- 3/2*d**3 + 7/30*d**6 - d**2. Let s(a) = 0. Calculate a.
-1, -2/7, 1
Suppose 4*c - 8 = -20. Let z be ((-78)/10)/c - 2. Let -1/5*p + 1/5*p**4 - 3/5*p**3 + 0 + z*p**2 = 0. What is p?
0, 1
Let y(t) be the second derivative of t**6/105 + 6*t**5/35 + 8*t**4/7 + 64*t**3/21 + 23*t. Suppose y(k) = 0. Calculate k.
-4, 0
Let d(r) be the first derivative of 2*r**5/5 + 3*r**4/2 + 2*r**3/3 - 3*r**2 - 4*r - 19. Solve d(i) = 0 for i.
-2, -1, 1
Let i(n) be the first derivative of n**6/495 + n**5/132 + n**4/132 - 4*n**3/3 + 1. Let a(o) be the third derivative of i(o). Suppose a(j) = 0. What is j?
-1, -1/4
Let g(r) be the second derivative of r**6/12 + r**5/2 + 25*r**4/24 + 5*r**3/6 - 21*r. Determine v, given that g(v) = 0.
-2, -1, 0
Let t be (-30)/(-135) - (-2)/9*2. Factor t*q**2 + 4/3*q + 2/3.
2*(q + 1)**2/3
Let h = 40691 - 3865567/95. Let d = h - 8/19. Suppose -d*y**2 + 4/5 - 2/5*y = 0. What is y?
-2, 1
Suppose 2*t - 4*t + 8 = 0. Let y be (3 - 1/1)*1. Factor -l**5 - 7*l**y - 2*l + 5*l**2 + 2*l**t + 3*l.
-l*(l - 1)**3*(l + 1)
Let w(t) = -4*t**2 - t - 1. Let a be (-8)/16*(-1 + 7). Let c(r) = -5*r**2 - r - 2. Let l(p) = a*c(p) + 4*w(p). Factor l(g).
-(g - 1)*(g + 2)
Let 121/8*f**4 + 1/2 + 213/8*f**2 - 13/2*f - 143/4*f**3 = 0. Calculate f.
2/11, 1
Let i = -17 + 17. Let q(c) be the first derivative of -1/4*c**3 + 2 - 1/20*c**5 + 1/8*c**2 + 3/16*c**4 + i*c. Factor q(r).
-r*(r - 1)**3/4
Suppose a = -3*v - 10, -9*a + 20 = -5*a - 3*v. Let q(l) be the second derivative of 1/4*l**2 + 1/12*l**3 - 5/24*l**4 + 3/40*l**5 - a*l + 0. Factor q(f).
(f - 1)**2*(3*f + 1)/2
Let k(p) be the third derivative of -p**6/1800 - p**5/600 + p**4/60 - p**3/2 - 2*p**2. Let x(m) be the first derivative of k(m). Factor x(u).
-(u - 1)*(u + 2)/5
Let r be (-24)/36 - (-2)/3. Let m(o) be the second derivative of r + 1/50*o**5 - 1/5*o**2 + 3*o + 1/5*o**3 - 1/10*o**4. Factor m(f).
2*(f - 1)**3/5
Let r be (12/(-15))/(4/10). Let x be (-49)/21*r/7. Factor x*b + 1/3 + 1/3*b**2.
(b + 1)**2/3
Let h = -705 - -707. Factor 0*d**h - 3/4*d**3 - 3/2 + 9/4*d.
-3*(d - 1)**2*(d + 2)/4
Let h = -20 + 22. Let p(q) be the second derivative of -4/105*q**6 - 1/21*q**3 - 2/21*q**4 + 0*q**2 - 1/147*q**7 + h*q - 3/35*q**5 + 0. Factor p(d).
-2*d*(d + 1)**4/7
Determine i so that 1/8 - 1/4*i**2 + 0*i**3 + 0*i + 1/8*i**4 = 0.
-1, 1
Let k(g) be the second derivative of 7/30*g**4 - 2/25*g**5 + 0 + 3*g - 1/5*g**2 - 2/15*g**3. Find x such that k(x) = 0.
-1/4, 1
Let s(q) = 2*q**3 + q - 1. Let b be s(1). Find g such that 2/9 + 4/9*g - 2/3*g**b = 0.
-1/3, 1
Suppose 0 = -z - 0*z - 2. Let y be (z - -5)*(-2)/(-6). Factor -s + 3*s - 3*s**3 + y - 5*s**2 + 4*s**4 + s.
(s - 1)**2*(s + 1)*(4*s + 1)
Let s(n) be the second derivative of n**4/20 + n**3/2 + 6*n**2/5 + 21*n. Solve s(v) = 0 for v.
