 0?
2
Let w(a) be the first derivative of -a**4/2 + 14*a**3/3 - 6*a**2 + 138. Factor w(h).
-2*h*(h - 6)*(h - 1)
Let r be (-7 + 58/8)/(-5*(-4)/160). Solve 4/5*i**r + 0 + 8/5*i**4 - 2*i**3 - 2/5*i**5 + 0*i = 0 for i.
0, 1, 2
Let h(y) = -6*y + 49. Let q be h(8). Suppose -7*u + 1 = q. Factor -2*m**3 + 0*m - 4/3*m**2 - 2/3*m**4 + u.
-2*m**2*(m + 1)*(m + 2)/3
Factor 0*q - 1/8 + 1/8*q**2.
(q - 1)*(q + 1)/8
Let v(g) be the third derivative of 0 - 242/3*g**3 - 2*g**2 + 19*g - 1/15*g**5 + 11/3*g**4. Suppose v(p) = 0. What is p?
11
Factor 2*z**4 + 34*z - 17*z - 3*z**4 + 3*z**3 - 20*z + 2 - z**2.
-(z - 2)*(z - 1)**2*(z + 1)
Let v(s) be the second derivative of -s**5/20 - 2*s**4/3 - 2*s**3 - 2*s + 14. Suppose v(w) = 0. What is w?
-6, -2, 0
Let j(y) = y**3 - 2*y**2 + 5*y - 5. Suppose 12*i = 9*i + 6. Let a be j(i). Factor -9*h**3 - 6*h**4 - 6*h**2 - 3/2*h**a - 3/2*h + 0.
-3*h*(h + 1)**4/2
Let w be (6/1332*-4)/(131/6). Let l = 387732/33929 - w. Factor -2/7 + l*p**3 - 16/7*p - 50/7*p**4 - 12/7*p**2.
-2*(p - 1)**2*(5*p + 1)**2/7
Let i(u) = u**2 + u + 1. Let b be i(-2). Factor -9*s**4 - 5*s**b - 3*s**3 + 4*s**4 - 7*s**3 - 10*s**2.
-5*s**2*(s + 1)*(s + 2)
Let m(w) be the first derivative of -7 - 15/2*w**6 + 0*w + 220/3*w**3 + 6*w**5 + 235/4*w**4 + 30*w**2. Find c such that m(c) = 0.
-1, -2/3, 0, 3
Factor -212*p**3 - 216*p**3 + 429*p**3.
p**3
Let c be (-6)/4*(3 + (-66)/20). Let h = c - 1/4. Factor 0 - 1/5*a - 1/5*a**2 + 1/5*a**4 + h*a**3.
a*(a - 1)*(a + 1)**2/5
Find g, given that 0*g - 5/2*g**5 - 3*g**4 + 9/2*g**3 + 0 + g**2 = 0.
-2, -1/5, 0, 1
Let v(y) be the first derivative of y**5/20 + y**4/8 - y**3 + 7*y**2/4 - 5*y/4 + 109. Factor v(a).
(a - 1)**3*(a + 5)/4
Let y(h) be the first derivative of 1/6*h**3 - 3*h**2 - 44 + 0*h + 1/8*h**4. Factor y(t).
t*(t - 3)*(t + 4)/2
Suppose -6 + 0 = -x. Let a(w) = -w**2 - 20*w + 20. Let k(f) = -f**2. Let t(u) = x*k(u) - a(u). Factor t(r).
-5*(r - 2)**2
Let g(t) = 175*t + 2 + 3*t**2 - 179*t + 4*t**4 - 2*t**3 - 3*t**4. Let v(j) = -j**4 + j**3 + j - 1. Let s(l) = -3*g(l) - 6*v(l). Factor s(w).
3*w*(w - 1)**2*(w + 2)
Let a(l) be the first derivative of l**7/5040 + l**6/540 - l**5/144 + 34*l**3/3 + 27. Let n(m) be the third derivative of a(m). Factor n(i).
i*(i - 1)*(i + 5)/6
Let u(m) = 6*m**5 - 40*m**4 + 15*m**3 - 7*m**2 + 7. Let v(d) = 2*d**5 - 13*d**4 + 5*d**3 - 2*d**2 + 2. Let z(i) = 6*u(i) - 21*v(i). Factor z(j).
-3*j**3*(j - 5)*(2*j - 1)
Factor 5/2*d + 25/4 + 1/4*d**2.
(d + 5)**2/4
Suppose -36*k + 0 + 5*k**3 + 6*k**2 + 1/2*k**4 = 0. What is k?
-6, 0, 2
Let t(y) be the first derivative of -y**5/100 - y**4/30 - y**3/30 + 11*y + 1. Let l(q) be the first derivative of t(q). Factor l(g).
