2
Let d(b) be the third derivative of -1/56*b**7 + 1/20*b**5 + 1/4*b**4 + 0*b - 1/448*b**8 + 0*b**3 + 0 + 31*b**2 - 3/80*b**6. Solve d(z) = 0.
-2, 0, 1
Let p(l) be the third derivative of l**8/1344 - l**7/120 - 13*l**6/160 - 53*l**5/240 - 11*l**4/48 - 595*l**2. Solve p(a) = 0 for a.
-2, -1, 0, 11
Let q be (1/(-6))/((-5)/20). Let v(t) be the first derivative of -5/4*t**2 + q*t**3 - 2 + 1/2*t. Factor v(b).
(b - 1)*(4*b - 1)/2
Let t be 2/((-16)/(-4))*-268. Let s = t - -403/3. Factor 5/6*p**3 + 1/3*p**4 + 0*p + 0 + s*p**2.
p**2*(p + 2)*(2*p + 1)/6
Find a such that -357*a**2 + 2*a**4 - 12 + 12*a - 34*a + 6*a**3 + 351*a**2 = 0.
-3, -1, 2
Let k(h) be the third derivative of h**8/1512 + h**7/105 + h**6/270 - 14*h**5/45 + 2*h**4/3 + h**2 + 129*h. Solve k(z) = 0 for z.
-6, 0, 1, 2
Let k(o) be the first derivative of 4*o**5/5 + 4*o**4 + 8*o**3 + 8*o**2 + 4*o + 265. Suppose k(w) = 0. Calculate w.
-1
Suppose 50 = 5*r - 30. Let q be (-4)/(-6)*(r + -10). Factor 0*w - 6/7*w**2 + 3/7*w**q - 3/7*w**3 + 0.
3*w**2*(w - 2)*(w + 1)/7
Suppose 5*x + 21 - 41 = 0. Let a(w) be the third derivative of 0 - 2/33*w**3 + 7/330*w**5 - 5/132*w**4 + x*w**2 + 0*w. Factor a(f).
2*(f - 1)*(7*f + 2)/11
Let w(a) be the second derivative of -2*a + 3*a**2 + 1/15*a**6 - 2/3*a**4 - 2/3*a**3 + 1/5*a**5 + 0. Factor w(s).
2*(s - 1)**2*(s + 1)*(s + 3)
Let c be (-8 - (-4 - 0)) + (-72)/(-12). Solve w - 1/5*w**3 + 2/5*w**c - 6/5 = 0 for w.
-2, 1, 3
Let g = -800 - -802. Suppose -4/13 + 6/13*t + 0*t**g - 2/13*t**3 = 0. What is t?
-2, 1
Let m(p) be the third derivative of p**5/80 - 2*p**3 + 5*p**2 + 25. Find n, given that m(n) = 0.
-4, 4
Let 1/4*v**3 + 0 + 1/4*v**4 - 1/2*v**2 + 0*v = 0. What is v?
-2, 0, 1
Let x(o) be the third derivative of -o**5/5 - 3*o**4/8 + o**3/2 - 252*o**2. Determine r so that x(r) = 0.
-1, 1/4
Suppose -c + 5*c - 2*g = 6, 2*c - 3*g = 1. Suppose 8*z**c + 2 + 4 + 4*z**3 - 6 = 0. What is z?
-2, 0
Let k(v) be the third derivative of -v**5/270 - 2*v**4/27 + 20*v**3/27 - 22*v**2 - 7*v. Factor k(h).
-2*(h - 2)*(h + 10)/9
Let w(r) = -6*r**3 - 302*r**2 - 887*r + 10. Let n(o) = -21*o**3 - 1056*o**2 - 3105*o + 36. Let q(a) = 5*n(a) - 18*w(a). Factor q(t).
3*t*(t + 3)*(t + 49)
Let r be (35/(-14))/((18/(-12))/3). Factor 2*w + r + 1/5*w**2.
(w + 5)**2/5
Let k(i) be the first derivative of i**6/24 - 5*i**4/8 + 5*i**3/3 + 2*i**2 - 4. Let z(t) be the second derivative of k(t). Let z(w) = 0. Calculate w.
-2, 1
Let b(r) = r**3 - 5*r**2 + 2*r + 2. Let f be b(5). Factor 8*i + 4*i**3 + f*i**2 + 325 - 325.
4*i*(i + 1)*(i + 2)
Factor -55*z**2 - 41*z - 19*z - 346*z**4 - 20 - 5*z**3 + 5*z**5 + 361*z**4.
5*(z - 2)*(z + 1)**3*(z + 2)
Suppose 5*r - 14 = 41. Suppose -3*n + 1 = -r. Solve -6*h**3 + 7*h**3 + 5*h**5 + 4*h**3 - 10*h**n = 0.
