- 16*k - 4. Let m(g) = 3*d(g) + 4*s(g). Determine y so that m(y) = 0.
-1/3, 0, 1, 4
Suppose 4*f - 21*n + 3 = -18*n, 0 = -2*f + n - 1. Factor f + 2/7*r**4 + 0*r**2 + 0*r - 2/7*r**3.
2*r**3*(r - 1)/7
Let f(g) be the first derivative of g**6/180 - g**5/60 - g**4/18 + g**3/18 + g**2/4 + 13*g - 16. Let o(z) be the first derivative of f(z). Factor o(x).
(x - 3)*(x - 1)*(x + 1)**2/6
Let u = -18909621316/1197 + 15797513. Let v = u - 5/171. Solve -v*s**2 + 0 + 4/7*s - 2/7*s**4 + 8/7*s**3 = 0 for s.
0, 1, 2
Let u(a) be the first derivative of -a**3 - 9*a**2/2 - 26. Let u(p) = 0. What is p?
-3, 0
Let x = 161/3620 + 1/181. Let r(g) be the third derivative of 0*g - 2*g**3 + 0 + 4*g**2 - 1/2*g**4 - x*g**5. Factor r(l).
-3*(l + 2)**2
Let s(k) be the first derivative of -k**3 + 27*k**2/2 - 24*k + 159. Factor s(c).
-3*(c - 8)*(c - 1)
Factor -201/4 + 1209/8*c - 3/8*c**4 + 411/8*c**3 - 1215/8*c**2.
-3*(c - 134)*(c - 1)**3/8
Factor 3*x**2 - 9*x**2 - 24 + 2*x + 3*x**2 + 5*x**2.
2*(x - 3)*(x + 4)
Let f(m) be the third derivative of 0*m**3 - 1/84*m**8 + 1/10*m**6 + 0*m**4 + 0*m + 2/15*m**5 + 0*m**7 + 0 - 13*m**2. What is x in f(x) = 0?
-1, 0, 2
Let t(y) be the first derivative of 2*y**3/15 + 16*y**2/5 - 348. Factor t(p).
2*p*(p + 16)/5
Suppose 1/6*d - 10/3 - 1/6*d**3 + 10/3*d**2 = 0. What is d?
-1, 1, 20
Let q(p) be the third derivative of -p**7/70 - 11*p**6/280 + 3*p**5/140 + 11*p**4/56 + 2*p**3/7 + 228*p**2. Solve q(d) = 0 for d.
-1, -4/7, 1
Let g(o) be the second derivative of o**4/36 - o**3/9 - 2*o + 39. Suppose g(v) = 0. Calculate v.
0, 2
Suppose q + 2 = -3*o + 4, -2*o - 4*q - 12 = 0. Let t be 66/220 - 2*(-177)/420. Factor -t*b**o - 2/7 + 10/7*b.
-2*(b - 1)*(4*b - 1)/7
Let m(j) be the second derivative of j**5/60 + 13*j**4/36 - 7*j**3/9 - 2*j - 453. Let m(f) = 0. What is f?
-14, 0, 1
Let b(r) be the first derivative of -9*r**5/5 + 21*r**4/4 - 16*r**3/3 + 2*r**2 + 55. Find v such that b(v) = 0.
0, 2/3, 1
Let r be (4 + (-105)/24)*((-56)/(-10) - 8). Suppose -r*i + 1/10*i**2 - 1 = 0. What is i?
-1, 10
Let p be 26 + -14 - (5 - -1). Let x(f) be the third derivative of 7/120*f**p + 0 + 1/12*f**5 - 2/3*f**4 + 2*f**2 + 2/3*f**3 + 0*f. What is t in x(t) = 0?
-2, 2/7, 1
Let r(h) be the first derivative of h**5 + 15*h**4/4 - 35*h**3/3 - 75*h**2/2 + 90*h - 826. Let r(z) = 0. Calculate z.
-3, 1, 2
Let n(d) = 4*d**2 - 2*d. Let v be n(2). Let l be (6 - 90/v)*(-1 + -1). Let 0 - 2*c**2 + 2/3*c + 2*c**l - 2/3*c**4 = 0. Calculate c.
0, 1
Suppose 157 = -5*k - 4*p, 2*p + 0*p = k + 37. Let v be (-7)/(-6) + (-11)/k. Solve -12 + 3*b**2 + v*b**3 - 6*b = 0.
-2, 2
Let i(l) be the first derivative of 32*l**6/135 + 4*l**5/45 - l**4/3 + 11*l**3/54 - l**2/18 + 18*l - 39. Let g(v) be the first derivative of i(v). Factor g(m).
