e second derivative of n(y). Factor k(r).
-2*r*(r - 1)*(r + 1)/7
Let r be (-2378)/(-123) + -14 + 2 - 7. Solve -r*q**2 - 2/3 - q = 0.
-2, -1
Let d(v) be the first derivative of 2/3*v**3 + 0*v**2 + 0*v + 0*v**4 - 2/5*v**5 + 29. Factor d(t).
-2*t**2*(t - 1)*(t + 1)
Factor 4866*u**3 - 24960*u**2 + 1218*u**3 - 3778 + 2512*u + 3714.
4*(u - 4)*(39*u - 2)**2
Let h(r) be the first derivative of -1/14*r**4 + 2/21*r**3 + 19 + 0*r + 0*r**2. Let h(x) = 0. What is x?
0, 1
Factor w**3 + 34*w + 65/3*w**2 + 40/3.
(w + 1)*(w + 20)*(3*w + 2)/3
Let n(o) be the first derivative of o**9/1512 + o**8/210 + o**7/210 - o**6/45 - o**5/20 + 38*o**3/3 + 41. Let d(q) be the third derivative of n(q). Factor d(w).
2*w*(w - 1)*(w + 1)**2*(w + 3)
Let n(a) = a**2 + 8*a + 4. Let t(b) be the second derivative of -b**4/4 - 5*b**3/2 - 7*b**2/2 + 8*b. Let u(d) = 10*n(d) + 6*t(d). Solve u(g) = 0 for g.
-1, -1/4
Let f(u) be the second derivative of -3*u**5/20 + 5*u**4/4 - 2*u**3 - 140*u. Factor f(z).
-3*z*(z - 4)*(z - 1)
Let n = 9 - -1. Factor 12 - 2 + 4*s**3 - n*s**2 - 2*s**2 + 6.
4*(s - 2)**2*(s + 1)
Find f such that 16/7*f - 2/7*f**4 - 16/7*f**3 + 0 + 2/7*f**2 = 0.
-8, -1, 0, 1
Suppose -4*j + 22 = -26. Suppose -2*x = -x - 5*u - 15, 5*x = -4*u - j. Factor x - 1/2*g**2 - 1/2*g.
-g*(g + 1)/2
Let r be 100/120*12/5. Factor 0*f - 3/4*f**r + 3/4.
-3*(f - 1)*(f + 1)/4
Suppose -30*d - 314 + 2*d**2 + 314 = 0. Calculate d.
0, 15
Suppose -2*z = -5*j, 2 = -9*j - 29*z + 33*z. Factor 4/11*s**3 - 16/11*s + 2/11*s**4 - 8/11*s**j + 0.
2*s*(s - 2)*(s + 2)**2/11
Let r(i) be the third derivative of -1/96*i**6 + 0 - 35/32*i**4 + 15/4*i**3 + 1/6*i**5 + 0*i + 17*i**2. Determine t so that r(t) = 0.
2, 3
Let n be (-12 - (-9 - -3))/(6/(-4)). Let f be (-6 - -8)/(14/n - -1). Find j such that -10/9*j**3 + 10/9*j - 4/9*j**2 + f = 0.
-1, -2/5, 1
Let y(p) be the third derivative of p**9/5040 + p**8/2240 - p**7/140 + 5*p**4/12 + 13*p**2. Let x(n) be the second derivative of y(n). Factor x(o).
3*o**2*(o - 2)*(o + 3)
Let a(s) = 45*s**2 + 1575*s - 945. Let q(v) = 4*v**2 + 143*v - 86. Let c(y) = -6*a(y) + 65*q(y). Suppose c(k) = 0. Calculate k.
-16, 1/2
Find t, given that -15*t**2 + 3*t**2 - 2*t**3 - 385*t + 184*t + 183*t = 0.
-3, 0
Let q(w) be the first derivative of -w**8/1680 + w**7/1680 + 2*w**3 + 12. Let t(k) be the third derivative of q(k). Suppose t(j) = 0. What is j?
0, 1/2
Let c(f) = 8*f + 0*f + 1 - 9*f. Let z(b) = -b**5 - 2*b**4 - b**3 - 5*b + 5. Let o(i) = 5*c(i) - z(i). Let o(j) = 0. What is j?
-1, 0
Let j(m) be the first derivative of 2*m**6/7 + 9*m**5/7 + 3*m**4/7 - 18*m**3/7 - 12*m**2/7 + 9*m/7 - 862. Find n such that j(n) = 0.
-3, -1, 1/4, 1
Suppose -74 = -11*l - 8. Let o(z) be the second derivative of -1/3*z**4 + 2*z + 0 + 4/3*z**3 + 3/5*z**l + z**2 - 6/5*z**5. Factor o(a).
