**4/48 - 3*k**2/2 + k. Let m(a) be the first derivative of h(a). Factor m(w).
-w*(w - 1)*(w + 1)**2/2
Let y(b) be the second derivative of b**6/30 + b**5/30 - b**4/6 - b**3/3 - 3*b**2/2 - b. Let v(s) be the first derivative of y(s). Let v(i) = 0. Calculate i.
-1, -1/2, 1
Let c(d) = -9*d - 1. Let v be c(-1). Factor -5 + 2*n**2 + 0 + 1 + 6*n**3 - v*n + 2*n**4 + 2*n.
2*(n - 1)*(n + 1)**2*(n + 2)
Suppose 2/9*d**2 + 0 - 4/9*d = 0. What is d?
0, 2
Let w(p) be the second derivative of p**4/66 + 2*p**3/11 + 9*p**2/11 + 50*p. Factor w(i).
2*(i + 3)**2/11
Let h(k) = -3*k**3 + 3*k**2 + 20*k - 22. Let t(n) = 65*n**3 - 65*n**2 - 440*n + 485. Let s(q) = -45*h(q) - 2*t(q). Factor s(g).
5*(g - 2)*(g - 1)*(g + 2)
Let p(g) be the second derivative of 3*g**5/40 - g**4/8 - 21*g. Let p(w) = 0. Calculate w.
0, 1
Let y(u) be the first derivative of u**3/3 - u**2 + u + 7. Factor y(s).
(s - 1)**2
Let u be (-1)/(36/32 - 1). Let k be (u/(-4) + -4)/(-1). Factor -4/5*n**3 + 0*n**k + 0*n**4 + 2/5*n + 0 + 2/5*n**5.
2*n*(n - 1)**2*(n + 1)**2/5
Suppose -12 = b - 3*o, 8 + 4 = 5*b + 3*o. Let a(h) be the second derivative of 0 - 1/2*h**2 + b*h**3 + 1/12*h**4 + 3*h. Factor a(y).
(y - 1)*(y + 1)
Let u(a) be the third derivative of -a**6/420 - a**5/70 + a**4/84 + a**3/7 - 48*a**2. Determine f, given that u(f) = 0.
-3, -1, 1
Let x(v) be the first derivative of -3*v**4/28 - 4*v**3/7 - 6*v**2/7 + 7. Suppose x(c) = 0. Calculate c.
-2, 0
Let j(z) be the third derivative of -1/90*z**5 - 3*z**2 + 0*z + 0*z**4 + 0*z**3 + 0 - 1/180*z**6. Factor j(t).
-2*t**2*(t + 1)/3
Let d(p) = p**3 - 5*p**2 + 4. Let y be 4 - (-2)/(2 - 0). Let a be d(y). Factor -4/7*z + 6/7*z**2 + 0*z**3 - 2/7*z**a + 0.
-2*z*(z - 1)**2*(z + 2)/7
Let u = 89/4 + -22. Let o(s) be the first derivative of 1 - 1/4*s - u*s**2 - 1/12*s**3. Factor o(v).
-(v + 1)**2/4
Let f(c) be the first derivative of -3*c**5/5 + 3*c**4/2 - 12. Let f(q) = 0. What is q?
0, 2
Solve 7*r**3 - 4*r**2 - 6*r**3 + r**3 = 0 for r.
0, 2
Suppose 5*r - 6 = u, u - 4*r + 0*r + 4 = 0. Factor v**5 + 0*v**4 + 0*v**u - v**3.
v**3*(v - 1)*(v + 1)
Let l(j) = j**3 + 23*j**2 + 43*j + 24. Let u be l(-21). Solve -1/2*t**4 - 1/2*t - 1/2 - 1/2*t**5 + t**2 + t**u = 0 for t.
-1, 1
Let j be 1 - (-5)/(15/6). Let m be j - ((1 - 1) + 1). Let 6/5*n - 4/5 - 2/5*n**m = 0. What is n?
1, 2
Let c(q) = 2*q + 3. Let s(f) = -f - 1. Let o(v) = c(v) + 3*s(v). Let l be o(-7). Factor -l*n**2 + 2 + 2*n**2 + 3*n**2.
-2*(n - 1)*(n + 1)
Let x(y) = -y**3 + 10*y**2 + 2. Let l be x(10). Let v(c) be the third derivative of 0 + 1/240*c**5 + 0*c**3 + 0*c + c**l + 1/96*c**4. Factor v(r).
r*(r + 1)/4
Let a(d) = 2*d**2 - 3*d - 3. Let n(v) be the second derivative of -v**4/4 + 2*v**3/3 + 2*v**2 - v. Let q(f) = 4*a(f) + 3*n(f). Factor q(w).
-w**2
What is o in 330/17*o**2 - 32/17 + 730/17*o**3 + 422/17*o**4 - 52/17*o + 42/17*o**5 = 0?
