3
Factor -1/10*j + 1/10*j**2 + 0.
j*(j - 1)/10
Suppose 5*u + 3*y + 6 = 2, -u = 5*y + 14. Let j(h) be the first derivative of 0*h + h**2 + u + 2/3*h**3. Factor j(d).
2*d*(d + 1)
Let a(c) be the third derivative of c**6/1260 + c**5/105 + c**4/28 + 16*c**2. Factor a(m).
2*m*(m + 3)**2/21
Let o = -1976/9 - -220. What is t in -o - 2/9*t**2 + 2/3*t = 0?
1, 2
Let i(n) = -9*n**2 - 9*n + 27. Let m(w) = w**3 + 10*w**2 + 8*w - 28. Let t(s) = -4*i(s) - 3*m(s). Suppose t(g) = 0. Calculate g.
-2, 2
Suppose 4*z + 5*p - 36 = 0, -z - 5*p + 2*p + 16 = 0. Suppose 0 = 3*h - 14 + 2. Factor -3*i**3 - h*i**3 + 3*i**3 - 6*i**z.
-2*i**3*(3*i + 2)
Factor -8/3*q**3 + 4/3*q**2 - 4/3*q**4 + 0 + 8/3*q.
-4*q*(q - 1)*(q + 1)*(q + 2)/3
Let v = -3 + 8. Let p = v - 1. Determine t, given that 4/3*t**3 - 2*t - 4/3*t**2 - 2/3 + 2*t**p + 2/3*t**5 = 0.
-1, 1
What is c in -9/7*c**3 + 69/7*c**2 - 120/7*c - 48/7 = 0?
-1/3, 4
Let y(o) be the second derivative of o**5/30 + 5*o**4/27 - 8*o**3/27 + o. Factor y(c).
2*c*(c + 4)*(3*c - 2)/9
Suppose 4*r + 25 - 67 = -3*g, -g - 2 = 0. Determine c so that -r + 3 + 9 + 4*c**2 - 4*c = 0.
0, 1
Factor 0 + 0*a**2 + a**4 - 5/4*a**3 + 0*a + 1/4*a**5.
a**3*(a - 1)*(a + 5)/4
Factor 4*i - 7 - 12*i**2 - 20*i + 2 + 1.
-4*(i + 1)*(3*i + 1)
Suppose -l = 5*d + 21, 2*l - 2*d + 18 = -2*l. Let n = 2 - l. Factor 3*w + 10*w**2 + 5*w + n*w**2 + 6*w**3 + 2*w**2 - 16.
2*(w + 2)**2*(3*w - 2)
Let t = 146/495 - 4/55. Factor 2/9*g**3 + 0 + t*g**2 - 4/9*g.
2*g*(g - 1)*(g + 2)/9
Let j(g) be the first derivative of g**4/26 - 4*g**3/39 - 4*g**2/13 + 16*g/13 - 10. Determine r, given that j(r) = 0.
-2, 2
Let i(j) be the first derivative of -j**6/540 + j**4/36 + 7*j**3/3 + 5. Let w(v) be the third derivative of i(v). Factor w(m).
-2*(m - 1)*(m + 1)/3
Let n(j) = -30*j**4 + 69*j**3 - 59*j**2 + 9*j. Let v(q) = 15*q**4 - 34*q**3 + 29*q**2 - 4*q. Let m(b) = 6*n(b) + 11*v(b). Find d such that m(d) = 0.
0, 2/3, 1
Let j = 293/2 - 146. Factor -j*q**3 + 0 - 1/2*q + q**2.
-q*(q - 1)**2/2
Let c(l) be the first derivative of -l**3/27 - l**2/6 + 10. Suppose c(v) = 0. What is v?
-3, 0
Let m be (1 + 0)*5/1. Suppose 15 = m*r + 5. Factor -2 + 2*p**5 - 7*p**4 - 4*p**3 + 2*p + 3*p**4 + 4*p**r + 2*p**4.
2*(p - 1)**3*(p + 1)**2
Suppose -6*j + 28 + 32 = 0. Suppose 8*y**2 + 0*y**3 - j*y - 22 + 26 - 2*y**3 = 0. Calculate y.
1, 2
Determine h, given that -h + 4*h**2 + 3*h + 4*h + 2*h = 0.
-2, 0
Let z be (-24)/(-16)*(-4)/(-6). Let t be z + 3/9*0. Factor -4*h - 3*h**2 + 1 - 1 - h**3 - t + h.
-(h + 1)**3
Suppose -5*z - 19 = i - 2*i, 2*i - 5*z = 23. Let t(o) be the first derivative of -3 - 1/14*o**i + 0*o + 0*o**2 + 2/21*o**3. Factor t(b).
-2*b**2*(b - 1)/7
Let c(m) = -5*m**5 + 7*m**4 + m**3 - 3*m. Let x(o) = 9*o**5 - 13*o**4 - o**3 + 5*o. Let u(l) = -5*c(l) - 3*x(l). Factor u(j).
