 + 0*z + 0 = 0.
-1/4, 0
Factor -1/4*t**3 - t + 0 - t**2.
-t*(t + 2)**2/4
Find p, given that 0 - 3/4*p**4 - 1/4*p**2 - 1/4*p + 5/4*p**3 = 0.
-1/3, 0, 1
Let f(b) = 4*b**3 + 16*b**2 + 16*b - 36. Let d(k) = 8*k**3 + 31*k**2 + 33*k - 72. Let m(h) = -4*d(h) + 9*f(h). Factor m(g).
4*(g - 1)*(g + 3)**2
Let j(k) be the first derivative of 1/16*k**5 - 1/12*k**4 - 2 + 1/24*k**3 + 2*k - 1/60*k**6 + 0*k**2. Let a(w) be the first derivative of j(w). Factor a(i).
-i*(i - 1)**2*(2*i - 1)/4
Let g(l) be the first derivative of -l**4/6 + 20*l**3/27 + 8*l**2/9 + 47. Factor g(a).
-2*a*(a - 4)*(3*a + 2)/9
Let m(x) be the second derivative of -5*x**7/42 - x**6/10 + 7*x**5/20 + x**4/4 - x**3/3 + 34*x. Solve m(q) = 0 for q.
-1, 0, 2/5, 1
Let k(t) = -4*t - 3. Let p be k(-2). Let q(i) be the third derivative of -1/300*i**p + i**2 + 1/40*i**4 - 1/15*i**3 + 0*i + 0. Factor q(s).
-(s - 2)*(s - 1)/5
Let m(w) be the second derivative of w**4/78 - w**2/13 - 7*w. Determine p so that m(p) = 0.
-1, 1
What is o in 102*o**2 + 69*o - 2*o**5 - 16*o**3 + 88*o**3 + 5*o**5 + 18 + 24*o**4 = 0?
-3, -2, -1
Let o(r) be the third derivative of r**5/75 + r**4/6 + 26*r**2. Factor o(h).
4*h*(h + 5)/5
Suppose -3*p + 10 + 2 = 0. Suppose 8*r + 4 = p*r + 4*h, -3*r - 5*h = -21. Factor 2/3*a**2 + 4/3 + r*a.
2*(a + 1)*(a + 2)/3
Suppose 1 - 21 = -5*c. Let o = 33/140 + 1/70. Factor 1/4 + 1/4*g**c - o*g**5 + 1/2*g**3 - 1/4*g - 1/2*g**2.
-(g - 1)**3*(g + 1)**2/4
Let g be ((-5)/15)/((-1)/18). Solve -5*h**3 - 4*h**2 + 2*h**3 - h**2 + 2*h**2 + g*h = 0 for h.
-2, 0, 1
Suppose -3*h + 2*s = -14, 2*h = -3*s + 2 + 3. Factor 3*w**2 - 11*w - w - 4 + h*w**2.
(w - 2)*(7*w + 2)
Let k be (-2)/(-1)*10/4. Let l be (6/15)/(1/k). Let -3*b**4 - l*b**4 + 4*b**4 + b**2 = 0. What is b?
-1, 0, 1
Let q = 649 + -175229/270. Let z(t) be the third derivative of 0 + 0*t**3 + q*t**5 + 4*t**2 + 0*t + 1/108*t**4. Factor z(u).
2*u*(u + 1)/9
Let h be (16/52 - 0)*10. Suppose 0 - 46/13*d**3 - h*d**2 - 14/13*d**4 - 8/13*d = 0. Calculate d.
-2, -1, -2/7, 0
Let j = -57 - -59. Suppose -4/5*a - 6/5*a**4 + 4/5*a**3 + 0 + 6/5*a**j = 0. What is a?
-1, 0, 2/3, 1
Let c = -65 - -67. Let 2/5*b + 2/5*b**c + 0 = 0. What is b?
-1, 0
Let t(g) be the first derivative of g**5/20 - 5*g**4/16 + 2*g**3/3 - g**2/2 - 1. Factor t(d).
d*(d - 2)**2*(d - 1)/4
Let v(j) be the first derivative of j**6 + 4*j**5 + 13*j**4/6 - 40*j**3/9 + 4*j**2/3 - 6. Factor v(s).
2*s*(s + 2)**2*(3*s - 1)**2/3
Suppose 5*x - 9 = 21. Let c(a) be the second derivative of 0*a**4 + 0*a**x + 1/70*a**5 + 0*a**2 + 0*a**3 - 1/147*a**7 + 0 + a. Factor c(o).
-2*o**3*(o - 1)*(o + 1)/7
Let y(k) be the first derivative of 7/4*k**6 + k**3 + 33/8*k**4 + 24/5*k**5 + 0*k**2 + 0*k + 5. Let y(w) = 0. Calculate w.
