 - 6/5*r**3 - 2/5*r**4 + 0 - 2/5*r = 0?
-1, 0
Suppose 3*k - 2 - 7 = 0. Let h = k - -1. Factor h*u + 10*u**2 - 8*u**2 + 3*u**4 - 5*u**4 - 4*u**3.
-2*u*(u - 1)*(u + 1)*(u + 2)
Let u be 1 + 1 - (3 - 7). Let n(q) = -q**3 + 6*q**2 + 2. Let h be n(u). Suppose -18*a**h - 1 - 21*a**3 + 21*a + a**4 + 4 + 11*a**4 + 3 = 0. What is a?
-1, -1/4, 1, 2
Let z(y) = -y**3 - 7*y**2 + 9*y + 11. Let b be z(-8). Suppose 0*t - b*t + 9 = 0. Factor 0 - 2/9*c - 2/3*c**t + 8/9*c**2.
-2*c*(c - 1)*(3*c - 1)/9
Let d(p) be the third derivative of 1/210*p**7 - 1/120*p**6 + 0*p + 0*p**3 + 1/24*p**4 + 0 - 1/60*p**5 - 2*p**2. Factor d(m).
m*(m - 1)**2*(m + 1)
Suppose -8*z + 32 - 16 = 0. Factor 4/5*n**3 + 2/5*n**4 - 2/5*n + 2/5 - 4/5*n**z - 2/5*n**5.
-2*(n - 1)**3*(n + 1)**2/5
Let k(b) be the second derivative of b**4/36 - 2*b**2/3 - 16*b. Factor k(z).
(z - 2)*(z + 2)/3
Let b = -2 + 6. Factor 5*i**5 + 5*i**b + 10*i**3 + 0 + 1 - 4*i**5 + 10*i**2 + 5*i.
(i + 1)**5
Let p(j) be the second derivative of j**8/840 + j**7/140 + j**6/90 - 5*j**3/6 + 3*j. Let d(u) be the second derivative of p(u). Factor d(q).
2*q**2*(q + 1)*(q + 2)
Let p(z) = -2*z + 12. Let b be p(5). Let w(a) be the first derivative of b + 1/10*a**5 + a**2 + 1/2*a + 1/2*a**4 + a**3. Factor w(i).
(i + 1)**4/2
Let t be ((-600)/2450)/((-2)/7). Determine c, given that -6/7*c**2 + t + 9/7*c**3 - 9/7*c = 0.
-1, 2/3, 1
Let w(u) be the first derivative of u**3/3 - 3*u**2 + 9*u + 12. Factor w(m).
(m - 3)**2
Let s(m) be the third derivative of m**7/105 - m**6/30 - m**5/30 + m**4/6 - 30*m**2. Factor s(j).
2*j*(j - 2)*(j - 1)*(j + 1)
Suppose 8*v - 16*v**2 - 44*v**2 - 88*v**4 + 122*v**3 - 49*v**5 + 67*v**4 = 0. Calculate v.
-2, 0, 2/7, 1
Factor -8*m + 3*m**2 - 36 - 2*m**2 - 16*m - 5*m**2.
-4*(m + 3)**2
Factor -146*n - 734*n**2 - 360*n**3 - 104*n - 35*n**4 - 241*n**2.
-5*n*(n + 5)**2*(7*n + 2)
Let m(l) be the third derivative of -l**9/3360 + l**8/2016 + 4*l**7/2835 + l**6/810 - l**5/30 - l**2. Let q(h) be the third derivative of m(h). Factor q(s).
-2*(s - 1)*(9*s + 2)**2/9
Find f such that 0*f**3 - f**2 - 2*f**2 + f**4 - 4*f**4 + 6*f**3 = 0.
0, 1
Let o(r) = -r - 10. Let g be o(-13). Factor -4*b - 1/3*b**g - 2*b**2 - 8/3.
-(b + 2)**3/3
Let n(f) be the second derivative of -f**4/6 + 2*f**3/3 + 3*f**2 - 4*f. Solve n(s) = 0.
-1, 3
Let z(u) be the second derivative of 0*u**2 + 0 - 2/65*u**5 + 4*u + 2/39*u**4 + 1/195*u**6 + 0*u**3. What is q in z(q) = 0?
0, 2
Let g(y) be the third derivative of y**7/1050 - y**6/600 - y**5/100 + y**4/120 + y**3/15 + 37*y**2. Factor g(m).
(m - 2)*(m - 1)*(m + 1)**2/5
Suppose -5*h - 2 = -3*t - 4*h, -2*t - h - 2 = 0. Determine r so that -15/4*r**2 - 9/4*r**3 + t + 3/4*r**5 - 3/2*r + 3/4*r**4 = 0.
