)/3
Let z be 5 + 3 - 3/(-6)*-6. Let i(y) be the first derivative of -1/2*y**6 + 0*y**z + 0*y**3 - 3/2*y**2 + 3/2*y**4 + 0*y + 4. Let i(k) = 0. What is k?
-1, 0, 1
Let r(z) be the second derivative of z**4/4 + z**3/3 + z**2/2 + z. Let w be r(-1). Factor w*j**4 + 2*j**2 - 4*j**4 - 29 + 29.
-2*j**2*(j - 1)*(j + 1)
Let y(f) be the second derivative of 7*f + 0*f**4 + 2*f**2 + 0 + 1/3*f**3 - 1/30*f**5. Let i(v) be the first derivative of y(v). Factor i(r).
-2*(r - 1)*(r + 1)
Factor -772/9*s + 40/3 - 52/9*s**2.
-4*(s + 15)*(13*s - 2)/9
Let a(m) be the second derivative of -6*m + 0 - 1/3*m**3 + 1/210*m**5 + 0*m**4 - 1/1260*m**6 + 0*m**2. Let c(t) be the second derivative of a(t). Factor c(h).
-2*h*(h - 2)/7
Determine q so that -2/11*q**4 + 400/11 - 156/11*q**2 + 38/11*q**3 - 280/11*q = 0.
-2, 1, 10
Let z be (-2)/(1 - -5)*-15. Suppose 0 = z*p - 4*p - 2. What is y in 4*y - y + 8*y**p - 8 - 7*y + 4*y**3 = 0?
-2, -1, 1
Suppose 0 = n - 3*d + 4, -n - 3*d + 4*d = 0. Determine q, given that -92/5*q**n + 126/5*q**4 + 18*q**3 + 16/5 - 8*q = 0.
-1, -2/3, 2/7, 2/3
Let u be (4 - 1) + -1 + 2. Suppose 2*k + u*v = 14, 4*k + k = v + 46. Solve -k*d**3 - 9*d**3 - 16 + 20*d**3 + 3*d**2 + d**2 - 8*d = 0 for d.
-2, 2
Let p be ((-4)/7)/(12/(-112)) + -4. Let z(s) = s**2 + 8*s. Let b be z(-8). Factor b - p*l**4 + 4/3*l**2 + 0*l + 2*l**3.
-2*l**2*(l - 2)*(2*l + 1)/3
What is y in 44652/5 + 147*y**2 + 45384/5*y + 3/5*y**3 = 0?
-122, -1
Let n(s) be the first derivative of 9 - 1/90*s**6 - 8/3*s**3 + 0*s - 1/60*s**5 + 0*s**2 - 1/96*s**4. Let k(v) be the third derivative of n(v). Solve k(r) = 0.
-1/4
Let r(l) be the second derivative of -l**5/5 + 11*l**4/12 - 5*l**3/6 - l**2 - 51*l + 2. Determine v, given that r(v) = 0.
-1/4, 1, 2
Let d(n) be the second derivative of -n**6/135 + n**5/18 - 20*n**3/27 + 16*n**2/9 - 7*n + 7. What is s in d(s) = 0?
-2, 1, 2, 4
Let x(u) be the third derivative of -u**7/4620 + u**6/495 - u**5/220 + 11*u**3/3 - 26*u**2. Let p(m) be the first derivative of x(m). Factor p(t).
-2*t*(t - 3)*(t - 1)/11
Let b(z) = -24*z**4 + 114*z**3 - 15*z**2 - 54*z - 15. Let n(x) = -x**4 + x**3 - 2*x**2 - x + 1. Let j(d) = b(d) + 3*n(d). Solve j(f) = 0.
-1/3, 1, 4
Let u(j) be the third derivative of -30*j**2 + 0*j**5 - 1/6*j**4 + 0 + 0*j**3 + 0*j + 1/120*j**6. Factor u(x).
x*(x - 2)*(x + 2)
Let x(t) = 3*t**3 - 4*t**2 - 2*t. Let d be (-6)/4*10/(-5)*-1. Let u(f) = f**3 - f**2 - f. Let g(k) = d*x(k) + 6*u(k). Factor g(b).
-3*b**2*(b - 2)
Let s(u) be the third derivative of -u**6/600 + 7*u**5/300 + u**4/120 - 7*u**3/30 - u**2 - 3*u. Factor s(c).
-(c - 7)*(c - 1)*(c + 1)/5
Let v(z) = 3*z**3 + 26*z**2 + 194*z + 516. Let d(l) = 4*l**3 + 27*l**2 + 195*l + 518. Let u(i) = -2*d(i) + 3*v(i). Suppose u(b) = 0. What is b?
-8
Let x(u) be the second derivative of 2*u**6/15 + 3*u**5/5 - 16*u**4/3 + 8*u**3 - 192*u - 2. Factor x(b).
