65*j = -96*j. Factor j + 8/17*v + 2/17*v**2.
2*v*(v + 4)/17
Let o = 0 - -15. Suppose -o = 9*t - 14*t. Factor 0*p + 2/7*p**t + 4/7*p**2 + 0.
2*p**2*(p + 2)/7
Let o(d) be the second derivative of d**6/10 + 19*d**5/40 + 25*d**4/36 + 17*d**3/36 + d**2/6 - 82*d. Solve o(m) = 0.
-2, -1/2, -1/3
Let j(y) be the third derivative of 2*y**2 - 1/35*y**5 + 2/21*y**3 + 0*y**4 - 1/105*y**6 + 0 + 0*y. Factor j(z).
-4*(z + 1)**2*(2*z - 1)/7
Let c(y) be the second derivative of y**5/4 - 25*y**4/3 - 215*y**3/6 - 55*y**2 - 3*y - 1. Factor c(f).
5*(f - 22)*(f + 1)**2
Let h(p) be the third derivative of p**6/120 + p**5/12 - p**4/6 - 10*p**3/3 - 108*p**2. Determine w, given that h(w) = 0.
-5, -2, 2
Factor 2/15*g**2 + 56/15*g + 392/15.
2*(g + 14)**2/15
Let w(r) be the second derivative of 1/80*r**5 - 1/12*r**3 - 1/40*r**6 + 0*r**2 - 3*r + 1/16*r**4 + 0 + 1/168*r**7. Factor w(u).
u*(u - 2)*(u - 1)**2*(u + 1)/4
What is n in 3/2*n - 5/6*n**4 + 0 + 3/2*n**2 - 13/6*n**3 = 0?
-3, -3/5, 0, 1
Factor -12 + 16/3*s + 1/3*s**2.
(s - 2)*(s + 18)/3
Suppose -47/2*t - 63/2 - 1/2*t**3 + 15/2*t**2 = 0. What is t?
-1, 7, 9
Let l be 6*(3 + (-3 - -1)). Suppose -3*t = 3, t = 4*s - t - 10. Let l*g**4 + 61*g**4 - 13*g**3 - 19*g**3 - 3*g**4 + 4*g**s = 0. Calculate g.
0, 1/4
Let m(i) be the first derivative of -i**3 + 3*i**2/2 + 36*i + 79. Let m(l) = 0. Calculate l.
-3, 4
Let q(u) = -10*u**2 - 77*u. Let w(o) = -3*o**2 - 26*o. Let m(d) = -4*q(d) + 14*w(d). Find c such that m(c) = 0.
-28, 0
Let z(f) = -68*f - 946. Let h be z(-14). Suppose 3/2*i + 9/2*i**2 - h = 0. Calculate i.
-4/3, 1
Let o = -2879/5 + 31689/55. Factor 0*w**2 + 0*w + 1/11*w**3 - o*w**5 + 0 - 3/11*w**4.
-w**3*(w + 1)*(4*w - 1)/11
Let f(r) be the third derivative of 0*r + 1/10*r**5 - 8*r**3 + 0 - 7/4*r**4 - 8*r**2. Let x(v) = v**2 - 6*v - 7. Let j(w) = 4*f(w) - 27*x(w). Factor j(c).
-3*(c + 1)**2
Let y be (-8)/56*2*(-14)/120. Let m(l) be the third derivative of 0*l - 1/24*l**4 + 0*l**3 + y*l**5 - 9*l**2 - 1/120*l**6 + 0. Factor m(x).
-x*(x - 1)**2
Determine t, given that 10*t**3 + 25*t**3 - 36*t**3 = 0.
0
Suppose -3*f = -6*f + 6. Suppose f = 3*q - 4. Factor 6*p - 3*p**q + 6*p**2 - 2*p**3 - p**3.
-3*p*(p - 2)*(p + 1)
Let a(m) be the first derivative of m**2 + 3*m + 7/9*m**3 + 5/18*m**4 + 3 + 1/30*m**5. Let o(r) be the first derivative of a(r). Factor o(v).
2*(v + 1)**2*(v + 3)/3
Find r, given that -68*r**2 + 50*r**2 + 115 + 110*r + 13*r**2 = 0.
-1, 23
Let m(j) be the first derivative of j**4 + 16*j**3/3 - 56*j**2 + 128*j + 311. Factor m(d).
4*(d - 2)**2*(d + 8)
Suppose 0 = 2*u - a - 175 + 177, 5*u = 5*a - 20. Factor 0*h**u + 0*h + 0 + 2/11*h**3 - 1/11*h**4.
-h**3*(h - 2)/11
Let t(j) be the third derivative of -6*j**2 - 1/420*j**7 + 1/240*j**6 + 0 - 1/48*j**4 + 1/120*j**5 + 0*j**3 + 0*j. Factor t(x).
