Find k, given that j(k) = 0.
1, 2
Let x(r) be the first derivative of r**4/54 - 16*r**3/27 + 64*r**2/9 - 8*r + 23. Let q(f) be the first derivative of x(f). Factor q(v).
2*(v - 8)**2/9
Suppose -15 = -60*h + 55*h. Suppose 3*r + 11 = 3*o - 1, 3*o = -h*r - 12. Factor -4/7*u**3 + 2/7*u**2 + 0*u + 2/7*u**4 + o.
2*u**2*(u - 1)**2/7
Let w(f) = 6*f**2 + 1326*f - 37632. Let m(y) = -y**2 - 332*y + 9408. Let j(b) = 9*m(b) + 2*w(b). Suppose j(z) = 0. Calculate z.
56
Let x(c) = -c**4 + 14*c**3 - 37*c**2 + 44*c - 16. Let v(z) = z**3 - z**2 + z. Let d(p) = 12*v(p) - 3*x(p). Find n such that d(n) = 0.
1, 4
Let g(t) be the first derivative of -3*t**5/5 + 69*t**4/28 - 20*t**3/7 + 6*t**2/7 + 232. What is m in g(m) = 0?
0, 2/7, 1, 2
Let r = -2658 - -2663. Let j(f) be the third derivative of 11*f**2 + 0*f + 0 + 0*f**3 - 1/24*f**4 - 1/180*f**r. Let j(c) = 0. Calculate c.
-3, 0
Let q(m) be the second derivative of m**7/147 - 13*m**6/21 + 127*m**5/70 - 3*m**4/2 + 17*m + 20. Factor q(f).
2*f**2*(f - 63)*(f - 1)**2/7
Let j(b) be the second derivative of 0*b**4 + 0*b**2 + 0 + 3/20*b**5 - 1/2*b**3 + 8*b. Suppose j(o) = 0. What is o?
-1, 0, 1
Let y be (-11)/44 - (-34)/8. Factor 8 - 72 - 54*o - y*o**2 + 86*o.
-4*(o - 4)**2
Let m = -2/863 + 871/3452. Factor -1/4*v + 1/2*v**4 - 1/2*v**2 + m*v**5 + 0 + 0*v**3.
v*(v - 1)*(v + 1)**3/4
Let -656*g + 1706 - 11968 - 1058*g**2 - 16675 + 41 + 1054*g**2 = 0. Calculate g.
-82
Factor -3/7*v - 6/7*v**2 + 6/7 + 3/7*v**3.
3*(v - 2)*(v - 1)*(v + 1)/7
Let w(b) be the second derivative of b**9/45360 - b**7/7560 - b**4/4 - 3*b. Let a(c) be the third derivative of w(c). Factor a(f).
f**2*(f - 1)*(f + 1)/3
Let v(y) = 3*y**2 + 4*y - 2. Let r be v(-2). Suppose 151 - u - 2*u**r - u**3 - 151 = 0. What is u?
-1, 0
Suppose -7*v + 2*o + 8 = -3*v, -5*o = 3*v - 6. Let g(m) be the first derivative of -5 + 0*m - 1/2*m**4 - 2*m**3 - v*m**2. Solve g(d) = 0.
-2, -1, 0
Let t(q) be the first derivative of 1/3*q**6 - 1/4*q**4 + 0*q**2 + 1/5*q**5 + 0*q + 0*q**3 + 26. Solve t(w) = 0 for w.
-1, 0, 1/2
Let d(z) = -5*z**3 - 19*z**2 - 18*z + 1. Let v(i) = -4*i**3 - 19*i**2 - 17*i + 2. Let l(t) = 6*d(t) - 7*v(t). Let j be l(10). Factor -1/2*o**2 + j*o + 0.
-o*(o - 4)/2
Let z(a) = -23*a**3 - 22*a**2 - 6*a + 2. Let o(k) = -45*k**3 - 45*k**2 - 13*k + 5. Let r(n) = -6*o(n) + 15*z(n). What is c in r(c) = 0?
-2/5, 0
Let -60/11 - 20/11*c**3 - 83/11*c**2 - 124/11*c - 1/11*c**4 = 0. Calculate c.
-15, -2, -1
Let r = 302 + -300. Let z(t) be the third derivative of -1/180*t**6 + 0*t + 0*t**3 - 1/90*t**5 + 3*t**r + 1/18*t**4 + 0. Factor z(h).
-2*h*(h - 1)*(h + 2)/3
Let b(g) be the second derivative of 1/27*g**3 + 1/15*g**5 + 9*g + 1/189*g**7 + 0*g**2 - 2/27*g**4 - 4/135*g**6 + 0. Factor b(p).
2*p*(p - 1)**4/9
Factor -22 - 71874*o**3 - 621*o + 85*o - 256*o + 6 - 13068*o**2.