4*b*(b - 2)*(b - 1)*(b + 6)
Let x(k) = -2*k**2 + 10*k + 12. Let m be x(6). Let d(t) be the third derivative of -1/20*t**5 - 4*t**2 + 1/2*t**4 + m*t - 2*t**3 + 0. Factor d(y).
-3*(y - 2)**2
Let d be (-3)/(-13) + (-3384)/(-9165). Factor -d*a**3 + 1/5*a**4 + 0 + 3/5*a**2 - 1/5*a.
a*(a - 1)**3/5
Let k(l) = -8*l**2 + 12*l + 4. Let o(i) = -7*i**2 + 12*i + 3. Let s(q) = -3*k(q) + 4*o(q). Solve s(u) = 0 for u.
0, 3
Let b(w) be the third derivative of -w**7/1050 - w**6/600 - 116*w**2. Factor b(g).
-g**3*(g + 1)/5
Let a be (949/(-182) - 4/14) + 6. Factor -p**2 - 1/4*p**3 - 5/4*p - a.
-(p + 1)**2*(p + 2)/4
Factor 6*r + 16/5 - 4/5*r**2.
-2*(r - 8)*(2*r + 1)/5
Let s = 79 - 51. What is f in 48 - s*f - 50*f - 2*f + 12*f**2 = 0?
2/3, 6
Let m = 4/43 - -3/430. Let v(a) be the third derivative of m*a**5 - 4*a**2 + 0*a**3 + 0 + 0*a - 1/8*a**4 - 1/40*a**6. Solve v(x) = 0 for x.
0, 1
Let s(v) be the second derivative of -v**8/6720 - v**7/840 + v**5/30 + 5*v**4/4 - 52*v. Let z(k) be the third derivative of s(k). Factor z(g).
-(g - 1)*(g + 2)**2
Let o(y) be the third derivative of y**11/776160 - y**9/141120 + 17*y**5/60 - 9*y**2. Let v(n) be the third derivative of o(n). Determine t so that v(t) = 0.
-1, 0, 1
Factor -18*o - 4*o**2 + 32*o + 24*o - o**2 + 7*o.
-5*o*(o - 9)
Suppose 3*w - 33 = 4*n - 3*n, -5*n = -4*w + 165. Let m be ((-55)/n)/((9/3)/9). Factor -4/5*f**2 + 4/5*f**4 - 2/5*f**m + 2/5*f + 0*f**3 + 0.
-2*f*(f - 1)**3*(f + 1)/5
Let f(k) = k**5 + 13*k**4 + 23*k**3 + 11*k**2. Let v(r) = 8*r**5 + 92*r**4 + 160*r**3 + 76*r**2. Let i(c) = -44*f(c) + 6*v(c). Solve i(g) = 0.
-1, 0, 7
Suppose 297/2*a + 1089/2 + 1/6*a**3 - 21/2*a**2 = 0. What is a?
-3, 33
Let a(t) be the third derivative of -2*t**5/105 + 25*t**4/168 - t**3/14 - 5*t**2 + t. Let a(u) = 0. Calculate u.
1/8, 3
Let i be 23 - -10*1/(-2). Let m be 0 + -1 - (-24)/i. Factor 0*a + 0 + m*a**3 - 1/3*a**2.
a**2*(a - 1)/3
Let o = -1 + 10. Let a be 4 + o/3 - 3. Factor 2*v**5 - 3*v**5 + a*v**5 - 2*v**5 - 3*v**3 - v**4 + 2*v + v**2.
v*(v - 2)*(v - 1)*(v + 1)**2
Let p be (-70)/(-28)*(-1)/(2/136). Let n = -677/4 - p. Let n*z**3 + 0 - 3/2*z - 3/4*z**2 = 0. What is z?
-1, 0, 2
Let s = 331 + -515. Let u be 26/16 + (-69)/s. Factor 3/5*h**3 + 2/5*h + 0 + 7/5*h**u.
h*(h + 2)*(3*h + 1)/5
Let h(r) be the second derivative of 11*r**6/600 + r**5/15 + 7*r**4/120 - r**3/15 + 2*r**2 + 20*r. Let o(l) be the first derivative of h(l). Factor o(q).
(q + 1)**2*(11*q - 2)/5
Let x(w) = -w**2 + 10*w - 22. Let y be x(5). Suppose 2 = 2*z - 3*a, 5*z + 2*a + y*a = 30. Factor 3/5*c**z + 6/5*c**3 + 0*c**2 - 3/5 - 6/5*c.
3*(c - 1)*(c + 1)**3/5
Suppose -q = 4*q - 10. Factor -3*u**4 + 3*u**2 + 32*u**3 + 0*u**q - 29*u**3 - 3*u**5.