-g*(g + 1)**2/5
Let d be (3/4 - (-203)/(-116))*(-13 + 11). Let -18/5*h + 6/5*h**d + 0 = 0. What is h?
0, 3
Let g(t) be the second derivative of -t**7/84 - t**6/20 - t**5/20 - 17*t - 4. Let g(u) = 0. What is u?
-2, -1, 0
Suppose -22*z = -32*z. Suppose z*j**2 + 0*j + 0 - 1/4*j**3 = 0. Calculate j.
0
Let h(l) = -6*l**3 - 5*l**2 + 2*l + 7. Let q(o) = -o**2 + o - 1. Let c(u) = -3*h(u) - 6*q(u). Factor c(i).
3*(i + 1)**2*(6*i - 5)
Factor -13/2*j - 1/2*j**2 - 6.
-(j + 1)*(j + 12)/2
Let k be 2/(-1 + 12/8) + 0. Let p(m) be the first derivative of 2/35*m**5 - 2/7*m**2 - 3 + 1/7*m**k + 0*m**3 - 2/7*m. Suppose p(a) = 0. Calculate a.
-1, 1
Let m(w) be the second derivative of 4*w**5/5 + 19*w**4/3 + 22*w**3/3 - 8*w**2 - 331*w. What is k in m(k) = 0?
-4, -1, 1/4
Solve 9*f + 15 + 3/5*f**3 - 27/5*f**2 = 0.
-1, 5
Factor 5*z + 28*z - 24 - 8 - 2*z**3 + 5*z - 14*z.
-2*(z - 2)**2*(z + 4)
Let o(f) = -3*f + 12. Let t be o(-3). Suppose -2*n - t + 5 = -4*v, -5*v = -n - 20. Suppose -42/5*x**3 + 4/5 + 18/5*x + 2/5*x**2 + 18/5*x**v = 0. Calculate x.
-1/3, 1, 2
Let y(o) be the first derivative of 16 - 1/3*o**3 - 6*o**2 - 36*o. Factor y(d).
-(d + 6)**2
Let l be ((-885)/130)/(-1*42/8). Let x = 28/13 - l. Factor -x*w + 3/7*w**2 + 0.
3*w*(w - 2)/7
Let f(d) be the first derivative of d**5 - 25*d**4/2 + 60*d**3 - 135*d**2 + 135*d - 254. Factor f(p).
5*(p - 3)**3*(p - 1)
Let t(q) be the first derivative of q**5/330 + q**4/132 - 8*q**2 + 5. Let y(k) be the second derivative of t(k). Factor y(g).
2*g*(g + 1)/11
Let 2/11*o**3 + 4/11 - 2/11*o**4 - 10/11*o + 6/11*o**2 = 0. Calculate o.
-2, 1
Factor -32*s + 100/3 + 7*s**2 + 1/3*s**3.
(s - 2)**2*(s + 25)/3
Let j be (-9)/4*16/(-3). Suppose u - 16 + j = 0. Factor 2*k**5 + 5*k**4 + 2*k**u - 5*k**4.
2*k**4*(k + 1)
Factor 0*z**3 + 0*z + 2/3*z**5 + 0 + 2*z**4 - 8/3*z**2.
2*z**2*(z - 1)*(z + 2)**2/3
Suppose 3*s - 97 = -4*h, -2*h + 2*s = 19 - 71. Find t such that -3*t**3 - 27 + h + 28*t + 11*t - 6*t**2 - 28 = 0.
-5, 1, 2
Let h be 88/484 - ((-50)/(-33) + -2). Let l(n) be the first derivative of 1/2*n**2 + h*n + 5 + 1/9*n**3. Let l(t) = 0. What is t?
-2, -1
Suppose 0*f = -5*f + 15. Let u be ((-140)/56)/(3/(f/(-5))). Determine m, given that 8 + 4*m + u*m**2 = 0.
-4
Let g(q) be the first derivative of 18*q**2 + 6*q**3 - 36 + 24*q + 3/4*q**4. Factor g(x).
3*(x + 2)**3
Let t(o) = -100*o + 800. Let f be t(8). Factor 0*k**2 + 0 - 4/3*k**4 + f*k + 2/3*k**3 + 2/3*k**5.
2*k**3*(k - 1)**2/3
Let t(j) = -j**2 - 14*j + 7. Let r be t(-13). Factor r*d + 1 + 22 + 5*d**2 - 3.
5*(d + 2)**2
Let t(z) = 16*z**3 + 1104*z**2 + 1090*z + 266. Let n(w) = -30*w**3 - 2208*w**2 - 2182*w - 534. Let c(f) = 4*n(f) + 7*t(f). Determine k so that c(k) = 0.