-2*(33*o + 2)**3
Let g(n) be the second derivative of -5*n + 1/48*n**4 + 0*n**3 + 1/80*n**5 + 0 + 0*n**2. Determine d, given that g(d) = 0.
-1, 0
Let u(h) = -h**3 + 17*h**2 - 15*h - 14. Let z be u(16). Determine p, given that 0*p**z - 9*p**3 + 7*p**3 - 4*p**2 = 0.
-2, 0
Let k(r) = 4*r**2 - 7*r. Let a(u) = -u**2 - u + 1. Let z(l) = -6*a(l) + 2*k(l). Determine c, given that z(c) = 0.
-3/7, 1
Let x be (-4 + 4 + 2)*(31 + 2). Let n = 68 - x. Factor 1/2*o - 1/2*o**n + 0.
-o*(o - 1)/2
Suppose 93*n - 91*n - 1076 = -267*n. Factor -n*l**3 - 32/5 + 16/5*l + 24/5*l**2 + 4/5*l**4.
4*(l - 2)**3*(l + 1)/5
Find c such that 0 - 5/4*c**2 - 5/4*c**3 + 5/2*c = 0.
-2, 0, 1
Solve 21*f + 11*f - 11*f + 4*f**2 - 183 + 3 + 27*f = 0.
-15, 3
Let r(a) be the second derivative of 5*a**7/42 + 16*a**6 + 768*a**5 + 40960*a**4/3 - 175*a. What is q in r(q) = 0?
-32, 0
Let g(z) be the second derivative of -3*z - 1/30*z**3 - 1/5*z**2 + 6 + 1/60*z**4. Suppose g(y) = 0. Calculate y.
-1, 2
Let p be 116/6 + 11/(-33). Factor p + 4*b**2 + 2*b**3 + 0*b**2 + 2*b - 19.
2*b*(b + 1)**2
Let r be (-4)/(-14) - 247/(-91). Suppose 0 = b + 5*i - 23, 16 = -0*i + 4*i. Factor -9*w + 5*w - 2*w**r - b*w**2 - 3*w**2.
-2*w*(w + 1)*(w + 2)
Let u = 68 + -60. Suppose -5*w - 12 = -u*w. Find m such that 1/5*m**2 + 0*m - 2/5*m**3 + 1/5*m**w + 0 = 0.
0, 1
Let r = -1/737 + 1483/6633. Find v such that 0 - 4/9*v**2 + 0*v**3 + r*v - 2/9*v**5 + 4/9*v**4 = 0.
-1, 0, 1
Let n = -2486/3 - -829. Let r(u) be the second derivative of 0 - 7/90*u**6 - 3/4*u**4 - n*u**2 + 23/60*u**5 - 11*u + 13/18*u**3. Factor r(y).
-(y - 1)**3*(7*y - 2)/3
Let b = 90 - 86. Find s, given that 3*s**3 + 9 - b*s**2 - 6*s**2 + s**2 - 3*s = 0.
-1, 1, 3
Let b(r) = 18*r + 39. Let f be b(-2). Let d = 3 + -1. Find t, given that d*t**2 + 2*t**2 - 8 - t - f*t + 0*t = 0.
-1, 2
Let x(q) be the first derivative of 2*q**5/25 - 3*q**4/10 - 14*q**3/15 + 27*q**2/5 - 36*q/5 - 278. Suppose x(h) = 0. What is h?
-3, 1, 2, 3
Let b(p) = -p**2 - 10*p + 3. Let y(v) = -9*v**2 + 2*v + 1. Let l be y(-1). Let w be b(l). Factor -g**4 + 2*g**3 - w*g**2 + 2*g**2 + g**2 - g**2.
-g**2*(g - 1)**2
Let z(w) be the third derivative of 20*w**2 - 17/114*w**6 - 5/399*w**7 + 0 - 31/57*w**4 + 0*w - 83/190*w**5 - 20/57*w**3. Determine x, given that z(x) = 0.
-5, -1, -2/5
Let j = -3851/7 + 551. Factor 3/7*s**3 + 15/7*s - j - 12/7*s**2.
3*(s - 2)*(s - 1)**2/7
Let v(f) be the third derivative of -f**7/840 + f**6/90 + f**5/24 - 2*f**3 - 16*f**2. Let t(n) be the first derivative of v(n). Factor t(a).
-a*(a - 5)*(a + 1)
Solve 2/3*g**2 + 0 - 2/3*g**4 + 0*g - 5/3*g**3 + 5/3*g**5 = 0 for g.
-1, 0, 2/5, 1
Find g such that -27/2 - 15/4*g + 1/4*g**2 = 0.
