determine m so that 0 + 0*m + 396/7*m**2 - 4/7*m**3 = 0.
0, 99
Find u, given that 28/5*u**2 - 8/5 - 44/5*u**3 - 4*u**4 + 16/5*u**5 + 28/5*u = 0.
-1, 1/4, 1, 2
Let u(i) be the second derivative of -i**4/12 - 53*i**3/6 + 27*i**2 + 10*i - 1. Factor u(s).
-(s - 1)*(s + 54)
Le