 Factor -16/7*c - 32/7 - g*c**2.
-2*(c + 4)**2/7
Let r(u) = u**4 + u**3 + 2*u**2 + u + 1. Let n(h) = -4*h**4 - 30*h**3 + 59*h**2 - 72*h + 17. Let c(w) = 2*n(w) + 10*r(w). Find g such that c(g) = 0.
1, 22
Let v(c) be the third derivative of -c**7/8 + 2*c**6/9 - c**5/6 + c**4 - 6*c**2. Let r(n) be the second derivative of v(n). Suppose r(t) = 0. Calculate t.
2/9, 2/7
Let s = -32 + 29. Let y be 25/20 - s/3. What is r in -7/4*r**2 - y + 15/4*r + 1/4*r**3 = 0?
1, 3
Find a, given that -1/3*a**3 - 2/3*a**2 + 0 - 1/3*a = 0.
-1, 0
Let t(f) = -5*f**4 + 53*f**3 + 96*f**2 + 13*f - 25. Let j(y) = -2*y**4 - y**3 + 3*y**2 + y - 1. Let a(x) = 5*j(x) - t(x). Factor a(r).
-(r + 1)**2*(r + 10)*(5*r - 2)
Factor 40*c**3 + 78*c**2 - 4*c**2 + 44*c**4 - 42*c**4 + 36*c.
2*c*(c + 1)**2*(c + 18)
Let l(u) = 8*u**2 - 4*u. Let c(t) = t**2. Let a = -10 - -4. Let p(y) = a*c(y) + l(y). Determine i so that p(i) = 0.
0, 2
Let r(j) = j + 1. Let b(a) be the first derivative of 4*a**3/3 - 2*a**2 - 8*a + 19. Let y(m) = b(m) + 4*r(m). Factor y(f).
4*(f - 1)*(f + 1)
Let m(k) = -14*k**3 + 8*k**2 + 13*k - 4. Let d(l) = -2*l**3 - l**2. Let g(c) = -20*d(c) + 4*m(c). Factor g(t).
-4*(t - 4)*(t + 1)*(4*t - 1)
Factor 2/11*t**2 - 12/11 - 2/11*t.
2*(t - 3)*(t + 2)/11
Let y be -3 - 1 - (-7 + -1). Let p(h) be the third derivative of -10*h**2 + 0 + 0*h + 1/120*h**5 + 0*h**3 + 0*h**y. Solve p(g) = 0 for g.
0
Suppose 15 - 25*u**2 + 3*u**3 + 43*u**2 + 3 + 33*u = 0. What is u?
-3, -2, -1
Let m(z) be the first derivative of -5*z**4/14 + 4*z**3/21 + 5*z**2/7 - 4*z/7 + 222. Find k such that m(k) = 0.
-1, 2/5, 1
Let f(d) = 5*d**2 - 83*d + 246. Let p(g) = -55*g**2 + 915*g - 2705. Let l(t) = -65*f(t) - 6*p(t). Suppose l(o) = 0. Calculate o.
3, 16
Suppose -4*w + 0*w = -8. Let k(j) = -3*j**w - 25*j - 12 - 10*j**2 + 9*j. Let y(x) = -3*x**2 - 4*x - 3. Let g(b) = -4*k(b) + 18*y(b). Factor g(d).
-2*(d + 1)*(d + 3)
Let w(c) = -c**2 + 7*c - 3. Let f be w(6). Factor -3*n**4 - f*n**4 + n**3 + 4*n**4 + n**5.
n**3*(n - 1)**2
Factor -2*o**2 + 4/3*o**3 - 2/9*o**4 + 0*o + 0.
-2*o**2*(o - 3)**2/9
Let f(b) be the third derivative of b**7/42 - b**6/4 + 11*b**5/12 - 5*b**4/4 + 22*b**2 - 2. Solve f(i) = 0 for i.
0, 1, 2, 3
Factor -40*b - 2*b**2 + 8982 - 9026 + 14*b.
-2*(b + 2)*(b + 11)
Let z be 217/(-14) - -17 - 2/(-4). Let 1/9*u - 1/9*u**3 - 1/9*u**z + 0 + 1/9*u**4 = 0. Calculate u.
-1, 0, 1
Factor -9/8*m - 15/4 + 3/8*m**2.
3*(m - 5)*(m + 2)/8
Suppose -3*h + 5 = -4. Let r(x) = -4*x**2 + 3*x - h*x - 1 + 0*x. Let f(l) = -l**2. Let o(t) = 5*f(t) - r(t). Factor o(j).
-(j - 1)*(j + 1)
Let i = -26443/336 - 15/112. Let v = 79 + i. Factor 8/3 + v*k**2 - 4/3*k.
(k - 4)**2/6
Factor 0*j - 5/3*j**3 + 5/3*j**2 + 0.
