
Let r = 28441/180 + -158. Let t(j) be the second derivative of -2*j + r*j**6 + 0*j**2 + 1/40*j**5 + 1/36*j**3 + 0 + 1/24*j**4. Let t(g) = 0. Calculate g.
-1, 0
Factor -250 + 347 + 190*t - 496 - 1406 - 29*t**2 + 24*t**2.
-5*(t - 19)**2
Let v(j) be the second derivative of 2*j**6/45 + 7*j**5/15 + 2*j**4 + 40*j**3/9 + 16*j**2/3 - 4*j. Find m, given that v(m) = 0.
-2, -1
Let l(b) be the first derivative of -b**4/2 - 46*b**3/3 + b**2 + 46*b - 279. Let l(z) = 0. What is z?
-23, -1, 1
Let y = -1480 - -1482. Let u(o) be the first derivative of 8 + o**2 + y*o**3 - 1/2*o**4 - 2/5*o**5 - 4*o. Solve u(d) = 0 for d.
-2, -1, 1
Suppose -45*t - 36*t = 0. Factor t - 2/3*f**3 + 0*f - 2/3*f**2.
-2*f**2*(f + 1)/3
Let z be 3 + -2 + (-30)/3. Let v be (-45)/z + -2 + -1. Let -v*i**2 - 4*i**3 + 4*i**3 + 7*i**3 + 2 - 7*i = 0. Calculate i.
-1, 2/7, 1
Suppose 83*d - 78*d = -4*l - 32, 5*l - 42 = 4*d. Factor -4/9*i - 2/9*i**l + 2/3.
-2*(i - 1)*(i + 3)/9
Let y(k) = 7*k**3 - k**2 + 7*k. Let s = -12 - -23. Suppose s = 4*d - 1. Let a(j) = -4*j**3 + j**2 - 4*j. Let h(r) = d*y(r) + 5*a(r). Factor h(i).
i*(i + 1)**2
Let c = -1274 + 2551/2. Factor -9/2*x + c*x**2 - 15.
3*(x - 5)*(x + 2)/2
Factor 42 - 34*a**4 + 16 + 166 + 352*a - 6*a**5 + 5*a**5 - 32*a**3 - 5*a**5 + 144*a**2.
-2*(a + 2)**4*(3*a - 7)
Let u be (8/28)/(8181/(-1701) + 10/2). What is p in 9/2 + u*p**2 + 6*p = 0?
-3, -1
Suppose b + k = 7, 0 = -2*b + 5*k - 3 + 31. Suppose 3*r = b - 0. What is z in -3*z**3 + 3*z + 0*z**3 + 0*z**r = 0?
-1, 0, 1
Let g be (-56)/960*3/(-14). Let p(m) be the second derivative of 0*m**3 + 0*m**6 + 2*m - 1/168*m**7 + 0*m**4 + g*m**5 + 0 + 0*m**2. Find i such that p(i) = 0.
-1, 0, 1
Let t(h) be the first derivative of -3*h**5/140 - h**4/14 - h**3/14 - 15*h + 8. Let a(v) be the first derivative of t(v). Factor a(r).
-3*r*(r + 1)**2/7
Suppose b = -3*o - 1, -149*b + 153*b - 9 = o. Factor 1/2*i + 0 - 1/4*i**b.
-i*(i - 2)/4
Factor 2*r**4 - 5/2*r + 1/2*r**5 + 2*r**3 - r**2 - 1.
(r - 1)*(r + 1)**3*(r + 2)/2
Let a(t) = -4*t**5 - 8*t**4 - 18*t**3 + 8*t**2 + 16*t + 6. Let h(w) = w**5 - w**3 - 2*w**2 + w + 1. Let n(i) = a(i) + 6*h(i). Let n(x) = 0. Calculate x.
-1, 1, 6
Let k(z) be the third derivative of z**6/12 + z**5/15 - 23*z**2. Factor k(o).
2*o**2*(5*o + 2)
Let i(s) be the third derivative of s**8/6720 - 11*s**3/6 + 6*s**2. Let y(x) be the first derivative of i(x). Determine v, given that y(v) = 0.
0
Let b be 8/3 + 5/15. Suppose -4*a + 3 = -4*l + 11, -4*a - 4 = -b*l. Solve -2/3 + 8/3*y - a*y**2 = 0 for y.
1/3, 1
Let k be (6/7)/(2/7). Factor -7*x**2 + 2 + 3*x**2 + k*x**2 + 3*x**2 - 4*x.
2*(x - 1)**2
Let g(v) be the third derivative of v**5/110 - v**4/66 + 98*v**2. Factor g(b).
2*b*(3*b - 2)/11
Let a(l) = 2*l**4 + 2*l**2 - l + 1. Let h(o) = -9*o**4 + 9*o**3 + 5*o**2 + 12*o - 5. Let u(g) = -20*a(g) - 4*h(g). Solve u(t) = 0 for t.