(m + 1)*(4*m - 1)**3/9
Let t be ((-2)/8 - 58/(-8))*58/203. Suppose 0*h**t + 0 + 1/4*h**3 + 0*h + 1/4*h**4 = 0. What is h?
-1, 0
Let h(x) be the second derivative of x**5/5 + 164*x**4/15 + 254*x**3/15 - 64*x**2/5 - 67*x. Factor h(f).
4*(f + 1)*(f + 32)*(5*f - 1)/5
Let z(j) be the second derivative of -j**6/165 + 6*j**5/55 - j**4/6 - j - 51. Find f, given that z(f) = 0.
0, 1, 11
Suppose -6*p = -3*p + 4*z + 6, 5*p - z = 13. Suppose -u + p*c = -0*u - 2, -3*u + 5 = -5*c. Factor 0*x**3 - x**2 + 1/3*x**4 + 2/3*x + u.
x*(x - 1)**2*(x + 2)/3
Let n = -17/26 + 523/780. Let t(o) be the third derivative of -o**2 + 1/12*o**4 + 0*o - n*o**6 + 0 - 1/3*o**3 + 1/30*o**5. Solve t(l) = 0.
-1, 1
Suppose -5*r + 17 = -2*c - 0*c, 0 = -c + 5*r - 16. Let l(x) = -2*x**3 + 4*x**2 + 7*x - 3. Let z(u) = u**3 - u + 1. Let a(m) = c*l(m) - 3*z(m). Factor a(s).
-s*(s + 2)**2
Find j, given that -36*j**3 + 164 - 60*j + 458*j**2 - 159*j - 24*j**3 - 140 + 49*j**2 = 0.
1/5, 1/4, 8
Let a be -3 - (4 - 2/((-6)/(-27))). Suppose 16/7*v**3 + 4/7 - 4/7*v**a - 16/7*v = 0. What is v?
-1, 1/4, 1
Let b be (-72)/(-45) - 2/(-5). Suppose -8*m + b*m = 0. Find o, given that -4*o**4 - 5*o**2 + m*o - 10*o + 9*o**4 + 8*o**3 + 2*o**3 = 0.
-2, -1, 0, 1
Let t(s) = -s**3 - 16*s**2 - 19*s - 5. Let v be t(-15). Let u = 58 - v. Determine g, given that 0*g + 2/3*g**2 - 2/3*g**u + 0 = 0.
0, 1
Factor 1156/3 + 238*t + 24*t**2 + 2/3*t**3.
2*(t + 2)*(t + 17)**2/3
Let v(g) be the third derivative of -g**7/630 - g**6/12 - 253*g**5/180 - 35*g**4/6 - 98*g**3/9 + 13*g**2 - 2. Factor v(l).
-(l + 1)**2*(l + 14)**2/3
Factor 19*f + 44*f**2 - 36*f**2 - 55*f.
4*f*(2*f - 9)
Let i(k) be the first derivative of k**4/40 + 23*k**3/10 + 1587*k**2/20 + 12167*k/10 - 3. Factor i(n).
(n + 23)**3/10
Let u(m) = -60*m + m**2 + 60*m. Let s(j) = -3*j**2 - 8. Let k(f) = s(f) + 5*u(f). Find c such that k(c) = 0.
-2, 2
Let g(p) be the second derivative of 3*p**5/25 + 43*p**4/15 + 322*p**3/15 + 98*p**2/5 + 69*p. Let g(t) = 0. Calculate t.
-7, -1/3
Suppose 2*a = -a - q + 8, 0 = 5*q - 10. Solve -15 + 6 - 7 - 4*i**a - 20*i = 0.
-4, -1
Let g(d) be the first derivative of d**5/5 + 3*d**4/2 + 13*d**3/3 + 6*d**2 + 4*d - 10. Solve g(v) = 0 for v.
-2, -1
Let v be 121/484*(-2)/(-45). Let g(d) be the third derivative of 1/9*d**3 + 0*d + 1/180*d**6 - 5*d**2 + 0 - 1/36*d**4 - v*d**5. Find y, given that g(y) = 0.
-1, 1
Let c(b) be the first derivative of -5*b**4/24 + 5*b**3/18 + 25*b**2/12 + 5*b/2 - 100. What is g in c(g) = 0?
-1, 3
Factor -8*a - 106*a - 432 + 2*a**3 + 3*a**4 + 24*a**2 - 174*a - 6*a**4 + 22*a**3.
-3*(a - 6)**2*(a + 2)**2
Let j be (-2)/((-7)/((-84)/(-8))). Let v be j/(-9) + 14/6. Factor 4/7 - 6/7*w**v - 2/7*w.