-1, -2/7, 0
Let u(w) be the second derivative of -w**6/1800 - w**5/600 + w**4/60 - 5*w**3/6 - w. Let i(y) be the second derivative of u(y). Find a such that i(a) = 0.
-2, 1
Factor 0 + 1/2*x - 1/4*x**2.
-x*(x - 2)/4
Factor 0*m - 144 - 3144*m**2 + 3140*m**2 + 48*m.
-4*(m - 6)**2
Determine r so that 314/9*r**2 - 44*r**3 - 88/9*r + 18*r**4 + 8/9 = 0.
2/9, 1
Let g be -1 + 0 + -1 - -9. Let z = 9 - g. Factor -12*x**3 - 35*x**2 - 13*x - 11*x - 2*x**4 + 9*x**z - 8.
-2*(x + 1)**2*(x + 2)**2
Let r(g) be the second derivative of -2*g**7/21 + 2*g**6/3 - 7*g**5/5 + g**4 + 16*g. Factor r(v).
-4*v**2*(v - 3)*(v - 1)**2
Let o be (-60)/(-35) + (-2)/(-7). Solve -10*w + 6*w**4 + 20*w**o + 0*w - 20*w**3 + 2 + 12*w**4 - 2*w**5 - 8*w**4 = 0.
1
Let b = 26/3 - 164/21. Solve 2/7*w**2 - 4/7 + 2/7*w**4 - 6/7*w + b*w**3 = 0 for w.
-2, -1, 1
Let y = 8 - 5. Let v(g) be the first derivative of 0*g**2 - 3 - 1/3*g**y + g. Solve v(b) = 0.
-1, 1
Let j(m) be the second derivative of -1/70*m**5 + 1/105*m**6 + 0 + 0*m**2 + 1/21*m**3 + 5*m - 1/42*m**4. Solve j(s) = 0.
-1, 0, 1
Let b(d) be the third derivative of -d**8/3360 - d**7/3360 + d**6/1440 + d**3/3 + d**2. Let h(a) be the first derivative of b(a). Factor h(k).
-k**2*(k + 1)*(2*k - 1)/4
Let r(l) be the third derivative of -l**6/150 + l**5/75 + 14*l**2. Factor r(k).
-4*k**2*(k - 1)/5
Let f(l) = 8*l + 42. Let p be f(-5). Factor 4/5*r**p - 6/5*r - 4/5.
2*(r - 2)*(2*r + 1)/5
Let w(t) be the second derivative of -2*t + 0 - 2/3*t**2 + 1/3*t**3 - 1/18*t**4. Find f such that w(f) = 0.
1, 2
Let g be 2/8 - 69/(-12). Let r = -6 + g. Factor -3/4*n**3 - 1/2*n**4 + r*n - 1/4*n**2 + 0.
-n**2*(n + 1)*(2*n + 1)/4
Let w(x) be the first derivative of -x**2/2 - 2*x - 2. Let a be w(-5). Factor 0 - h**a + h**2 + 1/3*h**4 - 1/3*h.
h*(h - 1)**3/3
Let q be ((-28)/98)/((-4)/7). Let z(t) be the first derivative of t**2 - 8/5*t**5 + 0*t - q*t**4 - 3 + 8/3*t**3. Determine r so that z(r) = 0.
-1, -1/4, 0, 1
Let w = -449/3 + 150. Factor 0 - w*z - 1/3*z**2.
-z*(z + 1)/3
Factor -2/5*k**2 + 0 - 6/5*k**3 - 6/5*k**4 + 0*k - 2/5*k**5.
-2*k**2*(k + 1)**3/5
Let f(k) be the third derivative of k**6/40 - 3*k**5/20 + k**4/4 - 5*k**2. Suppose f(x) = 0. Calculate x.
0, 1, 2
Let c be (-2)/8 + (-26)/(-8). Suppose 0*a = -c*a + 6. Factor -2*k**3 - 2*k**3 - 2*k**4 + 0*k**3 + a*k**5.
2*k**3*(k - 2)*(k + 1)
Let k = -11 - -23/2. Let a(o) be the first derivative of 0*o - o**2 + 0*o**3 + k*o**4 + 2. Factor a(h).
2*h*(h - 1)*(h + 1)
Let r(p) = -p**3 + 32*p**2 - 32*p + 31. Let h be r(31). Determine t so that 3/4*t**4 - 1/4*t**2 + 1/2*t**3 + h + 0*t = 0.
-1, 0, 1/3
Let u(o) be the second derivative of -o**5/90 - o**4/9 - 11*o**3/27 - 2*o**2/3 - 18*o. Factor u(h).
-2*(h + 1)*(h + 2)*(h + 3)/9
Let h(p) be the first derivative of 3/4*p**4 - 1 + 0*p**2 + p**3 + 0*p. Suppose h(s) = 0. Calculate s.
