et o(g) be the first derivative of 0*g**4 + 0*g**2 + 4/21*g**3 - 2/35*g**5 - 6 - 2/7*g. Factor o(b).
-2*(b - 1)**2*(b + 1)**2/7
Suppose 3*j - z = -5 + 15, -j = 3*z. Let m be 18/75*(-120)/(-48). Suppose 0 + 3/5*g**j + 0*g**2 - m*g = 0. Calculate g.
-1, 0, 1
Let g(p) be the first derivative of 4*p**3/3 + 4*p**2 - 222. Find f such that g(f) = 0.
-2, 0
Let m(x) be the second derivative of x**6/255 - x**5/85 - x**4/102 + 2*x**3/51 - 38*x. Factor m(z).
2*z*(z - 2)*(z - 1)*(z + 1)/17
Let f(a) = a**3 + 3*a**2 + a + 2. Let g be f(-2). Suppose 3*l = -3*b + 15, -g*l + 11 = -4*b + 5*b. Suppose 0 - 1/6*z - 1/6*z**l = 0. Calculate z.
-1, 0
Let c(v) be the third derivative of 0 + 1/24*v**4 + 0*v + 16*v**2 - 1/120*v**6 - 1/60*v**5 + 1/6*v**3. Let c(w) = 0. Calculate w.
-1, 1
Let p = -18607 + 93038/5. Solve 12/5*g**4 - 12/5*g**3 + 3*g - 6/5 - p*g**5 - 6/5*g**2 = 0 for g.
-1, 1, 2
Determine m, given that 16/5*m**2 + 24/5 + 38/5*m + 2/5*m**3 = 0.
-4, -3, -1
Let d(x) be the second derivative of -x**6/30 + 3*x**5/10 - 2*x**4/3 - x**3 + 9*x**2/2 + 84*x + 1. Factor d(v).
-(v - 3)**2*(v - 1)*(v + 1)
Let u(w) be the third derivative of w**5/48 + 11*w**4/8 + 13*w**3/6 - 844*w**2. Factor u(q).
(q + 26)*(5*q + 2)/4
Let c(h) be the second derivative of -h**6/75 - 3*h**5/50 - h**4/15 - 19*h - 9. Factor c(g).
-2*g**2*(g + 1)*(g + 2)/5
Let y(u) be the first derivative of -2/9*u**3 + 1/3*u**4 + 0*u**2 - 3 + 0*u. Factor y(o).
2*o**2*(2*o - 1)/3
Let m(y) be the second derivative of -y**4/4 - 9*y**3/2 + 5*y - 5. Find z, given that m(z) = 0.
-9, 0
Let 4*c + 4 - 2*c**3 - 72*c**4 + 146*c**4 - 73*c**4 - 3*c**2 = 0. Calculate c.
-1, 2
Factor 35*z - 5*z**3 - 2 + 294*z**2 + 17 + 5 - 284*z**2.
-5*(z - 4)*(z + 1)**2
Factor -16*d**2 - 6*d - 55*d**4 + 78*d**4 - 38*d**4 - 11*d**2 - 36*d**3.
-3*d*(d + 1)**2*(5*d + 2)
Let t(u) be the first derivative of -4*u**5/5 + 38*u**4 - 1108*u**3/3 - 3192*u**2 - 7056*u + 195. Factor t(j).
-4*(j - 21)**2*(j + 2)**2
Let l(v) = v**4 + v**3 - v**2 + 2*v + 1. Let f(y) = -5*y**4 - 33*y**3 + 9*y**2 + 80*y - 63. Let i(m) = f(m) + 3*l(m). Factor i(k).
-2*(k - 1)**2*(k + 2)*(k + 15)
Let k(a) be the third derivative of a**8/13440 + a**7/5040 - a**6/1440 - a**5/240 - a**4/24 - 7*a**2. Let z(v) be the second derivative of k(v). Factor z(h).
(h - 1)*(h + 1)**2/2
Suppose -399*w + 392*w = -14. Let o(p) be the first derivative of 1/4*p**4 + 5 + 5/2*p**2 + 4/3*p**3 + w*p. Factor o(c).
(c + 1)**2*(c + 2)
Let h(g) = g**2 + 27*g - 83. Let n be h(-30). Let k be 0 + n + -9 + 6. Factor -32/3*q + 16*q**2 + 4/3*q**k - 8*q**3 + 0.
4*q*(q - 2)**3/3
Let x(w) = 57*w**2 - 9*w - 60. Let c(h) = -56*h**2 + 6*h + 60. Let j(g) = 6*c(g) + 5*x(g). Determine o, given that j(o) = 0.
