- 86*j**2 + 75*j + 2. Let p(n) = 3*n**3 - 345*n**2 + 297*n + 9. Let v(a) = 2*p(a) - 9*q(a). Factor v(h).
-3*h*(h - 27)*(h - 1)
Let i(r) = r**2 - 2*r - 33. Let n be i(8). Suppose -b**2 + 9*b + 7*b - n*b + 12 = 0. What is b?
-3, 4
Suppose -4*y + 27 = 15. Let c(n) be the first derivative of 6 - 1/15*n**5 - 1/2*n**2 + 1/9*n**y + 1/4*n**4 + 0*n. What is j in c(j) = 0?
-1, 0, 1, 3
Let c = -3089 + 9269/3. Find v such that c*v**2 + 4/3 + 2*v = 0.
-2, -1
Let t = -189 - -196. Suppose 2*q + t = 11. Factor -50/7 - 2/7*g**q + 20/7*g.
-2*(g - 5)**2/7
Suppose 4*n + 4*w + 14 = 6*n, -n = w - 10. Let c be (-8)/(-6) - (-15)/n. Factor 0*i + 3*i**2 - 4*i + 4*i + c*i**4 + 6*i**3.
3*i**2*(i + 1)**2
Let t(i) = 64*i**4 - 199*i**3 - 48*i**2 + 640*i - 448. Let o(d) = 16*d**4 - 50*d**3 - 12*d**2 + 160*d - 112. Let n(w) = 9*o(w) - 2*t(w). Factor n(r).
4*(r - 2)**2*(r - 1)*(4*r + 7)
Let m(g) be the first derivative of g**3 + g**2 + 3*g + 5. Let i be m(-3). Let 18*z**2 + 3 - 6 - 30*z - i*z**2 - 69*z**2 = 0. Calculate z.
-1/5
Let g = 7 + 19. What is n in -92*n**2 - 13*n - 16 - 2*n**3 - 38*n - 29*n - g*n**3 = 0?
-2, -1, -2/7
Let l(y) = y**3 + y**2 - 2*y. Let v(o) = -o**4 + 7*o**3 + 6*o**2 - 12*o. Let p(q) = 15*l(q) - 3*v(q). Factor p(c).
3*c*(c - 2)*(c - 1)*(c + 1)
Let v(s) be the second derivative of s**4/108 - 41*s**3/54 + 74*s**2/9 - 32*s - 1. Factor v(x).
(x - 37)*(x - 4)/9
Suppose -3*c - 27 = 12. Let s(k) = -3*k**3 + 3*k**2. Let n be (-3)/(3/(-7)) + -1. Let w(b) = -6*b**3 + 7*b**2. Let y(j) = c*s(j) + n*w(j). Factor y(i).
3*i**2*(i + 1)
Suppose 35 = 3*a - i, -2*a - 5*i + 2 = -27. Suppose 9 = -a*h + 33. Find l, given that 2/15*l**4 - 2/5*l**h + 4/15 + 2/15*l**3 - 2/15*l = 0.
-2, -1, 1
Let c(p) = -2*p**3 + 79*p**2 + 67*p + 7. Let l(m) = -m**3 + 77*m**2 + 66*m + 6. Let v(k) = -6*c(k) + 7*l(k). Factor v(h).
5*h*(h + 1)*(h + 12)
Let c(g) be the second derivative of -1/4*g**3 - 3/16*g**4 - 3*g + 3/8*g**2 + 0. Factor c(u).
-3*(u + 1)*(3*u - 1)/4
Factor 54/5*s**4 + 21/5*s + 64/5*s**2 + 86/5*s**3 + 2/5 + 13/5*s**5.
(s + 1)**4*(13*s + 2)/5
Let j(v) be the first derivative of -1/6*v**6 - 10/3*v**3 - 2 - 1/4*v**4 + 2*v**2 + 4/5*v**5 + 8*v. Suppose j(h) = 0. What is h?
-1, 2
Determine v, given that -6 + 5/2*v**2 + 1/4*v**3 - v - 1/4*v**4 = 0.
-2, 2, 3
Let r(q) = 180*q**2 - 63*q + 2. Let h be (1 + 7)/1 + 0. Let g(c) = -415*c**2 - 36 + 29 + 188*c - 125*c**2. Let l(d) = h*r(d) + 3*g(d). Solve l(n) = 0 for n.
1/6
Let n(b) be the third derivative of b**8/3864 - b**6/1380 - 109*b**2. Let n(w) = 0. Calculate w.
-1, 0, 1
Let t(q) be the first derivative of 2*q**7/21 - 4*q**6/15 + 2*q**4/3 - 2*q**3/3 - 11*q + 1. Let c(y) be the first derivative of t(y). Factor c(s).