0, 1
Let r be ((-13)/(-52))/(3/42). Let m = 207/50 + 9/25. What is a in 0 + r*a**5 + m*a**2 - 5/2*a**3 - a - 9/2*a**4 = 0?
-1, 0, 2/7, 1
Let l = 31 + -27. Determine z so that 12*z**2 - 4*z**4 - 11*z + l*z**3 + 0 + 7*z - 8 = 0.
-1, 1, 2
Let x = -6279 - -50235/8. Find u, given that -9/4*u**3 + x*u**4 + 0 - 3*u + 9/2*u**2 = 0.
0, 2
What is o in -60*o + 242*o**2 - 83*o**2 + 140 - 84*o**2 - 80*o**2 = 0?
-14, 2
Let j(f) be the first derivative of 49*f**6/3 - 644*f**5/5 + 613*f**4/2 - 184*f**3 + 36*f**2 - 141. Suppose j(q) = 0. What is q?
0, 2/7, 3
Find b such that -3/2*b**2 - 48*b - 93/2 = 0.
-31, -1
Find r, given that 100*r + 125 + 1/5*r**4 + 4*r**3 + 30*r**2 = 0.
-5
Let w = 511 - 509. Factor 2*a**w - 1 + 3/2*a**3 - 5/2*a.
(a - 1)*(a + 2)*(3*a + 1)/2
Let b = -37 - -37. Let h(s) be the first derivative of 0*s - 3/5*s**5 + 3/2*s**4 - s**3 - 5 + b*s**2. Let h(l) = 0. What is l?
0, 1
Let y = 636 + -633. Let w(h) be the first derivative of 3 + 4*h**2 + 4*h + 4/3*h**y. Factor w(g).
4*(g + 1)**2
Let g = -33 + 35. Determine m so that -5*m**3 - 6*m**4 + 64 + g*m**4 + 64*m - 11*m**3 = 0.
-2, 2
Let d(h) be the second derivative of h**7/84 - h**6/10 + 13*h**5/40 - h**4/2 + h**3/3 - 9*h - 6. Find y such that d(y) = 0.
0, 1, 2
Let v(f) = -14*f**3 - 128*f**2 - 480*f - 142. Let i(t) = -13*t**3 - 126*t**2 - 480*t - 140. Let w(p) = -7*i(p) + 6*v(p). Factor w(q).
(q + 8)**2*(7*q + 2)
Let o(g) be the first derivative of g**4/42 + 10*g**3/63 - 2*g**2/3 + 335. Factor o(r).
2*r*(r - 2)*(r + 7)/21
Suppose 0 = -5*o - o. Suppose o*r + 4*r = -i, 0 = -2*r. Factor 1/4*j**3 + 1/2*j**2 + i + 1/4*j.
j*(j + 1)**2/4
Suppose 0 + 9*x**2 + 10*x - 23*x**2 + 39*x**2 + 5*x**4 + 20*x**3 + 0 = 0. What is x?
-2, -1, 0
Let a be 80/32 - 1/2. Suppose -6*w**a + 829 + 0*w**3 - 829 + 3*w**3 = 0. What is w?
0, 2
Factor 2*s**2 - 1047 + 152*s + 247 + 488.
2*(s - 2)*(s + 78)
Let h be (-4)/(-7)*(-35)/(-30) + (-16)/24. Find g, given that -3/4*g**2 - 1/2*g - 1/4*g**3 + h = 0.
-2, -1, 0
Let w(b) be the first derivative of -7*b**5/15 - 23*b**4/12 + b**3/9 + 23*b**2/6 + 2*b + 5. Solve w(u) = 0.
-3, -1, -2/7, 1
Let v(j) be the first derivative of j**5/5 - 7*j**4 - 10*j**3 + 14*j**2 + 29*j - 225. Factor v(y).
(y - 29)*(y - 1)*(y + 1)**2
Let q(t) = -5*t**4 - 60*t**3 - 50*t**2 + 54*t + 55. Let o(x) = 14*x**4 + 178*x**3 + 150*x**2 - 162*x - 164. Let g(s) = 3*o(s) + 8*q(s). What is z in g(z) = 0?
-26, -1, 1
Let a(h) = 10*h**2 + 2*h + 8. Let k be a(-2). Factor -k*t**4 + 68*t**3 + 68*t - 156*t**2 + 33*t**3 - 8 + 39*t**3.
-4*(t - 1)**3*(11*t - 2)
Let j(h) = 3*h - 22. Let a be j(7). Let p(t) = -t**3 - t**2. Let x(d) = -3*d**3 + 21*d**2 - 28*d + 12. Let o(f) = a*p(f) - x(f). Factor o(b).
4*(b - 3)*(b - 1)**2
Suppose 9*q + 5*c - 40 = 14*q, -3*c + 24 = -2*q. Find t, given that q + 6/7*t - 2/7*t**3 + 4/7*t**2 = 0.