-3, 18
Find d such that -24*d**4 - 22*d**3 - 24*d + 6*d - 9*d - 3*d**5 - 44*d**3 - 72*d**2 = 0.
-3, -1, 0
Let z(x) be the second derivative of -x**7/21 - x**6/10 + x**4/12 - 5*x + 3. Let z(r) = 0. What is r?
-1, 0, 1/2
Let 16/17 - 52/17*t - 14/17*t**2 = 0. Calculate t.
-4, 2/7
Let y(c) = -c**3 + 4*c**2 + 5*c - 10. Let d be y(4). Find n, given that -10*n**4 + 5*n**5 + n**5 + d*n**2 + 2*n - n**5 - 7*n = 0.
-1, 0, 1
Suppose 0*u**3 - 1/2*u**4 - 25*u + 27/2*u**2 + 12 = 0. Calculate u.
-6, 1, 4
Let d = -13571 + 122141/9. Factor -10/9*m**2 - d - 4/3*m.
-2*(m + 1)*(5*m + 1)/9
Let c(g) = g - 25. Let t be c(28). Find o such that -7*o**2 + 42*o**3 - o**2 - 48*o**t + 8*o + 0*o**2 = 0.
-2, 0, 2/3
Let s be (10 - (-2690)/(-270))/(1/3). Let f = 33/4 - 293/36. Determine i, given that -s*i**2 + f + 0*i = 0.
-1, 1
Suppose -3*y + 2*p - 5 = -25, -5*y - 5*p = 0. Let g be (-1 - (-3)/4)*-18 - y. Determine v so that v + g*v**2 + 1/2 = 0.
-1
Factor -25*q**2 + 3*q**2 - 8*q**2 - 21*q**3 - 9*q.
-3*q*(q + 1)*(7*q + 3)
Let s = -381 - -382. Let r(z) be the first derivative of 1/6*z**3 - 3/4*z**2 + s + z. Factor r(a).
(a - 2)*(a - 1)/2
Let d(j) = j + 0*j - 140 - j**3 + 139. Let b(n) = 7*n**3 - n**2 - 10*n + 10. Let t(m) = -b(m) - 6*d(m). Factor t(r).
-(r - 2)*(r - 1)*(r + 2)
Let j(i) be the first derivative of 8*i**5/5 + 23*i**4/2 - 140*i**3/3 + 16*i**2 + 279. Solve j(x) = 0.
-8, 0, 1/4, 2
Let k = -10932 - -10935. Find h, given that -6 + 99/2*h**k - 30*h + 51/2*h**2 = 0.
-1, -2/11, 2/3
Let d(s) = 2*s**3 - 8*s**2 + 7*s - 7. Let g(i) = 173*i**3 - 2*i + 16*i**2 - 11*i - 177*i**3 + 15. Let q(b) = 7*d(b) + 3*g(b). Factor q(y).
2*(y - 2)*(y - 1)**2
Suppose 0 = 3*p - 5*p + 6. Determine f, given that -2/11*f**5 + 0*f**4 + 0*f**2 + 0 + 4/11*f**p - 2/11*f = 0.
-1, 0, 1
Let w be ((-3)/(-27))/((-16)/(-48)). Let x(n) be the first derivative of 0*n + 1 + 1/9*n**3 + w*n**2. Find j such that x(j) = 0.
-2, 0
Let v be (6/9)/(9/(253 + -10)). Factor 162/5*d**4 + 0 + v*d**3 + 8/5*d - 64/5*d**2.
2*d*(d + 1)*(9*d - 2)**2/5
Let u(x) be the second derivative of x**6/1260 - x**4/21 - 7*x**3/6 + 9*x. Let g(z) be the second derivative of u(z). Suppose g(r) = 0. What is r?
-2, 2
Let h(p) be the third derivative of -p**6/1200 + 9*p**4/80 - 9*p**3/10 + 3*p**2 + 35*p. Find j, given that h(j) = 0.
-6, 3
Let t = 75 - 70. Factor -5*q**4 - 10 - 10*q**3 - t*q**2 - 17 + 27.
-5*q**2*(q + 1)**2
Let i(z) = 3*z**2 + 6*z. Let q(x) = -x. Let r(v) = 2*v + 13. Let p be r(-7). Let k(j) = p*i(j) + 15*q(j). Solve k(m) = 0 for m.
-7, 0
Let o(d) be the third derivative of -d**6/420 + d**5/210 + 4*d**4/21 - 16*d**3/21 - 134*d**2. Factor o(f).
-2*(f - 4)*(f - 1)*(f + 4)/7
Suppose -6 - 6 = -2*x + 4*k, -2*x + 2*k + 8 = 0. Factor -50 + 50 + 3*r + 35*r**4 - 31*r**3 + r - 8*r**x.
r*(r - 1)*(5*r + 2)*(7