4*s*(s - 1)**3*(s + 1)
Let b(r) = r**3 - r**2 - r - 1. Let z(w) = 6*w**3 - 6*w**2 - 13*w + 1. Let c(o) = -4*b(o) + z(o). Let y(l) = -l + 1. Let x(p) = 2*c(p) - 10*y(p). Factor x(u).
4*u*(u - 2)*(u + 1)
Suppose 2*g = 5*d - 7*d + 18, -5*g + 18 = -4*d. Factor -2*w - 11/2*w**d - 3/2*w**4 + 0 - 6*w**2.
-w*(w + 1)*(w + 2)*(3*w + 2)/2
Let h(t) = t**2. Let d(c) = 6*c**2 + 48*c + 51. Let a(y) = d(y) - 9*h(y). Factor a(s).
-3*(s - 17)*(s + 1)
Let l(z) = -z**3 - 13*z**2 + z + 8. Let b be l(-13). Let v be (3 - 138/45) + (-2)/b. Find c, given that v*c**2 + 0 - 2*c**3 + 0*c - 4/3*c**5 + 3*c**4 = 0.
0, 1/4, 1
Let o(x) be the first derivative of x**3/9 - 3*x**2 + 17*x/3 - 131. Solve o(h) = 0.
1, 17
Let c(v) be the second derivative of v**6/360 + v**5/40 + v**4/12 - v**3 - 11*v. Let u(k) be the second derivative of c(k). Let u(j) = 0. What is j?
-2, -1
Let m = 238771/615279 - -196/1059. Let v = m + -1/581. Factor v + 4/7*y**2 - 10/7*y.
2*(y - 2)*(2*y - 1)/7
Suppose b - 79 = -5*j, -2*b - 4*j + 31 + 133 = 0. Suppose 0 = 9*z - 8*z - b. Find v, given that z*v**4 + 8/3*v + 218/3*v**3 + 24*v**2 + 0 + 98/3*v**5 = 0.
-1, -2/7, 0
Let w(m) be the first derivative of m**3 + 3*m**2 - 9*m - 527. Factor w(z).
3*(z - 1)*(z + 3)
Let f(o) be the second derivative of o**4/12 + 35*o**3/3 + 49*o. Factor f(h).
h*(h + 70)
Factor 32 + 0*k**2 + 8*k + 2*k**3 - 13*k**2 + k**2 + 2*k**4 - 12*k**2 + 0*k**2.
2*(k - 2)**2*(k + 1)*(k + 4)
Let w be 8/(-22)*4026/(-3660). Factor 0 + 0*k + w*k**2 + 2/5*k**3.
2*k**2*(k + 1)/5
Determine n so that 4*n**5 + 12*n**3 + 10*n**3 + 52*n**4 - 20*n**4 + 6*n**3 = 0.
-7, -1, 0
Let t(i) = -i**3 + i**2 + i. Let y(w) = 8*w**3 - 257*w**2 + 7051*w - 65856. Let r(q) = 5*t(q) + y(q). Factor r(l).
3*(l - 28)**3
Let k be 2/((-8)/12)*(-5)/3. Suppose 5*h - 19 = -2*t, -7 = 5*t - k*h - 2. Let -2/5*i**3 - 6/5*i**t - 4/5*i + 0 = 0. What is i?
-2, -1, 0
Let p = 514 + -514. Let a(i) be the third derivative of -11*i**2 + 0*i + 1/15*i**5 + 2/21*i**3 - 5/42*i**4 + p - 1/70*i**6. Factor a(b).
-4*(b - 1)**2*(3*b - 1)/7
Let t(p) = 4*p - 2. Let k be t(2). Suppose -5*z - 13 = -k*z. Solve 8 - 12*f**3 + 90*f**2 - z*f**3 + 0*f**3 + 52*f + 0*f**3 - 125*f**4 = 0.
-2/5, 1
Factor -4*b + b - 882*b**2 + 867*b**2 - 4*b**3 + 9*b**3 + 13*b.
5*b*(b - 2)*(b - 1)
Let k be (1 + (-5 - -3))*-8. Factor -1072*f**3 + 4 + 1072*f**3 - k*f**2 + 4*f**4.
4*(f - 1)**2*(f + 1)**2
Suppose 4*h = -11*t + 6*t, -5*t - h = 0. Determine q so that -1/3*q**2 + 4/3 + t*q = 0.
-2, 2
Suppose -q = -5*g - 2, -5*q - 32*g + 27*g = -10. Solve -2/13*l**q + 12/13 - 10/13*l = 0 for l.
-6, 1
Let x = 653 - 650. Let v(c) be the third derivative of 41/30*c**5 - 5/12*c**4 + 0*c + 11/15*c**6 - 2*c**2 + 0 - 2/3*c**x. Solve v(m) = 0 for m.
