1
Let d be (52/(-12))/((-1)/3). Solve -d*j**3 + 16*j**3 + 0*j + j**4 + 2*j**2 + j**2 + j = 0.
-1, 0
Let l(n) = -n**3 + n. Let a(p) = 2*p**3 - 3*p + 1. Let q(w) = 6*a(w) + 11*l(w). Determine o, given that q(o) = 0.
-3, 1, 2
Let p(k) = 3*k**5 - k**4 + 2*k**3 + 2. Let f(a) = 10*a**5 - 4*a**4 + 7*a**3 + 7. Let x(o) = -6*f(o) + 21*p(o). Let x(d) = 0. Calculate d.
-1, 0
Let c(i) be the third derivative of 0*i**3 - 1/90*i**5 + 0 + 0*i + 3*i**2 + 1/180*i**6 - 1/36*i**4 + 1/315*i**7. Solve c(x) = 0 for x.
-1, 0, 1
Suppose 2*a + 2*a - 8 = 0. Let i(b) be the second derivative of 0*b**3 + 1/12*b**4 + 0*b**a + 0 - b. Solve i(n) = 0 for n.
0
Let j(k) be the third derivative of k**8/23520 - k**6/2520 + k**4/6 - 2*k**2. Let l(d) be the second derivative of j(d). Determine v, given that l(v) = 0.
-1, 0, 1
Let p(m) = m**3 - 4*m**2 - 7*m + 5. Let z be p(5). Let a = -3 - z. What is j in 1/2*j**a + 0*j + 1/2*j**5 + 0 + 3/2*j**3 + 3/2*j**4 = 0?
-1, 0
Let d = -1693/7 - -243. Factor -250/7*i**3 + 150/7*i**2 + 0*i - d.
-2*(5*i - 2)**2*(5*i + 1)/7
Let l = -194 + 196. Let -2/5*q + 2/5*q**4 - 2/5*q**l + 2/5*q**3 + 0 = 0. Calculate q.
-1, 0, 1
Let h be (4/(-2))/(2/(-4)). Let i(s) = -19*s**2 + 16*s + 8. Let r(g) = -9*g**2 + 8*g + 4. Let k(j) = h*i(j) - 9*r(j). Solve k(w) = 0.
-2/5, 2
Let h(w) = 9*w + 5. Let y(s) = -s**3 + 9*s + 6. Let z = 9 - 3. Let x(g) = z*h(g) - 5*y(g). Let o(l) = l**3 + 2*l. Let c(a) = -9*o(a) + 2*x(a). Factor c(k).
k**3
Suppose 19/4*j**2 - 2*j - 7/4*j**3 - 1 = 0. Calculate j.
-2/7, 1, 2
Let i(x) = -x**2 - 17*x - 4. Let y(o) = -3*o**2 - 69*o - 15. Let r(c) = -15*i(c) + 4*y(c). Factor r(k).
3*k*(k - 7)
Suppose 3*n = -3*n - 12. Let z be (n/(-21))/(4/7). Find v such that -1/2*v - 1/6*v**3 + 1/2*v**2 + z = 0.
1
What is f in -12*f**4 + f**3 + 8*f**2 - 4*f**3 - f**3 = 0?
-1, 0, 2/3
Suppose -3*n = n. Let p be 174/(-24) + 7 - (-15)/28. Factor -p*t + 2/7*t**2 + n.
2*t*(t - 1)/7
Find n such that 3/2*n - 1/4*n**2 - 2 = 0.
2, 4
Let w(o) be the first derivative of 3*o**5/5 - 3*o**4/2 - o**3 + 3*o**2 - 18. Factor w(t).
3*t*(t - 2)*(t - 1)*(t + 1)
Suppose -5*y = 8*t - 3*t - 5, -4*t + 22 = -2*y. Let u(s) be the second derivative of -2*s + 0 - 1/18*s**3 + 1/36*s**t + 0*s**2. Solve u(b) = 0.
0, 1
Let i(p) be the first derivative of -p**7/420 - p**6/180 + 2*p**3/3 + 1. Let v(b) be the third derivative of i(b). Let v(j) = 0. Calculate j.
-1, 0
Factor -2/3*l**2 + 2*l - 4/3.
-2*(l - 2)*(l - 1)/3
Let q be (22/121 - (-27)/33)*0. Suppose q*p + 1/2*p**2 + 1/4*p**3 + 0 = 0. Calculate p.
-2, 0
Let w = 5 - 3. Solve -3*l + l**4 + l**2 + 3*l - w*l**2 = 0 for l.
-1, 0, 1
Let i(p) be the second derivative of -p**5/20 - 5*p**4/12 - 7*p**3/6 - 3*p**2/2 + 11*p. Find c, given that i(c) = 0.