-20/17, 1
Let n be (-28)/(-8) - 5/(-10). Let v be (4 - 3) + -1 + n. Factor 0 - 68/7*k**2 + 160/7*k**3 + 8/7*k - 64/7*k**v.
-4*k*(k - 2)*(4*k - 1)**2/7
Let l be (-2)/(2 + (-12)/((-4 - 4)/(-8))). Solve 0*g + 0 - l*g**4 - 1/5*g**5 + 2/5*g**3 + 0*g**2 = 0.
-2, 0, 1
Let u be 0 + 26 + -9 + 7. Suppose 4*z + 28 = 2*v, -2*z - u - 6 = -5*v. Suppose 14*i**3 - 4*i + 5*i - 18*i**2 + 7*i - v*i = 0. What is i?
0, 2/7, 1
Let y(j) be the second derivative of j**4/9 + 17*j**3/18 + 2*j**2/3 + 92*j. Solve y(z) = 0.
-4, -1/4
Factor -16*p + 132 + 4*p**2 - 2*p**2 + 4*p**3 - 2*p**4 - 124 + 4*p**2 + 0*p**3.
-2*(p - 2)*(p - 1)**2*(p + 2)
Let x be 4 - ((3 - 6) + 3). Let y(p) be the second derivative of 0*p**2 + 0*p**3 + 3/20*p**5 - 1/6*p**x + 0 + 1/6*p**6 - 3*p. Factor y(w).
w**2*(w + 1)*(5*w - 2)
Suppose -830*y**2 + 196*y**5 + 3220*y**4 + 3992*y**3 + 480*y - 340*y**2 - 1918*y**2 = 0. Calculate y.
-15, -2, 0, 2/7
Let p(i) be the third derivative of i**7/210 + i**6/45 - 2*i**5/15 - 4*i**4/3 - 19*i**3/6 - 3*i**2. Let v(d) be the first derivative of p(d). Factor v(g).
4*(g - 2)*(g + 2)**2
Let l(m) be the third derivative of m**5/120 - 5*m**4/12 + 18*m**2 - 8*m. Let l(z) = 0. Calculate z.
0, 20
Let h(j) be the first derivative of -3/4*j**2 - 1/8*j**3 - 3/2*j - 2. Find r, given that h(r) = 0.
-2
Let q(p) = p + 9. Let i be q(-6). Suppose 2*a + 13 = i*b + 3, 3*a + 8 = b. Solve -37*x + 4*x**2 + 35*x - b*x**3 + 0*x**3 = 0.
0, 1
Suppose 4*u + 3 + 12 = -5*g, 15 = -5*g. Let j(k) be the third derivative of -2/3*k**3 + 2/15*k**5 - 5/12*k**4 + 1/20*k**6 + 3*k**2 + u*k + 0. Factor j(c).
2*(c - 1)*(c + 2)*(3*c + 1)
Let v(q) be the second derivative of -q**7/70 + q**6/25 + 3*q**5/100 - q**4/10 - 223*q. Suppose v(s) = 0. What is s?
-1, 0, 1, 2
Suppose 494*d + 86/3*d**2 - 14*d**3 + 1352/3 + 2/3*d**4 = 0. What is d?
-4, -1, 13
Let u(y) be the second derivative of -y**4/114 + 8*y**3/57 - 12*y**2/19 + 15*y + 9. Factor u(l).
-2*(l - 6)*(l - 2)/19
Let x be 0/((12/3)/2). Let k be (62 + -59)*(0 + 1). Factor 2/5*h**2 + 1/5*h**k + 0 + x*h.
h**2*(h + 2)/5
Let s(d) be the second derivative of -10*d**6/3 - 12*d**5 + 18*d**4 + 56*d**3/3 + 6*d**2 - 410*d. Suppose s(o) = 0. What is o?
-3, -1/5, 1
Let c(o) be the second derivative of 5*o**4/12 - 25*o**3/2 + 65*o**2 - 7*o - 12. Find u such that c(u) = 0.
2, 13
Let m(j) = -j**2 - j - 1. Let t(x) = 5*x**2 + 2*x + 1. Let p(y) = -4*m(y) - t(y). Determine f so that p(f) = 0.
-1, 3
Let n(c) = c**2 - 6*c + 1. Let z be n(4). Let o = z + 9. Determine v, given that -o*v + 2*v - v + 2*v**3 + 2*v**5 - 3*v**5 = 0.
-1, 0, 1
Suppose -4*r - 3*q = -259 - 363, -2*r + 312 = q. Suppose r - 169 = -2*c. Factor -4*b - c*b**2 - 8/3*b**3 - 2/3.
-2*(b + 1)**2*(4*b + 1)/3
Let g = 169 + -313. Let x = 433/3 + g. Suppose -1/3*b**5 - 4/3 - 4/3*b + 5/3*b**2 + 5/3*b**3 - x*b**4 = 0. What is b?