-x*(x - 1)**2*(x + 1)/2
Let y(s) = -2*s**3 + 14*s**2 + 36*s - 14. Let d(m) = -m**2 - 2*m + 1. Let h(b) = 28*d(b) + 2*y(b). Factor h(r).
-4*r*(r - 2)*(r + 2)
Let x be (-4)/(-5)*(-2 - -7). Suppose 5*t - 2 = x*t. Factor 6 + b**2 - b - 2*b + 3*b**3 - 7*b**2 + 0*b**t.
3*(b - 2)*(b - 1)*(b + 1)
Let q(i) = -9*i**3 - 2*i**2 - 2*i - 1. Let g be q(-1). Let p be (-3 - (-76)/28)/(g/(-12)). Factor p*f + 3/7*f**4 - 3/7*f**3 - 3/7*f**2 + 0.
3*f*(f - 1)**2*(f + 1)/7
Let i(p) be the first derivative of -p**7/7980 - p**6/3420 + 8*p**3/3 - 1. Let j(u) be the third derivative of i(u). Suppose j(q) = 0. What is q?
-1, 0
Let b(w) be the second derivative of w**4/24 + 59*w**3/3 + 3481*w**2 + 40*w - 1. Factor b(s).
(s + 118)**2/2
Let o(g) = g. Let t be o(4). What is p in -4*p**4 - 12*p**3 + 0*p**4 - 29*p**2 - t*p + 17*p**2 = 0?
-1, 0
Let y be (-24 - -30) + -4*(-12)/(-8). Factor y + 1/3*s**3 + 0*s - 2/3*s**2.
s**2*(s - 2)/3
Suppose 12*b - 14*b + 14 = 0. Factor p**3 + b*p**2 - 2*p**2 - 3*p**2.
p**2*(p + 2)
Let 0 + 2/13*o**3 + 4/13*o + 6/13*o**2 = 0. Calculate o.
-2, -1, 0
Suppose -11*f = -7*f. Suppose f = 5*c - 5*r - 115, 3*c + c - 88 = 5*r. Factor -14*g**3 + 5*g**3 - 2*g**2 + 3*g**4 - 3*g**3 + 36*g + c - 4*g**2.
3*(g - 3)**2*(g + 1)**2
Let f(g) be the second derivative of -g**6/345 + 47*g**5/115 + 2*g - 428. Let f(s) = 0. What is s?
0, 94
Let t(i) be the third derivative of i**5/240 - i**4/16 - i**2 + 6. Factor t(d).
d*(d - 6)/4
Suppose 2*c - 3*b + 1 = -0*c, 0 = -2*c - b + 19. Let m be ((105/(-10))/c)/((-6)/8). Factor -1/3*h**m + h - 2/3.
-(h - 2)*(h - 1)/3
Let d(z) be the second derivative of z**7/63 - 4*z**6/45 + z**5/5 - 2*z**4/9 + z**3/9 - 13*z. Factor d(j).
2*j*(j - 1)**4/3
Let z = 1784/55 + -304/11. Let w(p) be the second derivative of z*p**2 - 4/5*p**3 + 7*p + 0 + 1/20*p**4. Find v, given that w(v) = 0.
4
Let x(b) be the third derivative of -b**6/480 - b**5/48 + b**4/12 + 2*b**3 + 310*b**2. Factor x(r).
-(r - 3)*(r + 4)**2/4
Determine k, given that 0 + 6*k**3 + 0*k - 3/2*k**2 - 21/8*k**4 = 0.
0, 2/7, 2
Let r(p) be the first derivative of -p**6/2 + 3*p**5/5 + 6*p**4 - 12*p**3 + 62. Let r(s) = 0. Calculate s.
-3, 0, 2
Let v(a) = 2*a**3 + 46*a**2 - 3*a**3 + a - 69*a**2 + 33*a**2 - 4. Let r be v(10). Factor -1 - 9/2*h - r*h**2 - 5/2*h**3.
-(h + 1)**2*(5*h + 2)/2
Let d(m) be the first derivative of 2*m**3/3 - 18*m**2 + 162*m + 67. Let d(a) = 0. Calculate a.
9
Let -5/2*n**2 - 2*n - 1/2*n**3 + 0 = 0. What is n?
-4, -1, 0
Suppose 3304 = -8*m + 3336. Let u(y) be the first derivative of -1/4*y**m - y**3 + 5 - 3/2*y**2 - y. Factor u(x).
-(x + 1)**3
Let b(p) = -15*p**3 + 27*p**2 - 27*p + 15. Let g(f) = -7*f**3 + 13*f**2 - 13*f + 7. Let h(q) = -4*b(q) + 9*g(q). Factor h(y).
