-2*r**3 - r**3 + 6*r**q - 13*r + 3*r + 4 + 5*r**3 - 2*r**4.
-2*(r - 1)**3*(r + 2)
Factor 1/2*q - 3/4 + 1/4*q**2.
(q - 1)*(q + 3)/4
Let z(k) be the second derivative of k**9/756 - k**8/210 + k**6/45 - k**5/30 - 7*k**3/6 - 5*k. Let g(m) be the second derivative of z(m). What is s in g(s) = 0?
-1, 0, 1
Suppose 3*w - 2 = 10. Suppose 3*q**4 - 4*q**4 - q**3 + w*q**2 - 3*q**2 + q = 0. What is q?
-1, 0, 1
Let d(w) be the third derivative of w**6/300 - w**5/150 + 7*w**2. Factor d(j).
2*j**2*(j - 1)/5
Let m(q) = q**3 - q + 1. Let x(n) = 2*n**3 + 2*n - 2. Let j(s) = -2*m(s) - x(s). Factor j(p).
-4*p**3
Let b = 38074668 - 33810301037/888. Let m = -1/296 + b. Factor -m*o**2 - 32/3*o - 8/3.
-2*(o + 2)*(7*o + 2)/3
Let w = 7 + -12. Let o = w + 7. Factor -o*q**4 + 0*q**5 - 2*q**5 + 0*q**5.
-2*q**4*(q + 1)
Let i(y) = -5*y**2 - 7*y - 7. Let b(g) = 3*g**2 + 4*g + 4. Let c(p) = 7*b(p) + 4*i(p). Factor c(h).
h**2
Let m(j) = j**2. Let r(p) = -p**3 + 2*p**2 - 3*p + 1. Let a(h) = -m(h) - r(h). Factor a(b).
(b - 1)**3
Let a = -3 - -7. Suppose 17 = -n - a*k, 5*n - 25 = 3*k - k. Factor 0 - 1/3*l**n + 2/3*l**2 - 1/3*l.
-l*(l - 1)**2/3
Let t = -13 + 44/3. Factor -5/3*q**4 - 2/3*q + t*q**2 + 0 + 2/3*q**3.
-q*(q - 1)*(q + 1)*(5*q - 2)/3
Let x(m) be the second derivative of m**6/600 - m**5/40 + m**4/10 + 2*m**3/3 - 9*m. Let p(w) be the second derivative of x(w). Suppose p(y) = 0. What is y?
1, 4
Factor -s**2 - 2*s + 2*s**3 + 6*s - 5*s**2.
2*s*(s - 2)*(s - 1)
Let j = 3/14 - -19/42. Let c(s) be the first derivative of 7/6*s**4 + 2/5*s**5 + 3 - j*s**2 - 5/9*s**6 + 0*s - 2/3*s**3. Suppose c(f) = 0. Calculate f.
-1, -2/5, 0, 1
Suppose p = 9 - 6. Let -j - p*j**4 - 3*j**5 - 2*j**2 + 4*j**3 + 3*j**4 + 3*j**4 - j**4 = 0. What is j?
-1, -1/3, 0, 1
Let g(n) be the third derivative of -2*n**2 - 1/168*n**8 + 0 - 1/12*n**4 + 0*n**5 + 0*n + 0*n**3 + 1/30*n**6 + 0*n**7. Factor g(q).
-2*q*(q - 1)**2*(q + 1)**2
Let q be 3/6 + ((-26)/6 - -4). Factor 0 + q*y**2 + 1/6*y.
y*(y + 1)/6
Let c(z) = -2*z**2 - 21*z - 4. Let j(r) = -r**2 + r. Let d(f) = c(f) + 5*j(f). Factor d(v).
-(v + 2)*(7*v + 2)
Let b = 362/9 - 116/3. Factor -20/9*q**2 - b*q - 2/9 + 4*q**3 + 6*q**4 - 6*q**5.
-2*(q - 1)**2*(3*q + 1)**3/9
Let z be (189/28)/((-3)/(-8)). Suppose 19*q**5 - z*q**5 - 2*q**4 + 3*q**3 - q**4 - q**2 = 0. What is q?
0, 1
Let a be ((-9)/(-3) - 2)*1. Suppose 0 = -5*g + 15, 5*g - 18 = -j - a. Factor p**j + p + 1/3 + 1/3*p**3.
(p + 1)**3/3
Suppose 0 = o + 4*o - 35. Factor -o*d**4 - 5*d**4 + 14*d**4.
2*d**4
Let w be (-10)/4*1/(-5). Factor -g - w*g**2 - 1/2.
-(g + 1)**2/2
Let u = 265/2 - 132. Factor 0 + u*n**2 + 1/2*n.
n*(n + 1)/2
Factor -6*u - 1/4*u**3 + 5 + 9/4*u**2.