-8, -1, -1/3, 2/7
Let z(g) = 6*g - 26. Let s be z(6). Let d(k) be the first derivative of 22*k**3 + 32/5*k**5 + 2*k + 1 - s*k**2 - 20*k**4. Factor d(i).
2*(i - 1)**2*(4*i - 1)**2
Suppose -2*s + 6 = 2*i - 2, i - 1 = 0. Suppose -2/3*u**4 + 0*u**s + 0*u + 4/3*u**2 - 2/3 = 0. What is u?
-1, 1
Let q(t) be the first derivative of 1/18*t**6 - 6 - 1/4*t**4 + 0*t**2 + 0*t - 2/15*t**5 + 0*t**3. Factor q(r).
r**3*(r - 3)*(r + 1)/3
Let h(n) = n**3 - 3*n**2 + 2*n - 1. Let g be h(3). Solve 4*y**g - 7*y**2 + y**3 + 2*y**4 + 11*y**2 - 11*y**3 = 0.
-2, 0, 1/2, 1
Let a(y) be the second derivative of y**6/225 - y**4/90 + 18*y. Determine k, given that a(k) = 0.
-1, 0, 1
Let q(n) = -7*n**2 - 12*n + 9. Let u(p) = 7*p**2 + 11*p - 8. Let v(w) = -6*q(w) - 7*u(w). Let v(x) = 0. Calculate x.
-1, 2/7
Let g = -495/2 - -260. Find t such that -2*t + 0 - 8*t**2 + g*t**4 - 5/2*t**3 = 0.
-2/5, 0, 1
Let p(u) be the third derivative of -u**7/420 - 3*u**2. Let p(z) = 0. What is z?
0
Let u(j) be the third derivative of j**8/1680 + j**7/525 - j**6/200 + 36*j**2. Determine q so that u(q) = 0.
-3, 0, 1
Let h(n) be the third derivative of n**7/350 + n**6/100 + 5*n**2. Factor h(a).
3*a**3*(a + 2)/5
Factor -2/3 - 8/9*z - 2/9*z**2.
-2*(z + 1)*(z + 3)/9
Let v(l) = l**4 - l**3 + l - 1. Let f(g) = 4*g**4 - 2*g**3 - 2*g**2 + 5*g - 5. Let o(i) = -3*f(i) + 15*v(i). Factor o(x).
3*x**2*(x - 2)*(x - 1)
Let z(b) = -b**2 - 5*b + 3. Let i be (10/8)/(1/(-4)). Let f be z(i). Factor -1/3*o**f + 1/3*o**2 + 1/3*o - 1/3*o**4 + 0.
-o*(o - 1)*(o + 1)**2/3
Suppose 5*p = 4*p + 2. Let d(r) be the second derivative of -4/7*r**2 - 1/42*r**4 - 4/21*r**3 + 0 + p*r. Solve d(n) = 0.
-2
Let w be 2/(-21)*(-7 + 65/10). Let d(v) be the first derivative of 0*v**3 + 0*v**4 - 1 + 0*v + w*v**6 + 0*v**2 + 0*v**5. Factor d(u).
2*u**5/7
Let l(v) = -v. Let h be l(-2). Suppose -4*q + k + 7 = 0, 0 = -5*q - 5*k + 15. Factor -c**2 + h + q*c**4 + c**2 - 4*c**2.
2*(c - 1)**2*(c + 1)**2
Let b(c) be the second derivative of c**7/28 - c**6/15 - c**5/40 + c**4/12 + 2*c. Suppose b(d) = 0. Calculate d.
-2/3, 0, 1
Let z(i) be the first derivative of 3 + 1/8*i**2 + 1/12*i**3 + 0*i. What is x in z(x) = 0?
-1, 0
Factor -12 + 6*w**4 + 24*w**3 - 8*w**2 - 3*w**5 + 25*w - 46*w + 14*w**2.
-3*(w - 4)*(w - 1)*(w + 1)**3
Let t(c) be the second derivative of c**7/210 + 7*c**6/150 + 3*c**5/20 + 13*c**4/60 + 2*c**3/15 - c + 1. Factor t(m).
m*(m + 1)**3*(m + 4)/5
Let l be 2 - (3 - (-10)/(-8)). Let 0 + 1/4*z**2 + 0*z + l*z**3 = 0. Calculate z.
-1, 0
Let w(r) = r**2 - 6*r - 2. Let q(m) = 1. Let x(y) = -6*q(y) - 3*w(y). Factor x(t).
-3*t*(t - 6)
Let 4/9*i**2 - 4/9*i**4 - 4/9*i + 4/9*i**3 + 0 = 0. Calculate i.
-1, 0, 1
Let x be 2/(-6)*(-2 - 4). Find a, given that 4*a - x*a**2 - 5*a**2 + 5*a**2 - 2 = 0.