-1, -2/11, 1/4
Let k(t) = -t**3 - 7*t**2 + 2*t + 31. Let b be k(-7). Let x = 18 - b. Factor -x - 3/2*a - 1/2*a**2.
-(a + 1)*(a + 2)/2
Let v(u) be the first derivative of u**6/90 + u**5/30 - u**4/3 + 7*u**3 + 15. Let f(x) be the third derivative of v(x). Factor f(a).
4*(a - 1)*(a + 2)
Let i(p) be the third derivative of 0*p**3 + 1/70*p**7 - 1/20*p**5 + 0 + 0*p + 5/8*p**4 - 1/8*p**6 - 23*p**2. Factor i(c).
3*c*(c - 5)*(c - 1)*(c + 1)
Suppose -3*p - 15 = -96. Let x be -2 - (-4 - (-42)/p). Factor -2/9*c**3 + 0 - x*c**2 - 2/9*c.
-2*c*(c + 1)**2/9
Let z(i) = 2*i + 2. Let n be z(0). Let t(f) be the second derivative of 0*f**3 + 4*f + 0*f**n - 1/12*f**4 + 1/30*f**6 + 0*f**5 + 0. Find p such that t(p) = 0.
-1, 0, 1
Factor 3/8*g**2 - 69/8*g + 63/4.
3*(g - 21)*(g - 2)/8
Let o(a) be the second derivative of a**7/210 + a**6/120 - a**5/60 - a**4/24 + 15*a**2/2 + 37*a. Let f(m) be the first derivative of o(m). Factor f(i).
i*(i - 1)*(i + 1)**2
Suppose 186 - 132 = 18*c. Let p(r) be the first derivative of 0*r**4 + 0*r**2 + 2/15*r**5 - 2/9*r**c + 0*r + 8. Factor p(q).
2*q**2*(q - 1)*(q + 1)/3
Determine b so that -219 + 116 - 44*b**2 + 103 + 8*b = 0.
0, 2/11
Let k = 713 - 2137/3. Determine m so that 0*m - 1/3*m**2 + 0 - k*m**3 - 1/3*m**4 = 0.
-1, 0
Let z(w) be the first derivative of 2*w**3/27 - 38*w**2/9 + 722*w/9 - 77. Factor z(c).
2*(c - 19)**2/9
Let t(y) be the second derivative of -y**5/100 + y**4/60 + y**3/30 - y**2/10 + 80*y. Suppose t(f) = 0. What is f?
-1, 1
Let p(n) be the second derivative of 4/9*n**3 + 2/15*n**5 + 0 + 1/45*n**6 + 7*n + 1/3*n**4 + 1/3*n**2. Find y, given that p(y) = 0.
-1
Suppose 10 = 5*c + 2*j, j - 16 = -21. Let u(z) be the second derivative of -1/18*z**c + 1/3*z**2 + 0*z**3 + 0 + 7*z. Find r, given that u(r) = 0.
-1, 1
Let v(t) be the first derivative of 11 + 0*t + 4/5*t**5 + 2/15*t**6 + 9/5*t**4 + 28/15*t**3 + 4/5*t**2. Determine b so that v(b) = 0.
-2, -1, 0
Let b = 242 - 224. Factor b*q**2 - 3/2 - 6*q.
3*(2*q - 1)*(6*q + 1)/2
Let r = -41/23 - -146/69. Factor -1/3*g**2 + r + 1/6*g**3 - 1/6*g.
(g - 2)*(g - 1)*(g + 1)/6
Let k(c) = 2*c**3 - 38*c**2 + 192*c - 162. Let s(g) = -4*g**3 + 76*g**2 - 386*g + 324. Let d(l) = 5*k(l) + 3*s(l). Factor d(m).
-2*(m - 9)**2*(m - 1)
Let j(f) = 4*f**2 + f + 1. Suppose 2*z + z + 12 = -4*o, 5*o + 3*z = -18. Let l(m) = m**2 + m + 1. Let t(d) = o*l(d) + 3*j(d). Let t(g) = 0. What is g?
-1/2, 1
Let d = 649/2961 - -1/329. Let g = -1/342 - -17/38. Factor g*l**2 - d*l - 2/9 + 4/9*l**3 - 2/9*l**5 - 2/9*l**4.
-2*(l - 1)**2*(l + 1)**3/9
Let h(p) = -p**2 - 13*p. Let z be h(-13). Let w(t) be the first derivative of z*t**3 + 1 + 0*t + 1/3*t**6 + 0*t**2 - 2/5*t**5 + 0*t**4. Factor w(i).
2*i**4*(i - 1)
Solve 2/7*r**2 + 8/7*r + 0 = 0 for r.
-4, 0
Factor 1000*z + 0 + 1/10*z**3 + 20*z**2.
z*(z + 100)**2/10
Let p(f) be the second derivative of -f**7/63 + 2*f*