-4, -1
Let -4/3 - 16/3*x - 4*x**2 = 0. What is x?
-1, -1/3
Let a = 134815/35334 + -560/151. Let v = a + 3/26. Factor 0*r**3 - 4/9*r**4 - v*r**5 + 2/9*r + 4/9*r**2 + 0.
-2*r*(r - 1)*(r + 1)**3/9
Let i(w) = 17*w**2 - 5*w - 11. Let n(j) = -6*j**2 + 2*j + 4. Let q(y) = 4*i(y) + 11*n(y). Factor q(c).
2*c*(c + 1)
Let o(i) be the third derivative of 0*i**4 + 0 + 0*i**5 + 1/3*i**3 + 0*i**6 + 0*i - 2*i**2 + 1/1680*i**7. Let p(z) be the first derivative of o(z). Factor p(h).
h**3/2
Let -4/11*y**2 + 0 + 6/11*y - 2/11*y**3 = 0. Calculate y.
-3, 0, 1
Let w(o) = o**4 - 3*o**3 + 7*o**2 + 3*o + 1. Let d(k) = 2*k**4 - 4*k**3 + 8*k**2 + 4*k + 2. Let s = 3 + 1. Let j(m) = s*w(m) - 3*d(m). Solve j(g) = 0.
-1, 1
Let o = -63 + 66. Find r, given that -2/3*r**5 - 8/3*r**2 - 8/3*r**4 - 4*r**o - 2/3*r + 0 = 0.
-1, 0
Let f(g) = g**3 - 12*g**2 + g - 4. Let k be f(12). Let -26*j**4 + 175 - 14*j**2 + k*j**5 - 175 + 2*j + 30*j**3 = 0. What is j?
0, 1/4, 1
Let h = 242/63 + -32/9. Let a be 26/10 - (-3 - 26/(-10)). Let -2/7 + 2/7*p**2 + 2/7*p - h*p**a = 0. What is p?
-1, 1
Let -5/8*g + 1/4 + 1/8*g**5 - 1/2*g**4 + 1/2*g**3 + 1/4*g**2 = 0. Calculate g.
-1, 1, 2
Let m(f) be the third derivative of f**6/180 + f**5/60 - f**3/18 - 18*f**2. Factor m(u).
(u + 1)**2*(2*u - 1)/3
Let u(a) be the third derivative of a**6/40 - 3*a**4/8 + a**3 - 6*a**2. Factor u(g).
3*(g - 1)**2*(g + 2)
Let o(f) be the second derivative of 5*f + 0 - 7/135*f**6 - 2/27*f**3 + 2/15*f**5 - 1/18*f**4 + 0*f**2. Find b, given that o(b) = 0.
-2/7, 0, 1
Let i(r) be the second derivative of r**4/108 - 5*r**3/27 + 25*r**2/18 + 2*r + 3. Factor i(a).
(a - 5)**2/9
Let a(o) be the first derivative of -5*o**4/24 + o**3/12 + o + 2. Let x(i) be the first derivative of a(i). Find p such that x(p) = 0.
0, 1/5
Factor 16/11*w**2 + 10/11*w**3 + 2/11*w**4 + 0 + 8/11*w.
2*w*(w + 1)*(w + 2)**2/11
Let d(z) be the second derivative of 5*z**4/16 + 11*z**3/4 + 3*z**2 - 22*z. Factor d(i).
3*(i + 4)*(5*i + 2)/4
Let i(h) be the first derivative of 2/3*h**6 + 1 + 1/5*h**5 - h**4 + 0*h + 0*h**2 - 1/3*h**3. Solve i(p) = 0 for p.
-1, -1/4, 0, 1
Suppose -a + 2*a = -6. Let q be ((-1)/(-15))/((-1)/a). Find y, given that 0*y + q*y**3 + 1/5*y**4 + 0 + 1/5*y**2 = 0.
-1, 0
Let o = 393 - 777/2. Factor 3/2*p**2 + o*p + 3.
3*(p + 1)*(p + 2)/2
Let m(c) = -c**3 + 8*c**2 + c - 3. Let j be m(8). Let w be ((-4)/j)/((-18)/15). Find b such that 0*b**2 + 4/3*b - 4/3*b**3 + 2/3*b**4 - w = 0.
-1, 1
Suppose -4*v + 4*u = -2*v, 0 = v - 5*u. Suppose -3*r**4 + v*r**4 - 2*r**5 + r**4 = 0. What is r?
-1, 0
Let b(c) be the first derivative of c**3/3 + 3*c**2/2 + 2*c - 7. Let b(n) = 0. Calculate n.
-2, -1
What is o in 1/2*o**2 + 1/2*o**3 - 5/2*o + 3/2 = 0?