-1, 0
Let k(i) = 21*i**4 + 8*i**3 - 8*i**2 - 8*i. Let f(c) = -10*c**4 - 4*c**3 + 4*c**2 + 4*c. Let g(r) = -13*f(r) - 6*k(r). Factor g(w).
4*w*(w - 1)*(w + 1)**2
Let x = 6 - 12. Let y be (4/x*3)/(-1). Factor -6*h**2 + 2*h**5 + y*h**2 + 2*h + 0*h**5 + 4*h**4 - 4*h.
2*h*(h - 1)*(h + 1)**3
Let t(d) be the first derivative of -2*d**3/21 - 4*d**2/7 - 8*d/7 - 3. Suppose t(s) = 0. Calculate s.
-2
Let z(n) be the first derivative of -4 + 1/2*n**4 - 2/3*n**3 + 0*n**2 + 0*n. Factor z(t).
2*t**2*(t - 1)
Let t(r) be the third derivative of 7/540*r**6 + 3*r**2 - 1/15*r**5 - 8/27*r**3 + 0*r + 0 - 1/945*r**7 + 5/27*r**4. Suppose t(l) = 0. What is l?
1, 2
Let m(h) be the first derivative of -27*h**8/280 + 3*h**7/35 - h**6/45 + h**3/3 + 2. Let d(t) be the third derivative of m(t). Solve d(n) = 0.
0, 2/9
Let d(s) = 2*s**2 + 19*s + 35. Let r(c) = 6*c + 107*c - 3*c**2 + 209 + 9*c**2 + 6*c**2. Let z(b) = -34*d(b) + 6*r(b). Suppose z(p) = 0. Calculate p.
-4
Let y = 4 + -2. Let d = -45 - -48. Determine v, given that 2/7*v**y + 2/7*v**d + 0 - 2/7*v - 2/7*v**4 = 0.
-1, 0, 1
Suppose -3*k = 2*k + 5*r + 15, 0 = -5*k - 2*r. Suppose -2*c - k*h = -1 - 13, 4*c - 5*h = -17. Factor 2/3 - 2/3*m**c + 0*m.
-2*(m - 1)*(m + 1)/3
Factor -21/4*n + 3/8*n**2 + 147/8.
3*(n - 7)**2/8
Find f, given that 1/6*f - 1/3*f**2 + 1/6*f**3 + 0 = 0.
0, 1
Let m(t) = t**2 + 4*t + 1. Let i be m(-4). Factor i + 9*r**2 + 0 - 8*r**2 - 2*r.
(r - 1)**2
Let n = 1/55 - -2/11. Factor n*u**4 + 0*u**2 + 0 + 0*u**3 + 0*u.
u**4/5
Let n(f) be the third derivative of -f**5/120 - f**4/16 - f**3/6 + 8*f**2 + 2. Determine p, given that n(p) = 0.
-2, -1
Let w(x) = -7*x**2 + 4*x - 2. Let n = 2 - -3. Let q(p) = -20*p**2 + 12*p - 6. Let d(h) = n*q(h) - 14*w(h). Factor d(f).
-2*(f - 1)**2
Suppose 0 = 2*j - 0*j + 12. Let s be (-72)/8*2/j. Factor 0 - 1/4*p**s - 1/4*p**2 + 0*p.
-p**2*(p + 1)/4
Let d(h) be the third derivative of -h**7/70 + h**5/20 - 6*h**2. Find i such that d(i) = 0.
-1, 0, 1
Let g be ((-2)/2 + 1)*42/84. Solve 1/8*v + g + 1/8*v**2 = 0.
-1, 0
Let b(m) = 2*m**3 + 4*m**2 + 4*m - 4. Let s(o) = -3*o**3 - 7*o**2 - 7*o + 7. Let i(p) = 5*b(p) + 3*s(p). Determine y, given that i(y) = 0.
-1, 1
Let h be 1 + -1 - (9 + -6). Let q be h/(-2) + (-15)/20. Suppose -q*b**2 + 1 - 1/4*b**3 + 0*b = 0. What is b?
-2, 1
Let k be (-16)/(-15) - (2 + -1). Let b(s) be the first derivative of 1/10*s**2 - k*s**3 - 1/4*s**4 - 3/25*s**5 + 0*s - 2. Suppose b(y) = 0. Calculate y.
-1, 0, 1/3
Let q(l) = 13*l**2 - 6*l - 1. Let j(b) = 14*b**2 - 5*b - 2. Let v(g) = 3*j(g) - 4*q(g). Factor v(f).
-(2*f - 1)*(5*f - 2)
Let g be (-2)/(-7)*7/2. Let v(n) = 3*n**3 + n**2 - 2. Let y be v(g). Let 4/7*p + y*p**2 + 0 = 0. What is p?
-2/7, 0
Factor -3*m**2 - 4