-5*j**2*(j - 1)/3
Let j(m) be the third derivative of -1/6*m**4 - 1/3*m**5 + 0*m + 11/120*m**6 + 12*m**2 + 0*m**3 + 0. Factor j(t).
t*(t - 2)*(11*t + 2)
Let m(w) be the first derivative of w**5/160 + 5*w**4/96 + 7*w**3/48 + 3*w**2/16 + 14*w + 2. Let s(i) be the first derivative of m(i). Factor s(p).
(p + 1)**2*(p + 3)/8
Let g(s) be the second derivative of -s**5/120 - s**4/18 - s**3/12 - 761*s. Find j such that g(j) = 0.
-3, -1, 0
Suppose -3*k - t - 2*t = -21, 0 = -5*t + 20. Factor -3*h**k + 4*h**2 + 2*h**2 - 3*h**4 + 23 - 23.
-3*h**2*(h - 1)*(h + 2)
Let m(o) be the second derivative of 5*o**4/12 + 35*o**3/6 + 30*o**2 + 105*o. Suppose m(x) = 0. What is x?
-4, -3
Let r(i) be the third derivative of i**6/240 + 7*i**5/120 - i**4/6 - 118*i**2. Suppose r(w) = 0. Calculate w.
-8, 0, 1
Let u(n) be the second derivative of -2/9*n**3 - 5/18*n**4 + 0 - 1/15*n**5 + 3*n + 0*n**2. Find x, given that u(x) = 0.
-2, -1/2, 0
Let z(r) = 3*r**3 + 4*r**2 + 3*r + 2. Let i be (-1 + 4/12)*3. Let x(m) = -m**2 + 1. Let o(k) = i*x(k) + z(k). Factor o(l).
3*l*(l + 1)**2
Suppose 3*c - 114 = -4*b, 0 = -3*c - 2*b - 0*b + 120. Find i such that -14*i - i**4 + c*i**3 - 3*i**4 - 4 + 8*i**2 - 14*i**3 - 14*i**5 = 0.
-1, -2/7, 1
Let h(x) = 70*x**3 - x**2 + 2*x - 1. Let g be h(1). Suppose 7*a - g = 3*a - 2*b, 5*b - 22 = -a. Find u, given that 16 + 47*u + 20*u**2 + 18*u - a*u = 0.
-2, -2/5
Suppose -2*k + a + 16 = 0, -6*k + 3*a + 32 = -2*k. Let -k*l**2 + 2*l**2 - 2*l + 2*l**2 - 2*l = 0. What is l?
-1, 0
Let p(j) be the second derivative of -j**6/6 + 27*j**5/4 - 125*j**4/12 - 45*j**3/2 + 65*j**2 - 12*j + 12. Find d, given that p(d) = 0.
-1, 1, 26
Let r(y) be the first derivative of y**3/5 + 9*y**2/5 - 21*y/5 - 173. What is j in r(j) = 0?
-7, 1
Let y(v) = -6*v**2 - 3*v + 9. Let s(d) = 7*d**2 + 3*d - 9. Let t(p) = -6*s(p) - 5*y(p). Let a(b) = -b**2 + 1. Let x(r) = -44*a(r) + 4*t(r). Factor x(n).
-4*(n + 1)*(n + 2)
Let v(a) = 3*a + 30. Let q be v(-9). Let 35*k**4 - 90*k**2 - 2*k**5 - 79*k**3 - 3*k**5 + 135 + 135*k + 29*k**q = 0. What is k?
-1, 3
Determine k so that 130*k - 2*k**4 + 382*k - 64*k**3 - 23*k**3 + 25*k**3 + 448*k**2 + 4*k**4 = 0.
-1, 0, 16
Let g(k) = -k**3 - 20*k**2 - 35*k + 20. Let s be -15 - ((-1)/3 - (-100)/30). Let i be g(s). Factor 0*d**3 + 0 + 0*d - 2/11*d**4 + 0*d**i.
-2*d**4/11
Let j(k) = 24*k**2 - 672*k - 2266. Let t(v) = -3*v**2 + 84*v + 283. Let c(s) = -2*j(s) - 17*t(s). Determine m so that c(m) = 0.
-3, 31
Let z be (105/(-450))/((-7)/4). Determine b so that -2/15*b - 4/15*b**2 - z*b**3 + 0 = 0.
-1, 0
Let y be (128/(-48))/(254/6 - 2). Let c = 670/847 - y. Factor 8/7*f + 2/7*f**2 + c.
2*(f + 1)*(f + 3)/7
Factor 42*w**3 - 78*w**2 - 17 + 4*w**5 + 2 - 3*w**4 + 57*w - 7*w**5.