-(u - 5)*(u - 2)**2/4
Suppose 0 = -f + 7*f - 12. Factor 3/2*l**3 + 3*l**f - 3/2*l - 3.
3*(l - 1)*(l + 1)*(l + 2)/2
Let x be (-4)/(-12) + 8/(-6). Let l be x/2 + 51/54. Factor 0*c**4 + l*c**2 + 2/9*c**5 + 0*c - 2/3*c**3 + 0.
2*c**2*(c - 1)**2*(c + 2)/9
Let i = -382/19 + 3919/228. Let g = 19/6 + i. Factor g*d**2 + 1/2 + 3/4*d.
(d + 1)*(d + 2)/4
Let d = -16 - 4. Let h = -14 - d. Factor w - 3*w**2 + 6*w**2 - h*w**2.
-w*(3*w - 1)
Suppose -2/3*m**2 + 10/3 - 8/3*m = 0. What is m?
-5, 1
Let w be (-12)/(-18) + 10/3. What is m in -1 + 5 + m**3 - 3*m**3 + 2*m - w*m**2 = 0?
-2, -1, 1
Let m(u) be the first derivative of u**6/36 + u**5/30 - u**4/24 - u**3/18 - 6. Factor m(i).
i**2*(i - 1)*(i + 1)**2/6
Suppose 0 = -3*w + 2*w. Let 41*b**3 - 44*b**3 + 3*b**4 + w*b**4 = 0. Calculate b.
0, 1
Factor -1/3*k**2 - 1/2*k**3 + 1/2*k + 1/3.
-(k - 1)*(k + 1)*(3*k + 2)/6
Let t be ((-6)/8)/((-6)/24). Find j, given that -3*j**2 + j**2 + 3*j**3 - j**2 + 0*j - 3*j + t*j**4 = 0.
-1, 0, 1
Let p(c) = 2*c**4 - 2*c**3 - 4*c**2. Let z(l) = -3*l**4 + l**3 + 4*l**2. Let t(x) = 7*p(x) + 6*z(x). Factor t(f).
-4*f**2*(f + 1)**2
Suppose 2 = m - 0. Factor -o**3 - 4*o**2 - 5*o**3 - m*o + 4*o**3.
-2*o*(o + 1)**2
Suppose -3*d + 12*d - 45 = 0. Let z(q) be the first derivative of -1/6*q**3 - 3/8*q**4 + 0*q**2 + 0*q + 2/5*q**d - 4. Find w such that z(w) = 0.
-1/4, 0, 1
Let k be -1 + 3*(-2)/(-6). Suppose -5*x - x = k. Solve 2/11 + 4/11*z**3 - 2/11*z**4 - 4/11*z + x*z**2 = 0 for z.
-1, 1
Let u(a) be the third derivative of 1/540*a**6 + 0*a + 0*a**5 - 1/315*a**7 + 6*a**2 + 0 + 0*a**3 + 0*a**4 + 1/756*a**8. Factor u(q).
2*q**3*(q - 1)*(2*q - 1)/9
Let w(z) be the third derivative of z**6/180 + z**5/30 + z**3/6 - 3*z**2. Let y(d) be the first derivative of w(d). Suppose y(p) = 0. Calculate p.
-2, 0
Suppose -t + 3 = -0*t. Suppose -4*w + 1 = -7. Find a such that a**t - a - a**2 + 2*a - a**w = 0.
0, 1
Let y(t) be the first derivative of 0*t - 1 + 1/2*t**2 + 0*t**5 + 1/300*t**6 + 0*t**3 - 1/60*t**4. Let m(l) be the second derivative of y(l). Factor m(h).
2*h*(h - 1)*(h + 1)/5
Suppose 0 - 2/7*s**2 + 2/7*s = 0. What is s?
0, 1
Solve -3/4*i**2 - 3/4*i**3 + 0 + 0*i = 0 for i.
-1, 0
Let b be (0 - -2)/((-68)/(-153)). Solve -3/2*q**2 - b*q - 3 = 0.
-2, -1
Let z(j) be the first derivative of 2*j**3/15 + j**2/5 - 37. Factor z(w).
2*w*(w + 1)/5
Let g(z) = 4*z**3 + 2*z**2 - 3. Let n(v) = -8*v**3 + 0*v - 5*v**2 - v**3 + 7 + 0*v. Let d(o) = -7*g(o) - 3*n(o). Find h such that d(h) = 0.
0, 1
Let u(t) be the second derivative of 7*t - 110/21*t**7 + 0*t**4 + 64/15*t**6 + 0*t**2 - 4/5*t**5 + 0 + 0*t**3. Let u(k) = 0. What is k?
0, 2/11, 2/5
Suppose 2*v = i + 30, 168 = -7*i + 2*i + 4*v. Let z be 2/i + (-8)/(-16). Factor z*h - 2/9*h**2 - 2/9.
-2*(h - 1)**2/9
Let i(b) = b**3 - 4*b**2 + 3*b. Let w be i(3). Factor y**2 + w*y**2 - y + 3*y + 1.