-3*(y - 1)**3
Let n(a) be the first derivative of 8*a**4/9 + 14*a**3/3 + 44*a**2/9 - 2*a/3 - 580. Factor n(d).
2*(d + 1)*(d + 3)*(16*d - 1)/9
Suppose 42 = -2*p + 5*p + 33. Factor -30*k**p + 56/5*k + 16/5 - 4*k**2.
-2*(3*k - 2)*(5*k + 2)**2/5
Factor -1083/4*p - 363/2 + 9/4*p**2.
3*(p - 121)*(3*p + 2)/4
Let a = 1141 - 1136. Let p(c) be the third derivative of -1/50*c**a + 2*c**2 - 1/300*c**6 + 0*c**3 + 0*c + 0 + 0*c**4. Factor p(m).
-2*m**2*(m + 3)/5
Factor -3/5*d**2 + 9/5 + 6/5*d.
-3*(d - 3)*(d + 1)/5
Suppose 0 = -0*t - 3*t + 6. Suppose 12*i - 12*i**2 - 4*i + t*i**3 + 12*i**4 - 10*i**3 = 0. What is i?
-1, 0, 2/3, 1
Let o(z) be the third derivative of 3*z**7/56 + 163*z**6/480 + 89*z**5/120 + 17*z**4/24 + z**3/3 - 204*z**2. Determine j so that o(j) = 0.
-2, -1, -2/5, -2/9
Let x(f) be the second derivative of -27*f**5/20 + 31*f**4/2 - 638*f**3/9 + 484*f**2/3 - 3*f + 143. Solve x(i) = 0.
2, 22/9
Let p(s) = -s**3 - 3*s**2 + 3*s - 3. Let q be p(-4). Let w(f) = f**2 - 5 + 20 + 8*f - 6. Let k(y) = y. Let o(v) = q*w(v) - 2*k(v). Solve o(i) = 0.
-3
Let d(j) = -18*j**3 + 98*j**2 - 111*j + 25. Let b(c) = c**3 - c**2 + 2*c. Let y(p) = -3*b(p) - d(p). Factor y(o).
5*(o - 5)*(o - 1)*(3*o - 1)
Let f(i) = i**2 - 3*i + 8. Let q be f(7). Let l = -414 - -438. Suppose -3/2*n**4 - q*n + 9*n**3 - l - 3/2*n**2 = 0. What is n?
-1, 4
Suppose -3 = -3*n - 3*x, 3*n + 0*x - 17 = 4*x. Let u(h) be the first derivative of 0*h**n - 2 + 2/15*h**5 - 1/3*h**4 + 0*h**2 + 0*h. Find g such that u(g) = 0.
0, 2
Solve -3/5*s**3 - 36/5*s + 0 - 39/5*s**2 = 0.
-12, -1, 0
Let v(r) be the second derivative of -11*r**4/96 - 13*r**3/24 - r**2/2 - 2*r + 208. Suppose v(w) = 0. What is w?
-2, -4/11
Let o(q) be the third derivative of 1/210*q**5 - 7*q**2 - 1/280*q**6 + 0*q**4 + 0*q**3 + 0*q + 0 + 1/2352*q**8 + 0*q**7. Let o(r) = 0. Calculate r.
-2, 0, 1
Suppose 5*f + 24 = b, b - 14*f = -11*f + 16. Let z(l) be the second derivative of 2/13*l**2 + 0 + 1/39*l**3 - 1/78*l**b + l. Determine o so that z(o) = 0.
-1, 2
Let m(v) be the first derivative of -v**5/15 - 11*v**4/12 - 14*v**3/3 - 32*v**2/3 - 32*v/3 + 192. Factor m(q).
-(q + 1)*(q + 2)*(q + 4)**2/3
Let g be (7/27)/((-70)/(-60)). Determine m, given that 2/9 - 4/9*m + g*m**2 = 0.
1
Solve 23/5*p**2 + p**3 + 12/5 + 32/5*p = 0 for p.
-2, -3/5
Let k(w) be the first derivative of -w**4/18 - 2*w**3/27 + w**2/9 + 2*w/9 + 667. Factor k(f).
-2*(f - 1)*(f + 1)**2/9
Let f(q) = 3*q**3 - 2*q**2 + q. Let n be f(1). Let a = n - -1. Find b, given that 6*b**2 - 2*b**2 + 2*b**2 - a*b**3 = 0.
0, 2
Let n(b) be the first derivative of 3*b**5/100 - 3*b**4/20 + 20*b - 3. Let o(u) be the first derivative of n(u). Find w such that o(w) = 0.
0, 3
Determine w, given that -507*w**4 + 5*w**2 + w**5 - 9*w**3 + 255*w**4 + 251*