-7, -1, 0
Let b(u) be the first derivative of u**7/1120 - u**6/480 - u**5/160 + u**4/32 + u**3 - 9. Let p(g) be the third derivative of b(g). Factor p(m).
3*(m - 1)**2*(m + 1)/4
Factor -1044/11*q**3 - 2/11*q**5 + 6804/11*q**2 + 13122/11 + 74/11*q**4 - 18954/11*q.
-2*(q - 9)**4*(q - 1)/11
Suppose -n = -0*n - 5*x - 27, 8 = -n - 2*x. Solve -36 + 55*h + 8*h - 4*h**n + 21*h - 28*h**3 - 8*h**4 - 8*h**3 = 0 for h.
-3, 1/2, 1
Suppose -176 - 315*h - 435*h + 636 - 180*h + 5*h**2 + 465*h = 0. Calculate h.
1, 92
Let c(z) be the second derivative of 23*z**4/24 - 25*z**3/12 + z**2/2 + 13*z + 2. Factor c(o).
(o - 1)*(23*o - 2)/2
Let h(k) = -k**2 + 5*k - 2. Suppose 0 = -2*r + 2, -2*y + 11 = 3*r - 0*r. Let n be h(y). Factor 2 - 4*d**2 + 0 + 4*d**n + 2*d**2 + 4*d.
2*(d + 1)**2
Let r be (-86)/18 - (-36 - -31). Let c(z) be the second derivative of 0*z**2 + 0 - 3*z - 1/3*z**4 + 1/5*z**5 + r*z**3 - 2/45*z**6. Factor c(a).
-4*a*(a - 1)**3/3
Let x = -2603 + 23431/9. What is l in -4/9*l + x*l**2 + 4/9*l**3 - 4/9 = 0?
-1, 1
Let l(p) be the first derivative of 0*p**3 - 1/6*p**4 + 2*p**2 + 0*p - 7 + 4/15*p**5. Let v(u) be the second derivative of l(u). What is i in v(i) = 0?
0, 1/4
Suppose -51/8*t - 15/4 - 3*t**2 - 3/8*t**3 = 0. What is t?
-5, -2, -1
Let t(f) = f**3 + f**2 - 3*f + 3. Suppose 4*r = x - 2*x, -3*x = 4*r + 8. Let p be t(r). Solve 0*i**3 - 1/3*i**4 + 0*i + 0*i**p + 0 = 0 for i.
0
Factor 0 - 3/4*p**2 + 9/8*p**3 - 3/8*p**4 + 0*p.
-3*p**2*(p - 2)*(p - 1)/8
Let k be ((-2)/((-28)/6))/(3/189*9). Let -8/5*w**2 - 8/5*w + 16/5*w**k - 8/5*w**5 + 4/5*w**4 + 4/5 = 0. What is w?
-1, 1/2, 1
Find i such that 160*i - 710*i**2 - 17 - 125*i**5 + 2143*i**3 - 800*i**4 - 3528*i**3 + 177 = 0.
-4, -1, -4/5, 2/5
Suppose 3*a = -a - 5*k + 22, -a = -2*k - 12. Factor 2*n**5 + 13*n**4 - 15*n**4 - 5*n**3 + 16*n + a + n**2 - 5*n**3 + n**2.
2*(n - 2)**2*(n + 1)**3
Solve -16*m + 120/7*m**3 - 36/7*m**4 - 4/7*m**2 + 48/7 = 0 for m.
-1, 2/3, 3
Let g(k) be the second derivative of 13*k**6/30 - 16*k**5/25 - k**4/60 - k - 146. Determine o so that g(o) = 0.
-1/65, 0, 1
Let j = 152 - 148. Let i(d) be the second derivative of -1/168*d**7 + 3*d - 1/24*d**j + 0*d**6 + 3/80*d**5 + 0*d**2 + 0*d**3 + 0. Factor i(k).
-k**2*(k - 1)**2*(k + 2)/4
Let r(i) be the second derivative of -2/63*i**7 + 2/45*i**6 + 1/3*i**5 + 0 - 8/9*i**3 - 2*i - 5/9*i**4 + 8/3*i**2. Solve r(w) = 0.
-2, -1, 1, 2
Factor 361*c - 25*c - 128 - 4*c**3 - 424*c**5 + 428*c**5 + 36*c**4 - 244*c**2.
4*(c - 1)**3*(c + 4)*(c + 8)
Suppose 0 = 4*d + 18 + 14. Let w(u) = u**3 + 7*u**2 - 6*u + 18. Let l be w(d). Factor 0 - 3/5*k**l + 0*k.
-3*k**2/5
Factor 4/5*a**2 + 312/5*a + 6084/5.