-1, 0, 2
Let p(g) be the second derivative of 0 + 1/9*g**2 + 5*g - 2/27*g**3 + 0*g**4 - 1/135*g**6 + 1/45*g**5. Determine s so that p(s) = 0.
-1, 1
Let d = 4 + 0. Suppose 3*b = b + d. Factor -2*y + 2*y**3 - y**b + y**2.
2*y*(y - 1)*(y + 1)
Let u(i) be the second derivative of 0*i**2 - 4*i + 0 - 1/36*i**4 - 1/18*i**3 + 1/90*i**6 + 1/60*i**5. Factor u(y).
y*(y - 1)*(y + 1)**2/3
Let j = -1/4 - -1/2. Let r(m) be the first derivative of 2 + 1/4*m**2 - j*m - 1/12*m**3. Suppose r(a) = 0. What is a?
1
Suppose 0*a**2 - 2/9*a**3 + 2/9*a + 0 = 0. What is a?
-1, 0, 1
Suppose -15 = -2*k - k. Let o be (-2)/(-7) - (-4)/(-14). Factor -4*y**3 + 4*y**4 + o + 14*y**4 - 14*y**k + 0.
-2*y**3*(y - 1)*(7*y - 2)
Determine j so that -2/5*j**2 - 12/5*j - 18/5 = 0.
-3
Let g(y) be the second derivative of -3/2*y**2 - 3/20*y**5 + 1/4*y**4 - 6*y + 1/2*y**3 + 0. Factor g(a).
-3*(a - 1)**2*(a + 1)
Let l(f) be the third derivative of -1/270*f**5 - 1/54*f**4 + 0*f - 1/27*f**3 - 2*f**2 + 0. Solve l(m) = 0 for m.
-1
Suppose -28 = -16*u + 20. Factor -1/4*o**4 + 0*o - 1/2*o**2 + 0 - 3/4*o**u.
-o**2*(o + 1)*(o + 2)/4
Suppose 2*z = -0*z + 12. Suppose -z = -c - 3. Factor 2*h**c + 3*h**2 + 1/2 + 1/2*h**4 + 2*h.
(h + 1)**4/2
Let s(w) = w**2 + 2*w + 1. Let j be s(-3). Suppose 0 = -3*d + 5*d - j. Factor 4*a + 0*a**3 - a**5 - 5*a + d*a**3.
-a*(a - 1)**2*(a + 1)**2
Let c(d) = -d**3 + 14*d**2 - 4*d. Let b(p) = -5*p**3 + 55*p**2 - 15*p. Let q(x) = -4*b(x) + 15*c(x). Factor q(k).
5*k**2*(k - 2)
Suppose -6*w = -2*w + r, -5*r = 0. Let q be (5 - 2) + w/1. Suppose 4*b**4 - 3*b**4 - b**3 - q*b**4 - b**3 = 0. What is b?
-1, 0
Let s(o) be the third derivative of o**6/840 - o**4/56 + o**3/21 - 9*o**2. Factor s(x).
(x - 1)**2*(x + 2)/7
Let w(m) be the first derivative of 2*m**3/15 - 2*m**2/5 + 2*m/5 - 3. Factor w(q).
2*(q - 1)**2/5
Let m be (-3)/(-1) - (-322)/(-126). Suppose m*o**4 + 2/9*o**3 + 0*o - 2/9*o**5 + 0 - 4/9*o**2 = 0. What is o?
-1, 0, 1, 2
Let r = -4 + 4. Suppose 0*o - o - 3*j - 6 = 0, r = -o + 5*j + 10. Let 6*v**3 + o*v**3 - 3*v - 3*v**5 + 0*v**3 = 0. Calculate v.
-1, 0, 1
Let j = 905/4 - 226. Factor -j + 0*r + 1/4*r**2.
(r - 1)*(r + 1)/4
Let o(u) be the first derivative of u**3/5 + 3*u**2/5 + 3*u/5 - 10. Factor o(x).
3*(x + 1)**2/5
Let t(f) be the third derivative of f**6/1020 + f**5/510 - f**4/102 + 33*f**2. Find r, given that t(r) = 0.
-2, 0, 1
Let z(n) = 2*n**2 - 9*n - 3. Let k be z(5). Let i be (-26)/(-24) + 2/8. Factor -k*f**2 - 2/3*f**3 + 10/3*f + 2/3*f**4 - i.
2*(f - 1)**3*(f + 2)/3
Let n(a) be the second derivative of a**6/6 - 5*a**4/12 + 11*a. Factor n(k).
5*k**2*(k - 1)*(k + 1)
Let a(y) be the first derivative of y**4/6 - 2*y**3/3 + y**2 - 2*y/3 - 2. Determine k, given that a(k) = 0.
1
Suppose -5*z = -5*v + 15, -6 = z - 2*v + 2. Factor -2*b**2 - b**4 + b**2 + 2*b**z + 0*b**4.