-3*(w - 1)**4*(w + 5)
Let f(y) be the second derivative of 0*y**2 - 1/50*y**5 - 1/30*y**4 - 4*y + 2/15*y**3 + 0. Factor f(x).
-2*x*(x - 1)*(x + 2)/5
Let h be (35/40)/(120/(-16) + 11). Suppose -h*i**3 + 5/4*i**2 - i + 0 = 0. What is i?
0, 1, 4
Let k(t) be the first derivative of 32*t**2 - 28/3*t**3 + t**4 - 48*t - 10. Let k(u) = 0. What is u?
2, 3
Let w(q) = q**2 - 19*q - 23. Let o be w(23). Find f such that -o + 57 + 12*f - 3*f**2 + 0*f**2 = 0.
2
Suppose 444*g - 6*g**2 + 32*g + 10*g**2 = 0. Calculate g.
-119, 0
Let n(z) = -4*z**4 - 5*z**3 + 6*z**2 - 4*z - 11. Let g(f) = -f**4 - 2*f**3 - 1. Let i(s) = 6*g(s) - 2*n(s). Find q, given that i(q) = 0.
-2, -1, 2
Let l be (8/(-14))/(72/14 + -6). Let g(u) be the first derivative of 4*u - l*u**3 - u**2 - 3. Find c such that g(c) = 0.
-2, 1
Let c(j) be the second derivative of -j**5/80 - j**4/48 + 5*j**3/24 - 3*j**2/8 - 9*j. Solve c(n) = 0 for n.
-3, 1
Let d = -832 - -837. Let l**2 - 1/2 - l**d - 4*l**3 + 7/2*l**4 + l = 0. What is l?
-1/2, 1
Let y = 110/49 + -439/392. Determine l so that y*l - 3/4*l**2 + 1/8*l**3 - 1/2 = 0.
1, 4
Let o(s) be the second derivative of -1/12*s**4 + 0*s**2 - 15*s + 0 + 1/6*s**3. Let o(h) = 0. Calculate h.
0, 1
Let u(g) = -4*g**5 + 24*g**4 + 28*g**3 - 2*g - 1. Let v(j) = -j**5 + j**3 - 2*j - 1. Let o(p) = -u(p) + v(p). Factor o(a).
3*a**3*(a - 9)*(a + 1)
Let a(t) be the first derivative of t**4/2 - 8*t**3/3 + 3*t**2 + 112. Factor a(y).
2*y*(y - 3)*(y - 1)
Suppose 45*z**4 + 412*z + 78*z**2 + 888*z - 10*z**3 - 640 + 362*z**2 - 1445*z**3 = 0. Calculate z.
-1, 2/3, 32
Suppose -9 = -o - 0. Let t be 1/(-3) + 20/6. Factor -9*f**2 - 6*f**2 + 6*f**4 - 3*f + o*f**2 + t*f**5.
3*f*(f - 1)*(f + 1)**3
Suppose z - 5*a = -2*z - 14, 4*a = 2*z + 12. Solve -2*c**z - 12 + 11 + 3 = 0.
-1, 1
Let o(v) be the third derivative of -v**7/3360 + v**5/160 - v**4/48 + 4*v**3/3 - 5*v**2. Let h(t) be the first derivative of o(t). Factor h(g).
-(g - 1)**2*(g + 2)/4
Let f(a) = a**3 - a**2 + a - 1. Let w be 18/4*(1 - -1). Let r = w + -8. Let o(m) = 4*m**3 - 6*m**2 + 6*m - 4. Let c(h) = r*o(h) - 3*f(h). Solve c(z) = 0 for z.
1
Let p(x) be the first derivative of x**5/160 - x**4/64 - 3*x**3/8 - 11*x**2/2 + 39. Let g(u) be the second derivative of p(u). Factor g(k).
3*(k - 3)*(k + 2)/8
Let t(s) = -4*s**5 - s**4 + 7*s**3 - 5*s**2 - 3*s. Let l(u) = -5*u**5 - u**4 + 6*u**3 - 4*u**2 - 4*u. Let c(h) = 3*l(h) - 4*t(h). Suppose c(z) = 0. What is z?
-4, 0, 1, 2
Let z(c) be the second derivative of -3*c + 6*c**2 + 5/96*c**6 - 5/12*c**3 + 1/6*c**5 + 5/96*c**4 + 0. Let l(b) be the first derivative of z(b). Factor l(a).
5*(a + 1)**2*(5*a - 2)/4
Let b = 216 + -214. Suppose -1/8*q**b + 0 + 1/4*q = 0. What is q?
0, 2
Factor 2/7*h**2 - 38/7*h + 68/7.
2*(h - 17)*(h - 2)/7
Factor -12*k**3 + 0*k**2 - 20*k**2 + 2*k**4 - k**3 + 7*k**3.
2*k**2*(k - 5)*(k + 2)
Suppose