he third derivative of 14*y**2 + 0 + 1/140*y**6 + 2/105*y**5 + 0*y**7 - 1/2352*y**8 + 1/56*y**4 + 0*y + 0*y**3. Determine g, given that t(g) = 0.
-1, 0, 3
Suppose 2641 = k + 5*g + 979, 3336 = 2*k - 2*g. Factor -96*s**3 - 3859*s - 864*s**2 - 3517 - 4*s**4 - k + 403*s.
-4*(s + 6)**4
Let r(f) = -f**2 + 2. Let n be r(0). Let z be (-6)/9 + (-33)/(-9). Find t, given that -3*t - 2*t**n - 2*t**5 + 0*t**5 + z*t**5 + 2*t + 2*t**4 = 0.
-1, 0, 1
Let q = 145 + -101. Factor q + 5*l**3 - 21*l**2 + 15*l - 13 + 14 - 4*l**2.
5*(l - 3)**2*(l + 1)
Suppose -5*m - 5*l - 94 = 21, 0 = -5*m + 3*l - 131. Let j be (m/27 - -1)*48/8. Find w, given that 2/3*w**2 - j*w + 0 = 0.
0, 2/3
Suppose -2*z - 12 = -6*z. Let -3*x - 2*x + 21*x**2 + 3*x**4 - 4*x + 28*x**z - 43*x**3 = 0. What is x?
0, 1, 3
Let f(i) be the third derivative of -i**6/540 + i**5/90 + i**4/12 + 10*i**3/3 + 9*i**2. Let a(q) be the first derivative of f(q). Find b, given that a(b) = 0.
-1, 3
Let t(x) = 3*x**2 + 106*x + 44. Let m be t(-35). Let s(g) be the second derivative of 0 - 1/7*g**3 + m*g + 0*g**2 - 1/42*g**4. Factor s(y).
-2*y*(y + 3)/7
Let o(n) be the first derivative of n**3/24 + 47*n**2/4 + 2209*n/2 - 449. Determine y so that o(y) = 0.
-94
Let n be 30/45 + (-6)/9. Let t(m) be the third derivative of 0 + 1/18*m**4 + 0*m + n*m**3 - 1/120*m**6 - 11*m**2 - 1/630*m**7 + 0*m**5. Factor t(v).
-v*(v - 1)*(v + 2)**2/3
Let i = -13 - -10. Let y = -1 - i. Factor 0 - 5*a + 2*a + a**y + 2.
(a - 2)*(a - 1)
Let k(n) be the first derivative of 6*n**5/25 - 8*n**4/5 - 26*n**3/15 + 6*n**2/5 + 3. Suppose k(g) = 0. What is g?
-1, 0, 1/3, 6
Let j = 144 + -140. Factor 24*x**3 + 442*x**2 - 5*x**j + 24*x + x**4 - 486*x**2.
-4*x*(x - 3)*(x - 2)*(x - 1)
Let k = 163 + -163. Let j(y) be the third derivative of 1/360*y**6 + 1/72*y**4 - 4*y**2 + 0*y + 0 + k*y**3 - 1/90*y**5. Determine t so that j(t) = 0.
0, 1
Let u(a) = 1. Let f(p) = 3*p**2 + 3*p + 3. Let v(o) = -f(o) + 3*u(o). Factor v(n).
-3*n*(n + 1)
Let n(f) be the second derivative of -f**9/30240 - f**8/13440 - f**4/3 - 7*f. Let t(x) be the third derivative of n(x). Factor t(a).
-a**3*(a + 1)/2
Let z(b) = b**3 + 3*b**2 - 2*b - 2. Let s be z(-2). Let c be (-2)/(-6) + (2 - 2/s). Factor -4/7 - 6/7*g - 2/7*g**c.
-2*(g + 1)*(g + 2)/7
Let d(i) = -i**3 - 9*i**2 + 3*i - 13. Let u be d(-10). Let h be u/9 + (-2)/6. What is j in 22*j**2 - 20*j**2 - h*j + 0*j + 4 = 0?
1, 2
Let r(w) = w**3 - 31*w**2 - 26*w - 190. Let c be r(32). Determine q so that 0 + 0*q**c + 1/7*q**3 - 1/7*q = 0.
-1, 0, 1
Let m(n) = n**3 + n**2 - n. Let i(z) = 3*z**4 + 3*z**3 - 6*z**2 - 3*z. Let v(o) = i(o) + 3*m(o). Factor v(l).
3*l*(l - 1)*(l + 1)*(l + 2)
Suppose -4*n + 8 = 0, 2*v - 8*n - 6 = -9*n. Factor 9/2*f**4 - 3/2*f**3 - 1 - 13/2*f - 23/2*f**v.