(y + 1)**2
Let a(y) be the first derivative of y**6/360 - y**5/40 + y**4/12 - y**3/3 - 3. Let u(o) be the third derivative of a(o). Determine p so that u(p) = 0.
1, 2
Let m be 4/9 - (-8 + (-560)/(-72)). Suppose 0 + 0*p - m*p**3 - 2/3*p**2 = 0. Calculate p.
-1, 0
Let a be (-2)/((-4)/10) - 0. Let r(j) = 2*j**2 - 4*j + 2. Let t be r(2). Solve -6*c**a - 22*c**3 + c**2 + 3*c**2 + 4*c - t*c**2 + 22*c**4 = 0.
-1/3, 0, 1, 2
Let l(d) = -d**2 + 10*d - 1. Let y(k) = k + 1. Let m(z) = l(z) - 4*y(z). Let i be m(5). Factor 0 + 0*p + 2/5*p**5 + 0*p**3 + 0*p**4 + i*p**2.
2*p**5/5
Let q be (-2)/20*-34 + (-12)/(-20). Suppose 0 = 2*h - 0 - 4. Factor -4*w**h - 13*w - w**4 - q*w**3 - w**2 + 11*w.
-w*(w + 1)**2*(w + 2)
Let l(u) be the first derivative of u**6/9 + 2*u**5/5 + u**4/2 + 2*u**3/9 + 7. Solve l(g) = 0.
-1, 0
Factor -159*g**2 - 2*g**5 - 15*g**3 + 164*g**2 + 15*g**4 - 3*g**5.
-5*g**2*(g - 1)**3
Suppose 0 = -5*s + 8 + 7. Factor 1/2*q**s - 1/2*q - 1/2*q**4 + 1/2*q**2 + 0.
-q*(q - 1)**2*(q + 1)/2
Let r = -12 + 22. Suppose 0 = 2*m - 5*f - r, 3 + 1 = 3*m - 2*f. Let 0*w**2 + m + 2/3*w**4 + 0*w + 1/3*w**5 + 1/3*w**3 = 0. What is w?
-1, 0
Let u(a) be the third derivative of 1/600*a**6 + 0 + 1/300*a**5 - 1/1050*a**7 + 0*a - 1/120*a**4 + 2*a**2 + 0*a**3. What is f in u(f) = 0?
-1, 0, 1
Let h(x) be the first derivative of 4*x**3/3 - 4*x**2 + 4*x - 3. Factor h(m).
4*(m - 1)**2
Let h(z) be the second derivative of -z**4/4 - 3*z**3 - 27*z**2/2 - 3*z. Factor h(p).
-3*(p + 3)**2
Let y(b) be the second derivative of b**7/315 - 2*b**5/75 - b**4/45 + b**3/15 + 2*b**2/15 + 4*b. Suppose y(o) = 0. Calculate o.
-1, 1, 2
Let d(h) = -2*h**5 + 2*h**4 + 4*h**3 + 4*h**2 - 2*h + 2. Let u(r) = -4*r**5 + 5*r**4 + 7*r**3 + 8*r**2 - 5*r + 5. Let x(t) = -5*d(t) + 2*u(t). Factor x(w).
2*w**2*(w - 2)*(w + 1)**2
Let c(l) = 2*l**4 + 4*l**3 - 2*l**2 - 7*l - 3. Let o(f) = -f. Let x(d) = -4*d - 1. Let k(w) = 3*o(w) - x(w). Let s(n) = -c(n) - 3*k(n). Factor s(m).
-2*m*(m - 1)*(m + 1)*(m + 2)
Let k(r) be the second derivative of -r**4/102 + r**3/51 + 2*r - 30. Factor k(o).
-2*o*(o - 1)/17
Suppose -117*t**4 + 221*t**2 + 0*t**3 - 42*t**5 - 36*t + 22*t**3 + 11*t**3 - 24 - 35*t**2 = 0. What is t?
-2, -2/7, 1/2, 1
Let w(r) be the first derivative of -6*r**3/5 + 21*r**2/10 - 6*r/5 - 7. Factor w(j).
-3*(2*j - 1)*(3*j - 2)/5
Let s(n) = n**3 - 2*n**2 + n. Let m be s(2). Factor 4*r**m + 1 - 1 + 3*r - 2*r.
r*(4*r + 1)
Let t(a) be the first derivative of 0*a**2 + 1/21*a**3 - 1/42*a**4 - 2*a + 2. Let s(v) be the first derivative of t(v). Factor s(c).
-2*c*(c - 1)/7
Let f(i) be the third derivative of -i**6/300 - i**5/150 - 5*i**2 + 3. Solve f(n) = 0.
-1, 0
Let z(k) be the second derivative of -2*k**7/147 + 2*k**5/35 - 2*k**3/21 + 11*k. Determine f, given that z