-2, -1, 1, 2
Let v be (6*15/270)/((-5)/(-6)). Factor v*x**3 + 0 + 14/15*x**5 + 0*x - 8/5*x**4 + 4/15*x**2.
2*x**2*(x - 1)**2*(7*x + 2)/15
Let g(i) be the second derivative of -i**7/168 - i**6/120 + i**5/80 + i**4/48 - 4*i + 18. Factor g(d).
-d**2*(d - 1)*(d + 1)**2/4
Suppose 0 = -i + 10 - 5. Suppose -3*c = -10*y + 5*y + 51, i*y + 3*c - 39 = 0. Factor -f - 4*f**2 + 7*f + 3*f**2 - y.
-(f - 3)**2
Let l(x) be the third derivative of 11*x**7/70 - x**6/24 - 2*x**5/5 - x**4/6 - 5*x**2 + 2*x. Let l(r) = 0. What is r?
-2/3, -2/11, 0, 1
Let w(h) = -66*h**4 - 144*h**3 + 195*h**2 + 90*h - 129. Let l(f) = -5*f**4 - 11*f**3 + 15*f**2 + 7*f - 10. Let a(d) = 27*l(d) - 2*w(d). Solve a(k) = 0 for k.
-4, -1, 1
Determine d, given that -10*d**2 - 14*d - 72 + 89*d - 10*d**2 + 17*d**2 = 0.
1, 24
Factor 4/9*u + 2/9*u**3 - 10/9*u**2 + 16/9.
2*(u - 4)*(u - 2)*(u + 1)/9
Let 10/3*f - 16/3 - 1/3*f**2 = 0. Calculate f.
2, 8
Let q(p) = 190*p**3 - 945*p**2 + 1080*p + 2215. Let s(c) = -7*c**3 + 35*c**2 - 40*c - 82. Let r(x) = 2*q(x) + 55*s(x). Factor r(w).
-5*(w - 4)**2*(w + 1)
Let c(n) be the first derivative of -n**3 + 12*n**2 + 57. Suppose c(i) = 0. What is i?
0, 8
Let x(n) be the first derivative of -3 + 1/40*n**4 - 3/100*n**5 + 3*n**2 - 1/50*n**6 + 0*n + 0*n**3. Let a(u) be the second derivative of x(u). Factor a(w).
-3*w*(w + 1)*(4*w - 1)/5
Let i(d) be the third derivative of -d**9/3780 - d**8/5040 + d**7/945 + 19*d**4/24 + 6*d**2. Let b(v) be the second derivative of i(v). Factor b(r).
-4*r**2*(r + 1)*(3*r - 2)/3
Let d(c) be the second derivative of c**6/225 - 16*c**5/75 + 143*c**4/45 - 32*c**3/3 + 15*c**2 - 20*c. Find w, given that d(w) = 0.
1, 15
Let s(k) be the third derivative of 0*k + 0 + 3/40*k**6 + 1/4*k**4 - 7/20*k**5 + 13*k**2 + 0*k**3. Factor s(j).
3*j*(j - 2)*(3*j - 1)
Let p(t) be the first derivative of 14/45*t**5 + 0*t + 44 - 14/27*t**3 - 2/9*t**2 - 4/27*t**6 + 1/3*t**4. Determine y so that p(y) = 0.
-1, -1/4, 0, 1, 2
Let p(r) be the third derivative of 23*r**7/105 - 67*r**6/60 + 4*r**5/3 + r**4/3 + 2*r**2 + 2*r. Let p(u) = 0. Calculate u.
-2/23, 0, 1, 2
Let v(m) = m + 20. Let y be v(-18). What is o in -15 - 4*o - 51*o + 0*o**y + 20*o**2 = 0?
-1/4, 3
Suppose 61 + 29 = 45*y. Factor 0 + s - 1/3*s**y.
-s*(s - 3)/3
Let f(s) be the second derivative of 1/50*s**5 + 0 + 0*s**4 + 0*s**3 - 3*s + 0*s**2. Factor f(p).
2*p**3/5
Let k(r) = 3*r - 21. Let w = -28 - -36. Let m be k(w). Find o such that -1/4*o**5 + 1/2*o**m + 0*o**4 + 0 - 1/4*o + 0*o**2 = 0.
-1, 0, 1
Let y = -1120 + 1120. Let z(c) be the third derivative of -10*c**2 - 1/12*c**4 - 2/3*c**3 + 0 + 1/30*c**5 + y*c. Factor z(p).
2*(p - 2)*(p + 1)
Let t be (19 + -13)*(1 + 0). Factor -t*d - 5*d**2 + 16*d - 25 + d + 19*d.
-5*(d - 5)*(d 