2*(a - 1)**2*(3*a + 1)**2
Let m(j) be the third derivative of j**8/1008 - j**7/315 - j**6/120 + j**5/45 + j**4/18 - j**2 + 102*j. Factor m(s).
s*(s - 2)**2*(s + 1)**2/3
Suppose -4*l - 4 = -12. Factor 119*m**4 + l*m + 8*m**2 - 4*m - 115*m**4 - 10*m**3.
2*m*(m - 1)**2*(2*m - 1)
Let j be (-1)/((60/(-36))/(2/3)). Factor -j + 3/5*f**2 + 1/5*f**3 - 1/5*f - 1/5*f**4.
-(f - 2)*(f - 1)*(f + 1)**2/5
Let r(p) = p**2 + 5*p + 6. Let a be r(-4). Factor -13*h**2 + 10*h**2 + 7*h**a.
4*h**2
Let y(p) = 8*p**2 - 5*p + 1. Let z(m) = 7*m**2 - 4*m + 1. Suppose q - 27 = -5*v + 3*q, 0 = -2*v + 3*q + 2. Let x(j) = v*z(j) - 6*y(j). Factor x(t).
(t + 1)**2
Let w be (5 - -7)*(-2)/(-8). Find a, given that 3*a**5 - 12*a**4 - 12*a + 6*a**3 - 12*a**2 + 5*a**3 + 15*a + 7*a**w = 0.
0, 1
Let z(m) = m**2 + 3*m - 8. Let j be z(-5). Let i be (-4)/46 - -146*(-6)/(-552). Solve -1/2*f - 3/2 + 1/2*f**3 + i*f**j = 0.
-3, -1, 1
Let f be 4 + 4 + 3*-2. Let -4*k**2 + 7*k**f + 6*k**3 - 3*k**3 = 0. What is k?
-1, 0
Suppose -847 = 16*u - 927. Factor 0*p - 3/2*p**2 - 3/2*p**u + 0 + 3/2*p**3 + 3/2*p**4.
-3*p**2*(p - 1)**2*(p + 1)/2
Let f(a) be the third derivative of -a**8/3360 + a**7/252 - a**6/120 - 3*a**5/20 + 13*a**4/12 - 24*a**2. Let i(t) be the second derivative of f(t). Factor i(c).
-2*(c - 3)**2*(c + 1)
Let p(b) be the second derivative of -2*b**6/15 + 18*b**5/5 - 101*b**4/3 + 152*b**3 - 360*b**2 + 2*b + 770. Factor p(q).
-4*(q - 10)*(q - 3)**2*(q - 2)
Let l(s) be the second derivative of s**6/1440 - s**5/240 + 25*s**3/6 - 9*s. Let d(q) be the second derivative of l(q). Factor d(a).
a*(a - 2)/4
Let w(j) = -2*j - 12. Let h be w(-7). Find n, given that -2/7*n + 6/7 + 2/7*n**3 - 6/7*n**h = 0.
-1, 1, 3
Let l(b) be the second derivative of -b**5/110 + b**3/33 - 299*b. Determine z, given that l(z) = 0.
-1, 0, 1
Let b = 290 - 300. Let g be -1 - (4 + b)/2. Find r such that 0*r + 0 - 1/5*r**3 + 1/5*r**4 + 0*r**g = 0.
0, 1
Factor -27/4*f - 441/4*f**3 + 189/4*f**2 + 0 + 343/4*f**4.
f*(7*f - 3)**3/4
Let o be -6*(14/(-3) + 2). Determine s so that -5*s + o*s**3 - 40*s**2 + 3*s - 6*s + 12*s**2 = 0.
-1/4, 0, 2
Let -32*c**3 + 8*c**2 + 28*c**3 - 36*c**3 - 195*c**4 + 213*c**4 = 0. Calculate c.
0, 2/9, 2
Determine i, given that 2*i**4 + i**4 - 15*i**3 - 9*i**2 + 51*i + 9*i**3 - 51*i = 0.
-1, 0, 3
Let d(u) be the second derivative of -u**5/25 + 29*u**4/15 - 26*u**3 - 90*u**2 + 65*u. Suppose d(r) = 0. Calculate r.
-1, 15
Let i be 6/(-16)*(-23 + 19). Let y(s) be the second derivative of -3/8*s**4 + 0 + s - i*s**2 - 5/4*s**3. Suppose y(n) = 0. What is n?
-1, -2/3
Find m such that 49/3*m**4 + 32/3 + 216*m**2 - 260/3*m - 469/3*m**3 = 0.
2/7, 1, 8
Let o(p) be the first derivative of 0*p + 14/45*p**5 + 17 + 4/9*p**2 + 5/18*p**4 - 32/27*p**3. Suppose o(j) = 0. Calculate j.