(f - 2)*(f + 1)*(3*f + 1)**2/2
Let y(i) be the first derivative of -3/5*i**5 - 15/2*i**4 + 22 - 108*i + 90*i**2 - 13*i**3. What is j in y(j) = 0?
-6, 1
Find r such that -42/5 + 44/5*r - 2/5*r**2 = 0.
1, 21
Let a be 3/(1 + 2 - 2). Suppose 7 = -4*r - 0*r + 5*u, -5*r = u - 13. Suppose 12*k + 0*k**a - 6*k**3 + 12 - 3*k**r + 3*k**3 = 0. What is k?
-2, -1, 2
Factor 10353 + 3*g**2 - 9939 + 6*g**2 - 627*g.
3*(g - 69)*(3*g - 2)
Suppose -18/5*d**4 - 2/5*d**5 - 16/5 - 12*d - 58/5*d**3 - 86/5*d**2 = 0. Calculate d.
-4, -2, -1
Let m(b) be the third derivative of 2187*b**7/280 - 243*b**6/40 + 81*b**5/40 - 3*b**4/8 + b**3/24 - 266*b**2. Factor m(y).
(9*y - 1)**4/4
Let q = -60 + 62. Let 5*w**2 + q*w**2 - 2*w + 8*w**2 - 17*w**2 + 2*w**3 + 2*w**4 = 0. Calculate w.
-1, 0, 1
Let x = -96 + 101. Let y(j) = -j - 4. Let s be y(-7). Solve x*v**2 + v**3 - 2 - 5*v + 3*v + v**s - 3*v**2 = 0 for v.
-1, 1
Let k be 10/35 - 32/14. Let x(p) = 5*p**3 - 6*p**2 - p + 8. Let g(q) = q**3 + q + 1. Let m(w) = k*g(w) + x(w). Factor m(f).
3*(f - 2)*(f - 1)*(f + 1)
Let f(c) be the third derivative of -11*c**8/224 - 9*c**7/28 - 7*c**6/8 - 5*c**5/4 - 15*c**4/16 - c**3/4 + 335*c**2. Factor f(t).
-3*(t + 1)**4*(11*t + 1)/2
Find u, given that 3/8*u**4 + 3/8*u + 0 - 3/8*u**3 - 3/8*u**2 = 0.
-1, 0, 1
Let u = -25825 + 77477/3. Factor -u*w**4 + 0*w - 4*w**3 - 16/3*w**2 + 0.
-2*w**2*(w + 2)*(w + 4)/3
Suppose -4*t - 559 = -615. Find o such that -t*o - 1/2*o**5 + 4 - 25/2*o**3 + 4*o**4 + 19*o**2 = 0.
1, 2
Let h(l) be the third derivative of 0*l + 0 - 1/105*l**5 + 23*l**2 + 0*l**3 + 1/42*l**4. Solve h(p) = 0.
0, 1
Let u be 2/(-126)*-39 - (-24)/(-84). Let l(b) be the second derivative of -u*b**4 + 0 + 2/15*b**6 + 8*b + 0*b**3 + 3/10*b**5 + 0*b**2. Let l(r) = 0. What is r?
-2, 0, 1/2
Let m(v) be the first derivative of 3/5*v - 1/15*v**3 + 1/5*v**2 - 6. Factor m(g).
-(g - 3)*(g + 1)/5
Let q(b) = -b - 3. Let r be q(-6). Let -4 - 7*l**4 - 61*l**2 + r*l**4 + 69*l**2 = 0. What is l?
-1, 1
Let h be (-4)/(-5)*5/(-2). Let t be (3/h)/((-4)/8). Find o, given that -2*o**4 - 35 + 2*o + 35 + 2*o**2 - 2*o**t = 0.
-1, 0, 1
Let s(w) be the first derivative of 0*w - 1/18*w**3 - 2*w**2 + 15 + 1/60*w**5 + 1/36*w**4. Let k(g) be the second derivative of s(g). Factor k(p).
(p + 1)*(3*p - 1)/3
Let o = 178 - 253. Let i be (-160)/o + (-32)/40. Factor 8/3*w + 2/9*w**3 + 16/9 + i*w**2.
2*(w + 2)**3/9
Let m(i) be the first derivative of i**4 + 4*i**3/3 - 12*i**2 - 10. Determine n so that m(n) = 0.
-3, 0, 2
Suppose 45*g = 41*g + 200. Let y be (-20)/g - (-18)/20. Solve 0 - 3/2*b**4 - 1/2*b**2 - y*b + 5/2*b**3 = 0.
-1/3, 0, 1
Suppose 3*m = 8*m - 5*o + 10, -4*o + 14 = -m. Suppose -m - 2 = -n. Solve -3 - 7*p + n*p**2 - 7*p**2 + p = 0 for p.