-1, 0, 3
Let o be 14/(-7) + (210/99)/1. Let x = o - -79/165. Let 0 + 2/5*v + v**2 - x*v**3 = 0. Calculate v.
-1/3, 0, 2
Suppose -3*g + 749 - 743 = 0. Factor 25/4*z - 5/4*z**g + 0.
-5*z*(z - 5)/4
Let z(r) be the third derivative of r**6/200 + r**5/20 - 13*r**4/40 + 7*r**3/10 - 63*r**2 - 1. Factor z(d).
3*(d - 1)**2*(d + 7)/5
Let t(v) = v**3 - 21*v**2 + 20*v + 3. Let c be t(20). Suppose -c*z - 4*d = -1 - 18, 3*z + 3*d - 15 = 0. Factor z + 3/2*g + 1/2*g**2.
(g + 1)*(g + 2)/2
Let h be (-1)/((-27)/54*2/3). Let g(n) be the second derivative of -22/3*n**h - 7*n + 3*n**4 + 0 + 4*n**2. Let g(x) = 0. What is x?
2/9, 1
Let u(a) be the second derivative of -a**8/5880 + a**7/2940 + a**6/1260 - a**5/420 + 7*a**3/6 + 2*a. Let h(v) be the second derivative of u(v). Factor h(g).
-2*g*(g - 1)**2*(g + 1)/7
Let p(v) be the first derivative of -v**3/6 - 11*v**2/4 + 21*v + 401. Determine r so that p(r) = 0.
-14, 3
Let s(i) be the second derivative of 0*i**2 + 0 + 1/9*i**3 + 1/18*i**4 - 6*i. Factor s(v).
2*v*(v + 1)/3
Let p be (1 - 1 - -1)*0. Let f be 4 + 2 + p/3. Solve -4*h**3 - f*h + 2*h**5 + 5*h + 3*h = 0.
-1, 0, 1
Let r be ((-20)/108)/(-8 - (-215)/30). Factor -r*f**5 + 2/9 + 4/9*f**3 + 2/9*f**4 - 4/9*f**2 - 2/9*f.
-2*(f - 1)**3*(f + 1)**2/9
Let j(g) be the third derivative of g**8/840 - g**6/300 - g**2 + 54*g. Factor j(c).
2*c**3*(c - 1)*(c + 1)/5
Let z = -26502 - -26502. Factor -3/5*u + z + 1/5*u**3 - 2/5*u**2.
u*(u - 3)*(u + 1)/5
Let q(v) = 21*v**5 + 12*v**4 - 45*v**3 - 3*v**2 + 33*v - 18. Let w(h) = -2*h**5 + h**3 + h**2. Let o(a) = q(a) + 9*w(a). Factor o(u).
3*(u - 1)**3*(u + 1)*(u + 6)
Let f(t) be the third derivative of 1/210*t**5 + 0 + 0*t - 1/210*t**6 - 12*t**2 + 0*t**3 + 0*t**4 + 1/735*t**7. Suppose f(g) = 0. Calculate g.
0, 1
Let k(w) = w**5 + 15*w**4 + 11*w**3 - 5*w**2 - 12*w - 7. Let g(m) = -m**5 - 18*m**4 - 12*m**3 + 6*m**2 + 13*m + 8. Let h(u) = -3*g(u) - 4*k(u). Factor h(o).
-(o - 1)*(o + 1)**3*(o + 4)
Find p such that 8*p**2 - 12 + p**2 - 9*p**3 + 13*p**3 - 7*p**3 = 0.
-1, 2
Let t(f) be the first derivative of 2/3*f**3 + 16 - 1/3*f**6 + 0*f**2 + 0*f + 6/5*f**5 - 3/2*f**4. Determine l so that t(l) = 0.
0, 1
Factor -c**2 + 4*c**4 + 84*c**3 - 32*c**3 - 28*c**3 - 3*c**2 - 24*c.
4*c*(c - 1)*(c + 1)*(c + 6)
Find v such that -6/17*v**3 + 2/17*v**4 - 2/17*v**2 + 0 + 0*v + 6/17*v**5 = 0.
-1, -1/3, 0, 1
Let z be 294/(-28)*(-52)/1638. Let 75 + 31/3*h**2 + z*h**3 + 85*h = 0. What is h?
-15, -1
Let f(t) be the second derivative of -t**7/210 - t**6/150 + t**5/25 + t**4/15 + 418*t. Determine k so that f(k) = 0.
-2, -1, 0, 2
Factor 0*s + 1/8*s**3 + 0 + 0*s**2 + 0*s**4 - 1/8*s**5.
-s**3*(s - 1)*(s + 1)/8
Let g = 71 - 75. Let x be ((-63)/6)/3 - g. Fact