1
Let p(b) = -b**2 + 4*b + 1. Let u be p(2). Factor -u*w**3 + 14*w**2 + 4*w**3 - 14*w**4 - 3*w**3 + 4*w.
-2*w*(w - 1)*(w + 1)*(7*w + 2)
Let k(s) = 2*s**2 + 2*s + 1. Let q be k(-1). Let c(p) = 4*p**2 + 2*p. Let v(n) = n**2 + n. Let t(f) = q*c(f) - 3*v(f). Determine l so that t(l) = 0.
0, 1
Suppose 3*r + 2 = 4*w - 2, 3*w = -4*r + 28. Find c such that -3/4*c**4 - 29/4*c**2 - 1 + 5*c + w*c**3 = 0.
1/3, 1, 2
Suppose 3*i = -5*a + 24, 3*a - 11 = i + 9. Suppose -a*y = -4*y - 8. Solve 0*m + 6*m**2 - y*m**2 - 2*m = 0 for m.
0, 1
Suppose 2*t + 0*t = 0. Suppose 0*x + 4*x - 8 = t. Let 0*y - 2/5 + 2/5*y**x = 0. What is y?
-1, 1
Let r(h) be the second derivative of -h**6/75 + h**5/50 + h**4/15 - 18*h. Find p such that r(p) = 0.
-1, 0, 2
Let i = -22 + 24. Suppose -5*l = -i*m - 18, -8 = -l - l + m. Determine b, given that 24/5*b**3 - 4/5 + 26/5*b - 46/5*b**l = 0.
1/4, 2/3, 1
Let x(p) be the third derivative of p**7/42 - p**5/2 + 5*p**4/3 - 5*p**3/2 + 5*p**2. Factor x(h).
5*(h - 1)**3*(h + 3)
Let j = -3 - -31/10. Let u(t) be the first derivative of j*t**4 - 1 - 3/5*t**2 + 0*t**3 + 4/5*t. Factor u(r).
2*(r - 1)**2*(r + 2)/5
Suppose 11 = 4*s - 2*w - 13, -2*s + 2*w = -8. Factor 4*g + 5 - 7 + s - 2*g**2.
-2*(g - 3)*(g + 1)
Factor 7*d**4 - 24*d + 9*d**2 - 6*d - 44*d**2 - 2*d**4.
5*d*(d - 3)*(d + 1)*(d + 2)
Let p(y) = -y**3 + 4*y**2 - 9*y + 20. Let q be p(3). Factor 8/3*t**q + 8/9*t - 14/9*t**3 + 0.
-2*t*(t - 2)*(7*t + 2)/9
Factor 3/5*u**5 + 9/5*u**4 + 0*u**3 + 0*u + 0 - 12/5*u**2.
3*u**2*(u - 1)*(u + 2)**2/5
Let -2/7*v**3 + 0 - 10/7*v**2 - 8/7*v = 0. What is v?
-4, -1, 0
Let k(x) = -2*x - 9. Let c be k(-6). Let 14*p**2 + 10*p**c + 11*p**2 + 2*p - 9*p**2 + 2*p**4 + 6*p = 0. Calculate p.
-2, -1, 0
Let f(p) = p**2 - 5*p - 1. Let m(d) = d**2 - 6*d. Let b(t) = -3*f(t) + 2*m(t). Let y be b(3). Factor i**2 + 5/2*i**y + 0*i + 0 - 7/2*i**4.
-i**2*(i - 1)*(7*i + 2)/2
Solve 2/5*z**4 - 4/5*z**2 + 2/5 + 0*z + 0*z**3 = 0 for z.
-1, 1
Let o = -103 - -106. Let 15/2*p - 3 - 3*p**o - 3/2*p**2 = 0. What is p?
-2, 1/2, 1
Suppose v + 6 = 3. Let l be 2 + -2 + (-2)/v. Factor 2/3*g**4 - 2/3*g + 0 - l*g**2 + 2/3*g**3.
2*g*(g - 1)*(g + 1)**2/3
Suppose 7 = -13*z + 33. Factor 2/9*t**3 - 2/9*t + 2/9 - 2/9*t**z.
2*(t - 1)**2*(t + 1)/9
Let o(y) = 24*y**3 + 24*y**2 + 14*y. Let a(s) = -3*s + 0*s + 2*s**2 - 7*s**2 + s**3 - 6*s**3. Let m(n) = 14*a(n) + 3*o(n). Suppose m(l) = 0. What is l?
-1, 0
Let r = -41 - -291/7. Factor -r*f**2 - 2/7*f - 2/7*f**3 + 0.
-2*f*(f + 1)**2/7
Let h(s) be the first derivative of s**5 - 15*s**4/4 - 10*s**3/3 + 30*s**2 - 40*s - 42. Suppose h(x) = 0. Calculate x.
-2, 1, 2
Let h(l) be the second derivative of -1/15*l**4 