4*(a + 39)**2/5
Let w(l) be the first derivative of l**3/3 - l**2/2 - 2*l - 302. Factor w(u).
(u - 2)*(u + 1)
Let a(b) = 2*b**2 + 27*b - 8. Suppose -29*n + 27*n - 28 = 0. Let k be a(n). Find t such that 2/3*t**2 + k - 4*t = 0.
3
Let l(w) be the first derivative of 3 + 4/5*w**5 - 2/7*w**6 + w**4 + 16/7*w - 16/7*w**2 - 20/7*w**3. What is t in l(t) = 0?
-1, 1/3, 2
Suppose -203*b**3 + 120*b - 149*b**3 + 4302*b**3 - 4865*b**4 - 437*b**5 + 1662*b**5 - 1180*b**2 = 0. What is b?
0, 2/7, 2/5, 3
What is b in -5*b - 331 + 163 - 67*b + 156 - 33*b**2 = 0?
-2, -2/11
Factor 4*b**4 + 3838*b**3 - 3661*b**3 - b**4 - 180*b**2.
3*b**2*(b - 1)*(b + 60)
Determine b so that -104/5 + 2/5*b**2 - 102/5*b = 0.
-1, 52
Let z(o) be the second derivative of -o**6/50 - 3*o**5/25 - 3*o**4/10 - 2*o**3/5 - 3*o**2/10 - 421*o. Solve z(a) = 0 for a.
-1
Let z(o) = -2*o**4 + o**3 - o**2 + o + 1. Let u(a) = -2*a**5 + 12*a**4 - 6*a**2 - 2*a - 2. Let v(x) = u(x) + 2*z(x). Let v(k) = 0. Calculate k.
-1, 0, 1, 4
Let o(n) be the first derivative of n**6/120 + n**5/20 + n**4/12 - 9*n**2 - 14. Let g(y) be the second derivative of o(y). Factor g(f).
f*(f + 1)*(f + 2)
Factor -9*b + 27/5 - 3/5*b**3 + 21/5*b**2.
-3*(b - 3)**2*(b - 1)/5
Let j(t) be the second derivative of -5*t**7/42 + 11*t**6/6 - 9*t**5/2 - 5*t**4/6 + 95*t**3/6 - 45*t**2/2 + 225*t - 2. Solve j(u) = 0 for u.
-1, 1, 9
Let n = -28 + 80. Let b = n + -36. Solve 64/3*w - 4/3*w**3 + 16/3 + b*w**2 - 13/3*w**4 - w**5 = 0 for w.
-2, -1/3, 2
Let z(g) = -6*g**3 + 2*g + 5*g**2 - g**3 + 4 + 1. Let v(c) = -6*c**3 + 4*c**2 + 2*c + 4. Let f(h) = -5*v(h) + 4*z(h). Factor f(p).
2*p*(p - 1)*(p + 1)
Suppose -5*b + 5 = -20. Let j(o) be the third derivative of 6*o**2 + 0 - 1/48*o**4 + 0*o - 1/120*o**b + 0*o**3. Factor j(i).
-i*(i + 1)/2
Suppose q - 27 - 5 = 0. Find l, given that -2*l**2 + 32 - q = 0.
0
Let r(m) = 6*m**2 - 31*m - 37. Let y(v) = v**2 + 58*v + 39. Let f(u) = -14*u - 10. Let i(s) = -9*f(s) - 2*y(s). Let a(n) = 17*i(n) + 6*r(n). Factor a(g).
2*(g - 9)*(g + 1)
Let j(y) be the third derivative of 13*y**8/630 - 3*y**7/35 - 113*y**6/900 + 43*y**5/150 + 61*y**4/180 + 2*y**3/15 - 174*y**2. Solve j(o) = 0 for o.
-1, -1/4, -2/13, 1, 3
Solve 0*x**2 + 0 + 48/17*x**3 + 2/17*x**5 + 28/17*x**4 + 0*x = 0 for x.
-12, -2, 0
Let u(d) be the third derivative of 0 - 2/105*d**7 + 1/15*d**5 - 28*d**2 - 1/40*d**6 - 1/336*d**8 + 0*d**3 + 1/6*d**4 + 0*d. Determine n so that u(n) = 0.
-2, -1, 0, 1
Let d(n) = -n**2 + n + 156. Let q be d(-12). Let l(b) be the second derivative of 0 + 0*b**3 + 0*b**2 - 5*b + q*b**4 - 3/40*b**5 - 1/40*b**6. Factor l(w).
-3*w**3*(w + 2)/4
Solve 56*a**3 - 132 + 9200*a + 128*a**2 - 4603*a - 4653*a + 4*a**4 = 0 for a.
-11, -3, -1, 1
Factor 56/3*l - 20 - 11/3*l**2 - 1/3*l**3.
-(l - 2)**2*(l + 15)