-3*u**2*(u - 1)*(u + 1)**2
Let k(j) be the first derivative of 2*j**5/5 - 4*j**3/3 + 2*j - 20. Factor k(v).
2*(v - 1)**2*(v + 1)**2
Let d be ((-24)/(-32))/((-180)/98). Let x = -3/40 - d. Let 1/6*a - x*a**2 + 1/6*a**3 + 0 = 0. What is a?
0, 1
Let y(l) be the third derivative of l**7/42 - 11*l**6/12 - 6*l**5 - 185*l**4/12 - 125*l**3/6 - 77*l**2. Factor y(x).
5*(x - 25)*(x + 1)**3
Let n be (364/(-5733))/(2/(-7)). Factor -4/9 + 2/9*y - n*y**3 + 4/9*y**2.
-2*(y - 2)*(y - 1)*(y + 1)/9
Let q(r) = r**3 + 9*r**2 - r - 5. Let j be q(-9). Let l(h) = -3*h**2 + 9*h + 4. Let k(u) = -4*u**2 + 10*u + 4. Let d(n) = j*k(n) - 5*l(n). Factor d(a).
-(a + 1)*(a + 4)
Let k(r) be the second derivative of r**8/2520 - r**7/315 + r**6/180 - 7*r**3 - 10*r - 3. Let o(t) be the second derivative of k(t). Factor o(q).
2*q**2*(q - 3)*(q - 1)/3
Let i be (-12)/(180/3) - (-8)/15. Factor 1/2*v - i + 1/6*v**5 + 0*v**4 + 1/3*v**2 - 2/3*v**3.
(v - 1)**3*(v + 1)*(v + 2)/6
Let h(n) be the third derivative of -n**9/3780 + n**8/420 - n**7/210 - n**4/12 - 2*n**2. Let z(y) be the second derivative of h(y). Factor z(d).
-4*d**2*(d - 3)*(d - 1)
Let v be (2/(-20)*5/50)/(-1). Let u(y) be the third derivative of 0*y + y**2 - 1/75*y**5 + 0*y**4 - v*y**6 + 0*y**3 + 0. Factor u(p).
-2*p**2*(3*p + 2)/5
Suppose 3*u = -2*p + 6, -5*u + 17 - 39 = -2*p. Suppose -j = j - p. Solve -12*t**2 - 8*t - t**3 + 5*t**3 - 8*t**j = 0.
-2, -1, 0
Let h = 28 + -25. Solve 3*i**h - 5*i + 2*i - 25*i**2 + 50*i**2 - 31*i**2 + 6 = 0.
-1, 1, 2
Let u = -19/34 + 193/102. Solve -u - 2/3*d + 2/3*d**2 = 0 for d.
-1, 2
Let s(l) = -11*l**3 - 7*l**2 + 5*l - 5. Let x(c) = -5*c**3 - 4*c**2 + 2*c - 2. Let v(j) = 2*s(j) - 5*x(j). Let v(r) = 0. Calculate r.
-2, 0
Suppose 4*s - 12 = 0, x + x - 5*s + 15 = 0. Suppose 0*i + x*i = -i. What is a in 0 + 0*a**2 + 2/7*a**5 + i*a - 2/7*a**4 - 4/7*a**3 = 0?
-1, 0, 2
Let g(f) be the second derivative of 65*f**7/42 - 20*f**6/3 + 21*f**5/2 - 20*f**4/3 + 5*f**3/6 + 541*f. Suppose g(z) = 0. What is z?
0, 1/13, 1
Determine o so that 0 + 12769/5*o**2 + 226/5*o**3 + 1/5*o**4 + 0*o = 0.
-113, 0
Suppose 8 = -d - 2*s, -3 = 5*d + 4*s + 19. Let l(m) = m**2 - 2*m. Let p(k) = -2*k**2 + 3*k. Let y(v) = d*p(v) - 3*l(v). Let y(i) = 0. Calculate i.
0
Suppose -5 = 2*b + 2*f - 61, -3*f = 2*b - 57. Factor 20*m**3 - 9*m**2 + 4*m**4 - 25*m - 3*m**2 + 40 - b*m.
4*(m - 1)**2*(m + 2)*(m + 5)
Let g(o) be the second derivative of -o**7/98 + o**6/7 - 57*o**5/70 + 17*o**4/7 - 57*o**3/14 + 27*o**2/7 + 69*o - 2. Suppose g(k) = 0. Calculate k.
1, 2, 3
Let o(f) be the third derivative of -f**5/60 - 5*f**4/12 + 4*f**3 - 24*f**2 - 2*f. Factor o(c).
-(c - 2)*(c + 12)
Let n = 6/47 - -23/188. Let o(b) be the first derivative of 0*b + 8