-2, 0, 2/7, 1
Let x(m) = 2*m**2 - 4*m + 3. Let y be x(2). Let f = 230 - 224. Factor -b - 2*b + b**y - 6*b**3 + 2*b**3 + f*b**2.
-3*b*(b - 1)**2
Factor -7*l - 137*l**2 + 8 - 5*l + 141*l**2.
4*(l - 2)*(l - 1)
Let h(z) be the third derivative of 0*z + 0*z**3 + 3/20*z**5 + 3/112*z**8 - 19/70*z**7 - 9/4*z**4 + 15*z**2 + 31/40*z**6 + 0. Find v such that h(v) = 0.
-2/3, 0, 1, 3
Let b(y) = -2*y**2 + 8*y + 5. Let z(r) = 3*r**2 + r + 1 - 11 - 10*r + 4. Let j(d) = 6*b(d) + 5*z(d). Determine p so that j(p) = 0.
-1, 0
Suppose -4*n + 16 = 0, 0*r - n + 14 = 2*r. Find o such that 4*o**2 - 9*o**2 - r*o**3 + 5*o**2 + 20*o = 0.
-2, 0, 2
Let r = 6 - 12. Let s be r/(5 + -2 + -5). Let y**3 - 12*y + s*y**2 - 3*y**4 - 4*y**3 + 15*y = 0. What is y?
-1, 0, 1
Let p(n) = 6*n**3 + 20*n**2 - 47*n - 121. Let i be p(-4). Factor 14*h**2 + 200/3 + 2/3*h**i + 80*h.
2*(h + 1)*(h + 10)**2/3
Let b(a) be the third derivative of a**8/60480 - a**7/5040 + a**6/1080 - 23*a**5/60 - 19*a**2. Let q(r) be the third derivative of b(r). Factor q(g).
(g - 2)*(g - 1)/3
Let t(a) be the first derivative of 18 + 2/27*a**3 - 4/9*a + 1/9*a**2. What is l in t(l) = 0?
-2, 1
Let s(w) be the third derivative of w**5/180 - w**4/8 - 26*w**3/9 + 206*w**2. Determine k, given that s(k) = 0.
-4, 13
Let q(z) be the first derivative of -2*z**3/3 - 52*z**2 - 1352*z + 513. Suppose q(c) = 0. Calculate c.
-26
Find r, given that 16*r + 47/5*r**2 - 79/5*r**3 - 1/5*r**5 + 17/5*r**4 - 64/5 = 0.
-1, 1, 8
Let z(o) = -o**3 + o**2 + o - 1. Let y(v) be the first derivative of v**3 - 2*v**2 + v + 29. Let t(w) = 2*y(w) + 2*z(w). Factor t(x).
-2*x*(x - 3)*(x - 1)
Let n(d) = d**3 + 9*d**2 + 10*d - 15. Let a be n(-7). Let h(z) = z**2 - 12*z - 11. Let b be h(a). Find q such that 8/3 + 28*q + 98*q**b + 343/3*q**3 = 0.
-2/7
Let z(g) = g**2 - 10*g - 5. Let o = 111 - 131. Let u(f) = -4*f**2 + 30*f + 14. Let b(d) = o*z(d) - 6*u(d). Determine j so that b(j) = 0.
-4, -1
Let i(k) = -2*k - 13. Let o be i(-8). What is t in -6*t - 3*t**o + 9*t - 2*t**2 - t**2 - 4*t**4 + 7*t**4 = 0?
-1, 0, 1
Let h(m) be the second derivative of -4*m**7/63 + 26*m**6/45 - 35*m**4/9 - 16*m**3/9 + 8*m**2 - 78*m. Solve h(o) = 0.
-1, 1/2, 2, 6
Let j(d) = -5*d**2 + 2*d - 5. Let r(w) be the third derivative of w**5/15 - w**4/12 + 2*w**3/3 + 14*w**2. Let m(n) = -5*j(n) - 6*r(n). Solve m(f) = 0.
-1
Suppose 0 = -2*w + 6 + 24. Suppose s + 5*j + 0 + w = 0, -37 = -5*s + 3*j. Solve -1/2*b**s - 5/2*b**4 - 9/2*b**3 - b - 7/2*b**2 + 0 = 0 for b.
-2, -1, 0
Factor 215*k + 33*k - 4*k**2 - 2854 - 990.
-4*(k - 31)**2
Let n(g) be the first derivative of 36*g**5/5 - 25*g**4 + 28*g**3 - 6*g**2 - 8*g + 139. Suppose n(f) = 0. Calculate f.
-2/9, 1
Let f(u) be the second de