 0
Suppose 6*m - 46 = 2. Let a(r) = 3*r**2 - 5*r - 8. Let i(c) = -4*c**2 + 8*c + 12. Let h(j) = m*a(j) + 5*i(j). Factor h(t).
4*(t - 1)*(t + 1)
Let d(z) be the first derivative of -24 - 30*z + 35/2*z**2 - 5/3*z**3. Factor d(r).
-5*(r - 6)*(r - 1)
Let g(c) be the third derivative of c**7/630 - 2*c**6/45 + 8*c**5/15 - 3*c**4/8 - 3*c**2. Let j(d) be the second derivative of g(d). Let j(i) = 0. Calculate i.
4
Let f(t) = t**4 + t**3 - 2*t**2. Let j be 1 - (-2 + 2) - -6. Suppose j - 4 = q. Let o(y) = y**4 - y**3. Let v(c) = q*f(c) - 6*o(c). Suppose v(h) = 0. What is h?
0, 1, 2
Let s = -10515/7 + 1503. Solve -2/7*g**4 + 0 - 6/7*g + s*g**3 + 2/7*g**2 = 0.
-1, 0, 1, 3
Suppose 4*i + 3 = 2*r + 21, 0 = 4*i + 4*r. Suppose -n + i = w, -4*w = -2*w. Solve 6*m**2 + n*m - 6 + 0*m - 6*m**3 + 3*m**3 = 0.
-1, 1, 2
Let f(c) be the second derivative of 23*c**5/330 - 25*c**4/132 + 2*c**3/33 + 5*c**2/2 + 43*c. Let d(l) be the first derivative of f(l). Factor d(m).
2*(m - 1)*(23*m - 2)/11
Let d(y) = y**2 - 2. Let b(u) = -5*u**3 - 117*u**2 + 5*u + 114. Let i(g) = b(g) - 3*d(g). Factor i(k).
-5*(k - 1)*(k + 1)*(k + 24)
Let l = 825 + -823. Let a(u) be the first derivative of -2/21*u**3 - 1 - 2/7*u + 2/7*u**l. Determine m, given that a(m) = 0.
1
Let i be (6/4)/(2/4). Suppose 24*o = 61*o - 74. Factor 2*r**3 + 0*r**4 - i*r**4 + 3*r**4 + o*r**4.
2*r**3*(r + 1)
Let l be -170*(-10)/45 + 2/9. Let s be l/228 + (-67)/(-30) + -2. Solve -s*y + 0 + 6/5*y**3 - 4/5*y**2 = 0.
-1/3, 0, 1
Let u be (-2)/(-12) - (3 - (-84)/(-24)). Let s(q) be the second derivative of 1/12*q**4 + 2*q**2 + 0 + u*q**3 + q. Factor s(w).
(w + 2)**2
Let q(p) be the first derivative of -1/3*p**3 + 5/16*p**4 + 1/8*p**2 - 1/10*p**5 + 51 + 0*p. Factor q(x).
-x*(x - 1)**2*(2*x - 1)/4
Let w(s) be the second derivative of -7*s**6/360 - 19*s**5/120 + s**4/4 + s**3 + 6*s. Let l(m) be the second derivative of w(m). Factor l(t).
-(t + 3)*(7*t - 2)
Suppose 5*b + 5*j - 35 = 0, 4*b + j - 16 = -0*b. Factor 0*g**b + 6*g - 8*g**2 + 2 + 2*g**3 + 14*g**2.
2*(g + 1)**3
Suppose 9/4 + 3/4*k**2 - 3*k = 0. What is k?
1, 3
Let t = 12 + 3. Solve 14*n**2 + 0 + 12*n - t - 11*n**2 = 0 for n.
-5, 1
Suppose -22898/3 - 2/3*u**2 + 428/3*u = 0. What is u?
107
Let g(w) be the second derivative of -w**5/4 + 25*w**4/12 + 20*w**3/3 - 120*w**2 + 19*w + 7. Factor g(x).
-5*(x - 4)**2*(x + 3)
Let j = 542/5 - 539/5. Determine p, given that 1/5*p**5 + 3/5*p**3 + 0 + j*p**4 + 1/5*p**2 + 0*p = 0.
-1, 0
Let v be 3 - (-3 + (-177)/6*2). Factor 74*w + 4 + 10*w**3 + 24*w**2 - 121*w + v*w.
2*(w + 1)**2*(5*w + 2)
Let u(q) be the first derivative of 2*q**5/65 - q**4/13 - 40*q**3/39 - 24*q**2/13 - 97. Factor u(g).
2*g*(g - 6)*(g + 2)**2/13
Let c = 1296 + -1292. Factor 4/5*o**c - 2/5*o**3 + 0*o + 0*o**2 + 0 - 2/5*o**5.