-b**2*(b - 1)*(b + 1)
What is m in 4/13*m**4 - 16/13*m**2 - 2/13*m**5 + 0 + 6/13*m**3 + 8/13*m = 0?
-2, 0, 1, 2
Let m(c) = -1. Let a(i) = -i**2 - 5*i + 2. Let w be a(-5). Let h(r) = 13*r + 7*r**w - 4*r + 0*r**2. Let v(p) = -h(p) + 2*m(p). Solve v(f) = 0.
-1, -2/7
Suppose 0 = 2*y + 2*o - 0*o - 16, -11 = -2*y - o. Determine r so that 0*r**2 + 1 - y*r**3 - r**2 + 3*r + 2*r**3 - 2*r = 0.
-1, 1
Factor 3/2*a**4 - 6*a**2 + 0 + 0*a - 9/2*a**3.
3*a**2*(a - 4)*(a + 1)/2
Let p(m) = 5*m**3 + m + 1. Let i be p(-1). Let a(y) = y + 5. Let b be a(i). Determine r, given that r**2 - 1 + 2 + b*r**2 - r - 3 = 0.
-1, 2
Let c be (3/21)/(-1) + 1. Let w = -26 + 29. Factor 4/7 - 6/7*u + c*u**w - 4/7*u**2.
2*(u - 1)*(u + 1)*(3*u - 2)/7
Let c be (-12)/(-30) + 132/(-105) + 2. Let -6/7*p**3 + 2/7*p**5 - 8/7*p**2 + c*p + 0 + 4/7*p**4 = 0. What is p?
-2, 0, 1
Factor -3/7*w**2 - 4/7*w**4 + w**3 + 0 + 0*w.
-w**2*(w - 1)*(4*w - 3)/7
Let p(c) be the third derivative of c**7/735 + c**6/210 + c**5/210 + c**2. Factor p(v).
2*v**2*(v + 1)**2/7
Let i(n) be the second derivative of n**9/15120 - n**8/2240 + n**7/1260 - n**4/4 + 4*n. Let t(w) be the third derivative of i(w). Factor t(g).
g**2*(g - 2)*(g - 1)
Let w(k) be the first derivative of -20/3*k**3 - 1 + 14*k - 3*k**2. Let h(d) = -d**2 - d + 1. Let q(s) = 12*h(s) - w(s). Factor q(a).
2*(a - 1)*(4*a + 1)
Let w(y) be the second derivative of 3*y**4/2 + 20*y**3/3 + 4*y**2 - 19*y. Solve w(d) = 0 for d.
-2, -2/9
Let -8/7*u**2 + 1/7*u**5 + 2/7*u**4 - 2/7 - u - 2/7*u**3 = 0. What is u?
-1, 2
Let u be 848/24 - 1/3. Let j = u + -33. Factor -2/3*g**5 - 2/3*g + 0 + 8/3*g**j - 4*g**3 + 8/3*g**4.
-2*g*(g - 1)**4/3
Let s be (3/(-12))/(4/(-8)). Factor -1/2*a**5 + 0 + 0*a + s*a**4 + 1/2*a**3 - 1/2*a**2.
-a**2*(a - 1)**2*(a + 1)/2
Let x(l) be the third derivative of -l**10/15120 - l**9/3780 + l**7/630 + l**6/360 + l**4/8 - 6*l**2. Let j(u) be the second derivative of x(u). Factor j(g).
-2*g*(g - 1)*(g + 1)**3
Suppose -3*o + o = -4. Factor -h + 1/2 + 1/2*h**o.
(h - 1)**2/2
Find v such that -5/2*v**2 - 4*v + 2 = 0.
-2, 2/5
Let r(m) be the third derivative of m**7/105 + 13*m**6/300 + 2*m**5/75 - m**4/15 + 5*m**2. Suppose r(v) = 0. What is v?
-2, -1, 0, 2/5
Let z(w) be the first derivative of 3*w**4/4 - w**3 - 15. Determine l so that z(l) = 0.
0, 1
Let s(d) be the second derivative of -d**6/30 + d**5/5 - 7*d**4/16 + 11*d**3/24 - d**2/4 + d. Solve s(n) = 0 for n.
1/2, 1, 2
Let n(a) be the second derivative of 7/3*a**3 + 0 + a**2 + 49/24*a**4 - 3*a. Factor n(l).
(7*l + 2)**2/2
Let y(a) = -6*a**2 - 10. Let l(h) = h**2 + 1. Let r(t) = 8*l(t) + y(t). Factor r(i).
2*(i - 1)*(i + 1)
Let l(s) be the third derivative of 5*s**8/84 + s**7/6 + s**6/12 - s**5/12 + 9*s**2. Let l(n) = 0. Calculate