-2*j**3*(j - 1)**2
Suppose 0 - 22/15*f**4 - 14/15*f**3 + 22/15*f**2 - 4/15*f + 6/5*f**5 = 0. What is f?
-1, 0, 2/9, 1
Suppose -2*x + 4*x - 6 = 0. Suppose -3*t - 5*s = -t, 0 = 3*t + x*s. Factor -1/3*f + t - 1/3*f**2.
-f*(f + 1)/3
Let v(o) be the second derivative of -o**4/6 - o**3/3 + 2*o**2 - 37*o. Factor v(g).
-2*(g - 1)*(g + 2)
Let c(g) = -2*g - 14. Let s be c(-9). Suppose 11*a = 13*a - s. Suppose -1/2*y**a + 0*y + 1/2 = 0. What is y?
-1, 1
Let d(k) = k + 1. Let v(z) = -z**2 + 8*z + 1. Let u = 16 - 19. Let b(t) = u*v(t) + 12*d(t). Solve b(j) = 0.
1, 3
Let d be 0 + (0 - 2) + 9. Suppose 0 = -w + g + 1, 2*w + 5*g = 3*w + d. Let m**2 - m**5 - w*m**3 - m**4 + 4*m**3 + 0*m**2 = 0. Calculate m.
-1, 0, 1
Determine v, given that -4*v**3 - v - 15*v**2 - 16*v**3 - 4*v + 10*v = 0.
-1, 0, 1/4
Let b(r) be the first derivative of 0*r**3 + 1/8*r**2 + 6 - 1/16*r**4 + 0*r. Factor b(j).
-j*(j - 1)*(j + 1)/4
Let z(s) be the third derivative of -s**5/60 + s**4/12 - s**3/6 + 3*s**2. Solve z(v) = 0 for v.
1
Let k(q) = -q**4 + q**3 - q. Let z(n) = -25*n**4 - 12*n**3 + 5*n**2 - 3*n. Let l(r) = 5*k(r) - z(r). Determine y, given that l(y) = 0.
-1, -1/4, 0, 2/5
Let s(m) be the third derivative of -m**8/21 + 2*m**7/105 + 2*m**6/5 - 11*m**5/15 + m**4/3 + 2*m**2. Suppose s(y) = 0. Calculate y.
-2, 0, 1/4, 1
Let l be (-54)/(-72) - (-14)/(-24). What is d in l*d**2 + 1/3 - 1/2*d = 0?
1, 2
Let -2/9*j**2 + 0 + 2/9*j**3 - 4/9*j = 0. Calculate j.
-1, 0, 2
Let m(v) = v + 5. Let p be m(0). Find c such that -4*c + 3*c**2 + p*c + 3*c**4 - 6*c**3 - c = 0.
0, 1
Let s(n) = 3*n**3 + 12*n**2 - 3*n + 6. Let o(u) = 19*u**3 - 17*u**3 - 3*u + 5 + 6*u**2 + 5*u**2. Let w(c) = 6*o(c) - 5*s(c). Factor w(k).
-3*k*(k - 1)**2
Let g(d) = 3*d**3 - 3*d**2 + 2. Let z = 2 + -2. Suppose 0 = 4*n - z*n - 20. Let a(x) = -7*x**3 + 6*x**2 + x - 5. Let h(k) = n*g(k) + 2*a(k). Factor h(j).
j*(j - 2)*(j - 1)
Suppose -10 = -5*p - m + 8, 10 = 2*p - m. Suppose 0 = -5*x + 3*x + 4. Factor 0 - 3*l - 3*l + 10*l**x - p.
2*(l - 1)*(5*l + 2)
Let x = -2 - -14. Let d = x + -7. Factor -4*i + i**4 + 6*i**2 + 1 + 4*i**3 + 3*i + d*i.
(i + 1)**4
Let f be (-2)/8 + 86/336. Let j(n) be the third derivative of 0*n - f*n**8 - 1/105*n**7 - 2*n**2 + 0*n**4 + 1/60*n**6 + 0 + 1/30*n**5 + 0*n**3. Factor j(a).
-2*a**2*(a - 1)*(a + 1)**2
Let q(d) be the first derivative of -3*d**3/2 + 3*d**2/2 + 3*d/2 - 9. Suppose q(v) = 0. Calculate v.
-1/3, 1
Let n(f) = f. Let z(l) = -l**2 - 4*l - 20. Let y(o) = 6*n(o) - z(o). Let w be y(-8). Factor 1/5*t**w + 1/5*t**3 - 1/5*t**5 + 0*t + 0 - 1/5*t**2.