-137, -1/2
Let b(w) = w**5 + w**2 + w + 1. Let p(d) = 3*d**5 + 7*d**4 + 17*d**3 + 13*d**2 + 4*d + 4. Let h(v) = 4*b(v) - p(v). Factor h(l).
l**2*(l - 9)*(l + 1)**2
Let l be (225/(-270))/(30/(-18)). Factor -3/4*g**2 + 3/4*g + 1/2 - l*g**3.
-(g - 1)*(g + 2)*(2*g + 1)/4
Let v(c) be the third derivative of c**7/1575 + c**6/225 - 11*c**5/450 + c**4/30 - 2*c**2 + 162. Solve v(x) = 0.
-6, 0, 1
Let w(o) = -7*o**2 - 69*o + 289. Let y be w(-13). Factor 5/2*p**2 + 0 + 5/4*p + 5/4*p**y.
5*p*(p + 1)**2/4
Let d(c) be the third derivative of -9*c**3 + 0*c + 0 + 18*c**2 + 1/180*c**6 - 19/90*c**5 + 11/4*c**4. Find v, given that d(v) = 0.
1, 9
Let v be 10/(-45) + 2/(-45)*-50. Factor 0 + 1/2*i**4 + 9/2*i**v + 0*i + 3*i**3.
i**2*(i + 3)**2/2
Let x(n) be the third derivative of 8*n**2 + 0*n**4 + 0*n - 7/480*n**6 + 1/168*n**7 + 0*n**3 + 1/120*n**5 + 0. Factor x(h).
h**2*(h - 1)*(5*h - 2)/4
Let p(f) = -4*f**2 - f + 9. Let k be p(-7). Let y be ((k/(-5))/(-4))/(-3). Factor 0*g**y - 4/7*g**4 + 2/7*g**5 + 4/7*g**2 - 2/7*g + 0.
2*g*(g - 1)**3*(g + 1)/7
Suppose 0 = -9*h + 8*h. Let k = 105/202 + -2/101. What is n in -n**2 - 1/2*n - k*n**3 + h = 0?
-1, 0
Suppose 0 = 5*g + 25, 30 = -2*z - z - 6*g. Let o(l) be the first derivative of -1/6*l**6 + 0*l**5 + 1/2*l**4 - 1/2*l**2 + 8 + 0*l + z*l**3. Solve o(s) = 0.
-1, 0, 1
Suppose -3*g = -6*g + 12. Let r be (-4)/((-100)/5)*g/2. Let -r*l**2 - 6/5*l - 4/5 = 0. Calculate l.
-2, -1
Let q = 89/520 - -3/104. Let g(u) be the second derivative of -4*u + 1/10*u**4 + 1/5*u**2 + 1/50*u**5 + q*u**3 + 0. Find m, given that g(m) = 0.
-1
Suppose -5*t + 19 = -1. Factor -4*h**4 + 2*h**4 + 4*h**4 + 37*h**2 + t*h**3 - 35*h**2.
2*h**2*(h + 1)**2
Let g(h) = h**3 + 6*h**2 + h + 8. Let r be g(-6). Let s = 14660/7 - 2094. Factor 0*j + s - 2/7*j**r.
-2*(j - 1)*(j + 1)/7
Factor 152*w**2 - 96*w**3 + 30*w**4 + 378*w**5 - 56*w**2 - 381*w**5.
-3*w**2*(w - 4)**2*(w - 2)
Let l(y) be the second derivative of -1/12*y**4 + 5/18*y**3 - 1/3*y**2 - 1/60*y**5 + 1/90*y**6 + 12*y + 0. Factor l(p).
(p - 1)**3*(p + 2)/3
Let l(n) be the second derivative of n**9/68040 - n**8/30240 - n**7/5670 - 13*n**4/4 - n. Let m(o) be the third derivative of l(o). Factor m(g).
2*g**2*(g - 2)*(g + 1)/9
Let b(i) be the second derivative of i**5/60 + i**4/18 - 7*i**3/18 + 2*i**2/3 + 767*i. Determine h, given that b(h) = 0.
-4, 1
Let v(i) be the first derivative of -i**3/9 + 10*i**2/3 + 99. What is a in v(a) = 0?
0, 20
Let y(k) = 4*k**3 + 24*k**2 - 100*k + 72. Let j(h) = -2*h**3 - 12*h**2 + 50*h - 36. Let v(m) = 5*j(m) + 2*y(m). Factor v(l).
-2*(l - 2)*(l - 1)*(l + 9)
Suppose 0 = -6*l - 6*l + 4*l. Let q(g) be the third derivative of 1/4*g**4 + 0*g + 6*g**2 - 4/15*g**3 + l - 7/300*g**5. Factor q(c).
-(c - 4)*(7*c - 2)/5
Let k(w) be the second derivative of -w**7/42 + 16*w**6/75 - 57*w**5/100 + 19*w**4/30 - 4*w**3/15 + w + 24. Let k(d) = 0. What is d?
0, 2/5, 1, 4
Let v(p) be t