-2*o**3*(o - 1)**2/5
Let p(x) = x + 8. Let o be p(-6). Let h be 0 + (-704)/(-120) - 4/(-30). Factor 23*f**o + 1 - h*f - 15*f**2 - 1.
2*f*(4*f - 3)
Let 0*f - 4*f**2 + 0 - 1/9*f**4 + 4/3*f**3 = 0. Calculate f.
0, 6
Let b = -4270590 - -1550225129/363. Let d = b - -3/121. Factor d - 4/3*m**2 - 4/3*m.
-4*(m - 1)*(m + 2)/3
Let q(z) = z - 8 + 3*z - 3*z. Let t be q(13). Factor -a**t + 5*a**2 + 3*a**3 - 6*a**2 - a**2.
-a**2*(a - 1)**2*(a + 2)
Suppose 0 + 32*i**3 + 26/3*i**4 + 2/3*i**5 + 24*i**2 + 0*i = 0. What is i?
-6, -1, 0
Let w(y) = -7*y**2 + 12*y - 3. Let d(h) be the first derivative of 2*h**3 - 11*h**2/2 + 4*h + 8. Let u(t) = 6*d(t) + 5*w(t). Factor u(j).
(j - 3)**2
Let j(w) = w**2 + 6*w + 4. Let c be (27/(-12))/(-2 + (-19)/(-8)). Let o be j(c). Factor 2/5*r**3 + 0*r**2 + 0 - 4/5*r**o + 0*r + 2/5*r**5.
2*r**3*(r - 1)**2/5
Let x(b) be the first derivative of -b**5/10 - 3*b**4/2 + 42*b - 32. Let m(n) be the first derivative of x(n). Solve m(i) = 0.
-9, 0
Let q = -347/35 + 61/5. Let n = -2 + q. Factor 2/7*m**3 - 6/7*m**2 - n*m + 2/7*m**4 + 4/7.
2*(m - 1)**2*(m + 1)*(m + 2)/7
Let i = 21355/7 + -3049. Factor 0*n - 3/7*n**2 + i.
-3*(n - 2)*(n + 2)/7
Let p(g) = -6*g**3 - 2*g**2 + 14*g + 6. Let i(w) = 7*w**3 + 2*w**2 - 15*w - 9. Let v(o) = 4*i(o) + 5*p(o). Factor v(l).
-2*(l - 1)**2*(l + 3)
Suppose 2*s = 12 - 2. Let z be 0 + 15/s - (-14)/(-6). Solve -1/3*b**2 - 1/3*b + z = 0 for b.
-2, 1
Let t(g) be the second derivative of 9/4*g**4 + 6*g**2 + 0 + 6*g**3 + 9*g. Factor t(z).
3*(3*z + 2)**2
Let s(l) be the third derivative of l**5/140 + l**4/4 - 15*l**3/14 - 415*l**2. Determine h, given that s(h) = 0.
-15, 1
Factor -5 + 13*g - 8*g + 3*g - 3*g - g**2 + g.
-(g - 5)*(g - 1)
Let w(d) be the third derivative of -d**8/2184 - d**7/455 + d**6/780 + d**5/130 - 19*d**2 + 2*d. Find i such that w(i) = 0.
-3, -1, 0, 1
Let p(h) be the first derivative of -4*h**5/5 + h**4 + 28*h**3/3 - 26*h**2 + 24*h + 134. Suppose p(d) = 0. Calculate d.
-3, 1, 2
Let h be 1/(-3)*(-5 + (-2 - -7)). Let o(c) be the third derivative of 0 + 1/72*c**6 + 0*c**4 + 5*c**2 + 1/90*c**5 + 0*c - 1/90*c**7 + h*c**3. Factor o(w).
-w**2*(w - 1)*(7*w + 2)/3
Let z(b) = 16*b**4 + 60*b**3 + 61*b**2 + 15*b - 14. Let h(m) = -16*m**4 - 60*m**3 - 60*m**2 - 16*m + 16. Let v(c) = 3*h(c) + 4*z(c). Let v(i) = 0. What is i?
-2, -1, 1/4
Let q = -571 - -576. Let w(p) be the first derivative of -2/5*p**2 + 0*p + 1/10*p**4 + 2/15*p**3 + q. Factor w(r).
2*r*(r - 1)*(r + 2)/5
Suppose 3*s + 36 = 42. Let -12 + 12*j + 13*j - 37*j - 38*j + 18*j**s = 0. What is j?
-2/9, 3
Let b = 36 + -36. Let k be (b + 1)*(-4 + 13). Let 12*i**2 + k*i - 3*i**3 - 12*i**2 - 6 = 0. Calculate i.
-2, 1
Find z, given that 50/3*z - 9*z**2 + 4 + 1/3*z**4 - 27/2*z**3 + 3/2*z**5 = 0.