-t**2*(t - 1)**2*(t + 1)/5
Let i be (-20)/35 + 39/7. Let d(z) be the second derivative of 0 + 1/16*z**i - 7/48*z**4 + 1/12*z**3 - 2*z + 0*z**2. Factor d(s).
s*(s - 1)*(5*s - 2)/4
Factor 2*s**2 + 40*s**4 - 41*s**4 - s**2.
-s**2*(s - 1)*(s + 1)
Let q(x) be the third derivative of 0*x**4 + 0 + 1/945*x**7 - 1/270*x**5 + 0*x**3 + 0*x + 0*x**6 - x**2. Factor q(u).
2*u**2*(u - 1)*(u + 1)/9
Suppose -m**3 + 11*m**3 + 5*m**2 - 10*m + 39*m**4 - 44*m**4 = 0. Calculate m.
-1, 0, 1, 2
Suppose -5*q + 15 = -10. Find d such that 6/11*d**2 + 0 - 2/11*d**q - 2/11*d**3 + 4/11*d - 6/11*d**4 = 0.
-2, -1, 0, 1
Suppose 4/5*u**2 - 8/5*u - 12/5 = 0. Calculate u.
-1, 3
Let i be 42/(-44) - (-6)/3. Let s = i - 6/11. Solve 0 - s*y**3 + 0*y + 1/2*y**2 = 0 for y.
0, 1
Let f(w) = 7*w**3 + 18*w**2 + 81*w + 6. Let k(l) = 13*l**3 + 36*l**2 + 162*l + 11. Let v(m) = -11*f(m) + 6*k(m). Factor v(u).
u*(u + 9)**2
Let m(d) be the second derivative of d**4/6 + 7*d**3/3 + 6*d**2 + 3*d + 3. Find f such that m(f) = 0.
-6, -1
Let g = 0 + -8. Let x = -8 - g. Let 0*o + 1/2*o**3 + 1/2*o**4 + x*o**2 + 0 = 0. Calculate o.
-1, 0
Let f(s) be the third derivative of -s**8/90720 - s**5/15 - 2*s**2. Let d(b) be the third derivative of f(b). Let d(l) = 0. Calculate l.
0
Let a = -2 - -15. Let z = -13 + a. Factor z + 2/5*i**2 - 2/5*i**4 + 2/5*i**3 - 2/5*i.
-2*i*(i - 1)**2*(i + 1)/5
Let o(z) = -6*z**4 - 3*z**3 - z**2 + 2. Let y(p) = -p**4 - p**2 + 1. Let h(c) = -o(c) + 2*y(c). Factor h(f).
f**2*(f + 1)*(4*f - 1)
Let x be 10/(-70) - (-4)/28. Let -18/13*l**3 + 0 + x*l**2 + 8/13*l = 0. Calculate l.
-2/3, 0, 2/3
Let c = -22 - -26. Let m(j) be the second derivative of -3/2*j**c - 1/15*j**6 + 1/2*j**5 + 0 + 2*j - 2*j**2 + 7/3*j**3. Determine k so that m(k) = 0.
1, 2
Let p be ((-1)/2)/(3/(-12)). Let f(r) be the second derivative of r - 1/36*r**4 - 1/18*r**3 + 0 + 0*r**p. Factor f(z).
-z*(z + 1)/3
Let a = -31/3 - -11. Factor -1/3*o**2 - 1/3*o**4 + 0*o + 0 - a*o**3.
-o**2*(o + 1)**2/3
Let p(i) be the first derivative of -4*i**3/21 - 6*i**2/7 - 8*i/7 + 28. Determine z, given that p(z) = 0.
-2, -1
Let o(h) be the second derivative of -h**8/10080 - h**7/1890 - h**6/1080 - h**4/3 - 4*h. Let k(n) be the third derivative of o(n). Determine r so that k(r) = 0.
-1, 0
Let i = -21 + 65/3. Factor -2/3*q**5 - 4/3*q**2 + 2*q - i + 2*q**4 - 4/3*q**3.
-2*(q - 1)**4*(q + 1)/3
Suppose 5*v - 243 = -223. Solve -1/2*l**3 + 0 + 1/4*l**v + 0*l + 1/4*l**2 = 0 for l.
0, 1
Let s(k) be the third derivative of 0*k**7 + 0 + 1/84*k**4 + 1/1176*k**8 + 0*k**5 + 0*k**3 - 1/210*k**6 + 4*k**2 + 0*k. Suppose s(a) = 0. Calculate a.
-1, 0, 1
Let n(w) be the third derivative of -w**8/84 - 2*w**7/21 - 3*w**6/10 - 7*w**5/15 - w**4/3 + 11*w**2. Factor n(h).
-4*h*(h + 1)**3*(h + 2)
Let b(c) be the second derivative of c**5/90 - c**4/9 + 4*c**3/9 + 3*c**2/2 + c. Let p(t) be the first derivative of b(t). Factor p(r).
2*(r - 2)**2/3
Suppose 0 = 2*r - 2*o -