-3, -1
Let i(o) be the third derivative of -3*o**7/70 + o**6/8 - o**5/20 - o**4/8 + 9*o**2. What is a in i(a) = 0?
-1/3, 0, 1
Let y be 0/(-2 + 3 + -2). Factor y + 1/2*k - 1/2*k**2.
-k*(k - 1)/2
Let h = -256 - -258. Factor 2/5*o**3 + 24/5*o + 16/5 + 12/5*o**h.
2*(o + 2)**3/5
Suppose h = -3*h + 24. Let y(p) = -p**3 + 7*p**2 - 6*p. Let l be y(h). Let l*x**3 - 3*x**3 - 2*x + 5*x**3 = 0. Calculate x.
-1, 0, 1
Let b(p) be the second derivative of -1/6*p**3 + 1/8*p**4 - p + 0 + 1/120*p**6 - p**2 - 1/20*p**5. Let k(q) be the first derivative of b(q). Factor k(s).
(s - 1)**3
Let m(q) be the second derivative of -29/54*q**4 + q + 4/9*q**2 + 0 - 7/30*q**5 - 4/27*q**3. Solve m(k) = 0.
-1, -2/3, 2/7
Let d(i) be the first derivative of -i**7/210 + i**6/120 + i**5/60 - i**4/24 + 5*i**2/2 + 4. Let a(s) be the second derivative of d(s). Factor a(v).
-v*(v - 1)**2*(v + 1)
Let w(a) be the third derivative of a**6/600 + a**5/150 - a**4/30 - 4*a**3/15 + 15*a**2. Factor w(h).
(h - 2)*(h + 2)**2/5
Let h = 19 + -34. Let y be (-11)/h + 3/(-9). Factor -1/5*l**2 - y*l - 1/5.
-(l + 1)**2/5
Determine x, given that -6*x**2 - 2*x**5 + 22/3*x**3 - 8/3 - 32/3*x + 10/3*x**4 = 0.
-1, -1/3, 2
Let c(y) = -7*y**2 + 5*y - 4. Let j(n) = -20*n**2 + 16*n - 11. Let m(q) = 11*c(q) - 4*j(q). Factor m(g).
3*g*(g - 3)
Suppose -2*s - s = -6. Let y be (28/(-10) - (-6)/3)*-1. Solve 0*i**s + 2/5*i**4 - y*i - 2/5 + 4/5*i**3 = 0 for i.
-1, 1
Let s be 3*19/76*(-16)/(-6). Determine y so that 1/2*y**4 + 0 - 1/2*y**s - y + y**3 = 0.
-2, -1, 0, 1
Let g = -2 - -5. Suppose -s - 1 = x, -2 = -2*x - g*s - 7. Factor 3*v - v - 2*v**x - 2*v**3 + 2*v.
-2*v*(v - 1)*(v + 2)
Let w be ((-1 - 5)/12)/(-2 - -1). Factor w*v - 1/4 - 1/4*v**2.
-(v - 1)**2/4
Let r(s) = s**4 - s**3 - s**2 + s + 1. Let g(m) = 3*m**5 - 21*m**4 + 21*m**3 + 9*m**2 - 12*m - 12. Let d(n) = -g(n) - 12*r(n). What is a in d(a) = 0?
0, 1
Solve -2/5*t**3 + 2/5*t - 8/5*t**2 + 8/5 = 0.
-4, -1, 1
Let o(g) be the third derivative of -2*g**7/105 - g**6/10 - g**5/5 - g**4/6 + 3*g**2. Determine x, given that o(x) = 0.
-1, 0
Let i(o) be the second derivative of o**5/20 - 5*o**4/6 - o**3/6 + 7*o**2 + 3*o. Let q be i(10). Solve 2*w + 1/2*w**q + 3*w**2 + 2*w**3 + 1/2 = 0 for w.
-1
Suppose 6 = -f - 6. Let h = f + 37/3. Solve 0 + 1/3*o**2 + 0*o - 1/3*o**4 + 1/3*o**5 - h*o**3 = 0 for o.
-1, 0, 1
Let z(l) be the second derivative of 0*l**3 + 0*l**5 + 0*l**2 + 0*l**4 - 1/15*l**6 - 1/21*l**7 + 3*l + 0. What is x in z(x) = 0?
-1, 0
Let w(m) be the first derivative of 2*m**3/27 - 8*m/9 + 2. Factor w(g).
2*(g - 2)*(g + 2)/9
Let q = -2/37 - -88/259. Let m(s) be the first derivative of 1/14*s**4 - 2 + q*s + 3/7*s**2 + 2/7*s**3. Factor m(b).
2*(b + 1)**3/7
Let s(a) be the third derivative of 0 - a**2 - 1/180*a**5 + 0*a**3 + 0*a + 1/36*a**4. Factor s(t).