-2, -2/9, 1, 3
Let b(u) be the first derivative of -u**4/28 + 23*u**3/7 + 165. Suppose b(p) = 0. Calculate p.
0, 69
Let -5/4*f**3 + 7/2*f - 17/4*f**2 + 2 = 0. Calculate f.
-4, -2/5, 1
Suppose -16 = 7*i - 877. Solve 3*c**2 - i*c**3 + 125*c**3 - c**2 = 0.
-1, 0
Factor -1/2*s**5 - s + 0 - 5/2*s**4 - 9/2*s**3 - 7/2*s**2.
-s*(s + 1)**3*(s + 2)/2
Let b(i) be the second derivative of -i**4/36 - i**3/3 + 7*i**2/6 - i - 10. Factor b(m).
-(m - 1)*(m + 7)/3
Let w(j) be the first derivative of j**4 + 328*j**3/3 - 166*j**2 + 68. Factor w(x).
4*x*(x - 1)*(x + 83)
Let q = -10090/11 + 918. Let p = 40 + -38. Find t such that -2/11*t**p - q*t - 8/11 = 0.
-2
Factor -2*a + 16/3*a**2 + 0*a**4 - 4*a**3 + 2/3*a**5 + 0.
2*a*(a - 1)**3*(a + 3)/3
Let z(m) be the second derivative of m**4/36 - 23*m**3/18 - 4*m**2 - 959*m. What is i in z(i) = 0?
-1, 24
Suppose -24/5*w + 12 - 3/5*w**2 = 0. What is w?
-10, 2
Let r(f) be the first derivative of 5*f**3/9 + 10*f**2/3 - 20*f - 335. Let r(g) = 0. Calculate g.
-6, 2
Suppose 0 = w - 3*m - 5, -2*m - 6 + 0 = -2*w. Suppose 4*c - w*p = 0, -4*p + 14 + 2 = 0. Factor -52*d**3 + d - c*d - 12*d**2 - 16*d**4 + d.
-4*d**2*(d + 3)*(4*d + 1)
Suppose -9 = -9*c + 18. Factor 4*b**c + 4*b - 8*b**2 + 13*b - 29*b.
4*b*(b - 3)*(b + 1)
Let h(w) be the second derivative of -5*w**4/48 - 5*w**3/2 - 175*w**2/8 + 34*w. Factor h(t).
-5*(t + 5)*(t + 7)/4
Let c(b) be the second derivative of -1/28*b**5 + 2/105*b**6 + 0*b**3 + 0 + 1/42*b**4 + 52*b + 0*b**2 - 1/294*b**7. Find i, given that c(i) = 0.
0, 1, 2
Determine k, given that 5 - 9*k**2 + 155*k + 25 - 43*k**2 + 2*k**2 - 5*k**2 = 0.
-2/11, 3
Let 984*t**2 + 884 - 3*t**5 - 484*t**3 + 96*t**4 - 1467 - t**5 - 880*t + 871 = 0. Calculate t.
1, 2, 18
Suppose 8/9*k - 10/9*k**3 + 0*k**2 + 2/9*k**5 + 0 + 0*k**4 = 0. What is k?
-2, -1, 0, 1, 2
Let 0*f + 0 - 48/5*f**3 - 4/5*f**4 - 144/5*f**2 = 0. What is f?
-6, 0
Let n be (-6)/(-4) - 36/(-24). Let a(l) be the first derivative of -l**n + 16*l + 7*l**4 - 6*l**4 - 4 - 3*l**3. Factor a(g).
4*(g - 2)**2*(g + 1)
Let q be (-62)/(-8) - 15/(-60). Factor 26 - h**2 - 8*h - 16 - 9 - q.
-(h + 1)*(h + 7)
Suppose 0 = -8*z + 7 + 25. Let -7*m**3 + 4*m**5 + 0*m**3 + 3*m**3 + 4*m**2 - z*m**4 + 0*m**4 = 0. Calculate m.
-1, 0, 1
Suppose -10*z + 5*z = -4*x + 8, -3*x = z - 6. Let j(o) be the second derivative of 1/20*o**4 + 5*o + 0*o**3 - 3/10*o**2 + z. Factor j(c).
3*(c - 1)*(c + 1)/5
Find k, given that 0 - 2/7*k + 1/7*k**2 = 0.
0, 2
Let d(i) be the second derivative of i**8/560 - 3*i**7/280 + i**6/40 - i**5/40 - 7*i**3/3 - 18*i. Let f(t) be the second derivative of d(t). Factor f(q).
3*q*(q - 1)**3
Let m(j) be the third derivative of j**7/1680 - j**6/160 + 13*j**5/480 - j**4/16 + j**3/12 - 2*j**2 + 74. Factor m(i).
(i - 2)*