-3, 1
Let f = 55 + -161/3. Factor -f*z**2 - z + 1/3.
-(z + 1)*(4*z - 1)/3
Let z be -1 - 4/(16/(-4)). Suppose 5*l = -4*x, 5*l + 0*l = z. Let -1/4*o + 0*o**2 + 1/4*o**3 + x = 0. What is o?
-1, 0, 1
Let g(j) be the third derivative of 0 - 1/315*j**7 - 1/504*j**8 + 0*j + 0*j**3 + 0*j**6 + 0*j**4 + 8*j**2 + 0*j**5. Factor g(q).
-2*q**4*(q + 1)/3
Let a(d) = d - 1. Let k(s) = 2*s**2 + 6*s - 8. Let p(c) = 2*a(c) - k(c). Suppose p(m) = 0. What is m?
-3, 1
Let p be (6/4)/(21/28). Factor t**2 - t + 5*t - 5*t**2 - p*t + 2*t**3.
2*t*(t - 1)**2
Let n(w) = w**3 + 3*w**2 - w + 14. Let d be n(-4). Let 0*f**3 + 0*f + 1/4*f**4 + 0 - 1/4*f**d = 0. Calculate f.
-1, 0, 1
Factor -1/4*y**2 - 1/2*y + 0.
-y*(y + 2)/4
Let c(k) be the third derivative of -1/168*k**8 + 0 + 0*k - 1/300*k**6 + 0*k**3 + 8/525*k**7 - 1/75*k**5 + k**2 + 0*k**4. Determine p so that c(p) = 0.
-2/5, 0, 1
Let u be (-2)/6 - (-70)/30. Let h be ((-6)/9)/(2/(-4)). Factor 7*f**u + 20/3*f + h.
(3*f + 2)*(7*f + 2)/3
Let n(t) be the second derivative of -t**7/56 - t**6/12 - 7*t**5/80 + t**4/12 + t**3/6 - 9*t. What is c in n(c) = 0?
-2, -1, 0, 2/3
Let x(k) be the third derivative of 1/33*k**4 + 1/330*k**5 + 0*k - k**2 + 0 + 4/33*k**3. Solve x(j) = 0.
-2
Let o(z) be the third derivative of z**10/378000 - z**9/151200 - z**5/12 + z**2. Let p(i) be the third derivative of o(i). What is q in p(q) = 0?
0, 1
Determine p, given that 0 + 3/4*p - 3/4*p**2 = 0.
0, 1
Let h = -363 + 5453/15. Factor 2/15 + h*z - 2/3*z**2.
-2*(z - 1)*(5*z + 1)/15
Let m(j) be the first derivative of -2*j**5/35 - j**4/7 + 2*j**2/7 + 2*j/7 - 4. Factor m(l).
-2*(l - 1)*(l + 1)**3/7
Let k(y) be the second derivative of 2*y**7/735 - y**6/140 + y**5/210 + 2*y**2 + 3*y. Let l(q) be the first derivative of k(q). Let l(i) = 0. Calculate i.
0, 1/2, 1
Let g = -2 - -3. Let u be (1/g)/((-1)/7). Let f(y) = 11*y**2 + 8*y + 7. Let c(p) = 5*p**2 + 4*p + 3. Let a(i) = u*c(i) + 3*f(i). Factor a(s).
-2*s*(s + 2)
Let u(s) be the third derivative of 0*s - 1/5*s**3 - 3/100*s**5 + 0 + 6*s**2 + 7/40*s**4. Factor u(y).
-3*(y - 2)*(3*y - 1)/5
Let r = 40 - 34. Let i(q) be the first derivative of 0*q**3 + 2 + 0*q + 0*q**2 - 1/5*q**5 + 0*q**4 - 1/6*q**r. Determine x, given that i(x) = 0.
-1, 0
Find x, given that 5*x**5 - 140 - 5*x**3 + 140 = 0.
-1, 0, 1
Let g = 146 - 143. Factor 0*h**2 + 0*h + 2/9*h**4 + 2/9*h**g + 0.
2*h**3*(h + 1)/9
Let b = 361/1288 + 1/184. Determine g so that 2/7*g**2 - b*g + 0 = 0.
0, 1
Let w(j) be the third derivative of -j**6/60 + j**5/30 + j**4/6 - 11*j**2. Let w(l) = 0. Calculate l.
-1, 0, 2
Determine h, given that -4*h**3 - 10*h**2 - 5*h**5 - 10 + 1 + 7 + 9*h + 12*h**4 = 0.
-1, 2/5, 1
Let h(w) be the second derivative of -w**8/3360 + w**7/1260 + w**4/12 - 2*w. Let t(v) be the third derivative of h(v). Solve t(k) = 0 for k