-t*(t - 2)/3
Let c(a) be the third derivative of -1/360*a**6 + 0*a - 9*a**2 + 0 + 0*a**4 + 1/630*a**7 + 0*a**5 + 0*a**3. Determine n so that c(n) = 0.
0, 1
Let w(h) = h**3 + 8*h**2 + 6*h - 7. Let k be w(-7). Suppose k*a - a = -2. Factor -1 + 2*t**a - 3/2*t**3 + 5/2*t.
-(t - 2)*(t + 1)*(3*t - 1)/2
Let i(j) be the first derivative of -j**6/180 - 2*j**5/45 - j**4/9 + j**2/2 - 3. Let r(u) be the second derivative of i(u). Let r(g) = 0. What is g?
-2, 0
Find b, given that 4/15*b**3 + 2/3*b**2 - 28/15*b - 16/15 = 0.
-4, -1/2, 2
Let g(a) = -a**2 + 8*a - 3. Let b be g(6). Find c, given that c**2 - 5*c**4 + 3*c + b*c**5 - c - 8*c**2 + 9*c**3 - 8*c**5 = 0.
0, 1, 2
Suppose s = b, -5*s + 14 = 5*b - 3*s. Let h be 3/((-18)/b) - -1. Let 2/3*d**4 - 4/3*d**2 - 4/3*d**3 + h*d**5 + 2/3*d + 2/3 = 0. What is d?
-1, 1
Let g(r) = -10*r**2 + 15*r + 65. Let j(a) = 15*a**2 - 23*a - 98. Let q(v) = -8*g(v) - 5*j(v). Find z, given that q(z) = 0.
-2, 3
Let d = -2/77 + 87/385. Factor 0*q + 0 + 0*q**2 - d*q**3 + 1/5*q**4.
q**3*(q - 1)/5
Let a(y) be the first derivative of -1/3*y**3 + 2*y - 1 - 1/2*y**2. Factor a(f).
-(f - 1)*(f + 2)
Let b(n) be the second derivative of n**6/30 - n**5/5 + n**4/4 - 41*n. Factor b(k).
k**2*(k - 3)*(k - 1)
Suppose -4*o = 2 + 10. Let b(i) = 103*i**2 - 41*i + 6. Let l(g) = -51*g**2 + 21*g - 3. Let q(n) = o*b(n) - 7*l(n). Let q(v) = 0. Calculate v.
1/4
Let a(t) be the first derivative of -9*t**6 - 186*t**5/5 - 355*t**4/6 - 134*t**3/3 - 16*t**2 - 8*t/3 + 4. What is w in a(w) = 0?
-1, -2/9
Let f(k) be the second derivative of k**7/1680 - k**5/240 - k**3 + 8*k. Let j(v) be the second derivative of f(v). Factor j(a).
a*(a - 1)*(a + 1)/2
Suppose -2*q = q - 3. Let b be 0 + (18/10 - q). Suppose -b*k**4 + 0*k**2 + 0 - 2/5*k**3 + 0*k - 2/5*k**5 = 0. What is k?
-1, 0
Let d be 18/(-120) + (-4)/(-10). What is k in -1/4*k**2 + 1/4*k**5 + 0 - 1/4*k**3 + d*k**4 + 0*k = 0?
-1, 0, 1
Let x(k) be the third derivative of 0*k - 1/18*k**5 - 1/36*k**6 - 1/126*k**7 - 5/72*k**4 - 1/1008*k**8 + 0 + 10*k**2 - 1/18*k**3. Factor x(y).
-(y + 1)**5/3
Suppose 5*w = 23 - 8. Factor 9*g - 2 + 1 + w*g**2 + 7.
3*(g + 1)*(g + 2)
Let u(r) be the third derivative of r**5/105 + r**4/3 + 14*r**3/3 - 7*r**2. Suppose u(s) = 0. What is s?
-7
Determine o, given that 15*o + 0*o - 2546*o**2 + 2541*o**2 = 0.
0, 3
Let k(b) be the first derivative of -b**6/6 - 6*b**5/5 - 7*b**4/2 - 16*b**3/3 - 9*b**2/2 - 2*b + 5. Factor k(i).
-(i + 1)**4*(i + 2)
Find j such that -9/2 - 3/4*j**3 - 11*j**2 + j**5 - 51/4*j + 3*j**4 = 0.
-3/2, -1, 2
Let r be 2 + 5*6/15. Let u(g) = 2*g**4 - 3*g**3 + g**2 + 3*g + 3. Let l(n) = -3*n**4 + 4*n**3 - n**2 - 4*n - 4. Let k(t) = r*u(t) + 3*l(t). Solve k(y) = 0.
-1, 0, 1
Let k(f) be the second derivative of 0 +