-2*(w + 1)*(3*w - 2)/7
Suppose 4*r + 2 = -u + 11, -r + 4*u - 2 = 0. Let o(h) = -7*h**2 - h - 4. Let x(m) = 3*m**2 + m + 2. Let w(p) = r*o(p) + 5*x(p). Factor w(g).
(g + 1)*(g + 2)
Let n(t) = 36*t**2 - 64*t - 100. Let k(m) = 7*m**2 - 13*m - 20. Let r(a) = 11*k(a) - 2*n(a). Find d, given that r(d) = 0.
-1, 4
Let i(d) be the second derivative of 2*d**6/5 + 127*d**5/5 + 455*d**4 + 294*d**3 - 8*d - 78. Factor i(a).
4*a*(a + 21)**2*(3*a + 1)
Let h(q) be the first derivative of -q**6/270 + q**5/90 + 19*q**3/3 + 12. Let m(g) be the third derivative of h(g). Factor m(t).
-4*t*(t - 1)/3
Factor -676/3 + 17*q**2 + 208*q + 1/3*q**3.
(q - 1)*(q + 26)**2/3
Let l(p) be the first derivative of -5*p**8/336 + p**7/14 - p**6/8 + p**5/12 - p**2/2 - 10*p - 44. Let s(b) be the second derivative of l(b). Factor s(d).
-5*d**2*(d - 1)**3
Let r(v) be the third derivative of 0*v**3 + 0*v**5 + 1/150*v**6 + 0 + 7*v**2 + 0*v + 1/280*v**8 - 1/105*v**7 + 0*v**4. Let r(n) = 0. Calculate n.
0, 2/3, 1
Let g(y) be the first derivative of -1/12*y**3 - 1/4*y - 1/4*y**2 + 19. Factor g(l).
-(l + 1)**2/4
Let f(d) = 2*d**3 - 23*d**2 + 11*d + 2. Let k(p) = 5*p**2 + 16*p - 5. Let g be k(-4). Let r be f(g). Factor 0 - 3/5*b**3 + 3/5*b**r + 0*b.
-3*b**2*(b - 1)/5
Let x(i) be the first derivative of -i**6/9 - 2*i**5/15 + 7*i**4/2 + 98*i**3/9 - 8*i**2/3 - 40*i - 558. Find w such that x(w) = 0.
-3, -2, 1, 5
Factor 2*b**2 - 16 - 121 - 60*b + 11 + 22 - 6*b**2.
-4*(b + 2)*(b + 13)
Let n(q) = q**2 - 429*q + 430. Let h be n(1). Suppose 0*c**h + 2/7*c + 1/7 - 1/7*c**4 - 2/7*c**3 = 0. What is c?
-1, 1
Let p(y) be the second derivative of y**5/50 + y**4/30 - 34*y - 3. Find v, given that p(v) = 0.
-1, 0
Suppose -27*j - 38 - 96 = -94*j. Factor 2/3*q**4 + 0*q - 2/9*q**5 - 2/3*q**3 + 0 + 2/9*q**j.
-2*q**2*(q - 1)**3/9
Determine v so that 15*v - 113*v**2 + 98*v**2 + 33*v - 9 = 0.
1/5, 3
Let y(m) be the second derivative of 1/55*m**5 + 0*m**2 + 8*m + 0*m**3 + 1/231*m**7 + 0 - 1/55*m**6 + 0*m**4. Factor y(k).
2*k**3*(k - 2)*(k - 1)/11
Suppose 0 = 31*b - 24*b. Let i(u) be the second derivative of 3/2*u**3 - 4*u + 3*u**2 + b - 3/4*u**4 - 3/10*u**5. Factor i(j).
-3*(j - 1)*(j + 2)*(2*j + 1)
Let y be -3*3/(3/(-1)). Suppose 5*d**3 - 5*d**2 + 4*d**2 - 9*d**2 - y*d + 10*d**4 - 2*d = 0. Calculate d.
-1, -1/2, 0, 1
Let a(u) be the third derivative of -u**10/201600 - u**9/40320 - 19*u**5/60 - 7*u**2. Let w(d) be the third derivative of a(d). Let w(m) = 0. What is m?
-2, 0
Let x = 3923 - 3921. Factor p + 0 + 1/2*p**3 + 3/2*p**x.
p*(p + 1)*(p + 2)/2
Let y(z) = z**2 - z. Let w be y(2). Let s be (-1*6)/(-155 - -137). Solve 1/3*o**4 - s*o - o**3 + o**w + 0 = 0 for o.
0, 1
Let p(y) be the second derivative of y**6/75 - y**5/10 + 2*y**4/15 - 62*y. Solve p(r) = 0 for r.
0, 1, 4
Let o = 217 - 214. Suppose -4*y + 32 = 3*u - 0*y, -4*u = -y - 