-1
Let q(k) be the third derivative of -k**7/105 + k**6/20 - k**5/30 - k**4/4 + 2*k**3/3 - 8*k**2. Factor q(b).
-2*(b - 2)*(b - 1)**2*(b + 1)
Let t(x) be the second derivative of -16*x + 0 - 5/48*x**4 - 35/12*x**3 - 245/8*x**2. Factor t(h).
-5*(h + 7)**2/4
Let s = 7154/45 + -1420/9. Factor -14/5*b - 36/5*b**2 - 44/5*b**3 - 2/5 - s*b**5 - 26/5*b**4.
-2*(b + 1)**4*(3*b + 1)/5
Let n(k) be the second derivative of -k**3 - 1/20*k**5 + 1/2*k**2 + 3/8*k**4 - 5*k + 0. Let l(o) be the first derivative of n(o). Factor l(r).
-3*(r - 2)*(r - 1)
Let h(k) be the third derivative of 0 - 12*k**2 + 1/15*k**5 + 6*k**3 - k**4 + 0*k. Solve h(z) = 0.
3
Let v be ((-2574)/1001)/(45/(-21)). Determine f so that -v*f + 4/5*f**2 + 2/5 - 6/5*f**4 + 4/5*f**3 + 2/5*f**5 = 0.
-1, 1
Let z(l) be the third derivative of l**5/60 + 5*l**4/24 + 27*l**2. Let z(d) = 0. Calculate d.
-5, 0
Let v be -8 - -1 - -32 - (3 - -1). Factor -v*q**3 - 11*q**3 - 8 - 36*q**2 + 12*q**3 - 28*q - q**4 - 3*q**4.
-4*(q + 1)**3*(q + 2)
Suppose -2*w + 10 = 5*r, 3*w = -4*r + 12 - 4. Suppose -r = -3*b + 4, c + b = 6. Factor 0*m**3 - m - 2*m**c - 2*m**3 - 2 + 3*m**2 - m**5 + 4*m**3 + m**2.
-(m - 1)**2*(m + 1)**2*(m + 2)
Suppose -i + 7*i + 12 = 0. Let q be -5 + i*92/(-32). Factor g + q*g**2 + 1/4.
(g + 1)*(3*g + 1)/4
Let x(f) be the third derivative of f**5/75 - 31*f**4/40 + 23*f**3/30 + 174*f**2. Factor x(n).
(n - 23)*(4*n - 1)/5
Let r be 211140/2430 - (2 + 28). Let -1088/9*t - 68/9*t**3 + r + 214/3*t**2 + 2/9*t**4 = 0. What is t?
1, 16
Let r(l) = -l**5 - 4*l**4 - 2*l**2 - 5*l. Let q(u) = 13*u + 18*u + 11*u**4 + 3*u**5 + 6*u**2 - 17*u. Let x = 57 - 40. Let k(y) = x*r(y) + 6*q(y). Factor k(d).
d*(d - 1)**3*(d + 1)
Let j(i) = -i + 6. Let s be j(3). Factor -4 - 8 + s*f**2 - 12*f - 6*f**2 + 3.
-3*(f + 1)*(f + 3)
Let c = -1799/3 - -600. Factor 2/3 + i + c*i**2.
(i + 1)*(i + 2)/3
Let m(r) be the second derivative of -r**4/12 + 5*r**3/2 - 28*r**2 + r + 164. Find i such that m(i) = 0.
7, 8
Suppose 0 = t - g, -2*t - g + 3 = -0*g. Let c(f) = -f**2 - 1. Let k(q) = -2*q**3 + 5*q**2 + 2*q + 1. Let h(j) = t*k(j) + 3*c(j). Factor h(n).
-2*(n - 1)**2*(n + 1)
Let i(j) be the first derivative of j**5/130 - 5*j**4/78 + 2*j**3/13 + 19*j + 16. Let g(x) be the first derivative of i(x). Suppose g(c) = 0. What is c?
0, 2, 3
Suppose -l - 3*d - 23 - 1 = 0, -3*l - 4*d = 67. Let i be (-48)/l + (-8)/28. Let 3*h**2 + h - 2*h - i*h - 3*h = 0. What is h?
0, 2
Let s = -183 + 171. Let m be s/(-6)*(4 + (-1 - 2)). Factor -15/7*f**m + 27/7 - 9/7*f - 3/7*f**3.
-3*(f - 1)*(f + 3)**2/7
Suppose -4 = 4*v - 0, -14 = h - 4*v. Let n = -6 - h. Let -4*y**3 + 8*y**2 + 2*y + n*y**3 - 2*y**3 = 0. What is y?
-1, -1/3, 0
Factor 2*p**2 - 4*p**2 + 3*p**2 + 4*p + 24 - 29*p**2 + 4 - 4*p**3.
-4*(p - 1)*(p + 1)*(p + 7)
Let j(x) be the seco