l*a**2 + 0*a + 2*a**3 + 0*a + 2*a = 0.
-1, 0
Let i(u) = 20*u**3 + 8*u. Let w(t) = -7*t**3 - 3*t. Let f(c) = 3*i(c) + 8*w(c). Factor f(x).
4*x**3
Let g(f) be the third derivative of 5*f**8/84 + 5*f**7/42 - f**6/8 - 5*f**5/12 - 5*f**4/24 + 19*f**2. What is t in g(t) = 0?
-1, -1/4, 0, 1
Let w(y) = y**5 - y**4 + y**3 + y**2 + y - 1. Let h(v) = 8*v**5 - 6*v**4 + 6*v**3 + 6*v**2 + 7*v - 7. Let t(q) = -3*h(q) + 21*w(q). Factor t(l).
-3*l**2*(l - 1)*(l + 1)**2
Let s be 21/44*40/15. Let a = s + 2/33. Suppose 2/3*c**2 + a*c + 0 - 2/3*c**3 = 0. Calculate c.
-1, 0, 2
Let y be ((-8)/(-6) - 1)/((-12)/(-18)). Factor 1/4*s + 1/4*s**2 - y.
(s - 1)*(s + 2)/4
Let x = 117 - 115. Solve 0*m - 4/5*m**2 + 0 - x*m**3 = 0.
-2/5, 0
Let s(v) be the second derivative of -v + 0 - 1/20*v**4 - 3/10*v**2 + 1/5*v**3. Determine m so that s(m) = 0.
1
Let r = 67 - 739/11. Let f = 17/33 + r. Find p, given that 0 - f*p**2 + 1/3*p = 0.
0, 1
Let s be -9 - -11 - ((-1)/21 - -2). Let l(z) be the second derivative of 0 + 0*z**2 + 2*z + s*z**3 - 3/70*z**5 - 1/21*z**4. What is g in l(g) = 0?
-1, 0, 1/3
Let p = 1 - 0. Suppose -4*b - 5*n + 10 = 0, -2*n + p = -2*b - 3. Factor -3*y + b*y + 2*y - y**2.
-y*(y + 1)
Suppose 3*z - 60 = -r - 38, z - 4*r - 29 = 0. Factor -9*v - 1/3*v**3 + z + 3*v**2.
-(v - 3)**3/3
Let w = 3463/21 + -487/3. Factor -w*a + 2*a**2 + 4/7.
2*(a - 1)*(7*a - 2)/7
Let l(y) = -y**3 - y**2. Let r be l(0). Determine a, given that 2/3*a + 2/3*a**2 + r = 0.
-1, 0
Let m = -33 + 35. Let d(t) be the third derivative of -7/135*t**7 + 32/27*t**4 + 56/135*t**6 + t**m - 16/27*t**3 + 0 - 52/45*t**5 + 0*t. Factor d(s).
-2*(s - 2)**2*(7*s - 2)**2/9
Let l = 45 + -43. Let h(n) be the first derivative of -3 - 1/4*n**l - 1/16*n**4 + 0*n + 1/4*n**3. Factor h(v).
-v*(v - 2)*(v - 1)/4
Let m be 42/9 + (-4)/6. Suppose -3*x = -m*t - 17, 2*x = -3*t + t + 2. What is k in -2 + 2*k**2 - 2*k + 2*k**3 - 3*k**2 + x*k**2 = 0?
-1, 1
Let p(h) = -h**2 + 1. Let i(f) = 2*f**2 + 7*f + 5. Let u(x) = i(x) - 5*p(x). Let k(c) = 22*c**2 + 22*c. Let y(r) = 5*k(r) - 16*u(r). Solve y(m) = 0 for m.
-1, 0
Let y(u) be the first derivative of 0*u + 0*u**2 - 7/16*u**4 + 3 + 1/6*u**3. Factor y(r).
-r**2*(7*r - 2)/4
Let n be (-1 - -2) + -3 - (-91)/14. Suppose 15/2*y + 3 + n*y**2 = 0. What is y?
-1, -2/3
Determine z so that 0*z**2 + 5*z**3 + 25*z**2 + 11*z**2 + 120 + 140*z + 14*z**2 = 0.
-6, -2
Let k = 8 - 2. Solve -3*z + 2*z**2 + 0*z**2 + k + 3*z**3 - 8*z**2 = 0.
-1, 1, 2
Suppose 4*f = 2 + 10. Factor 2/3*u**2 + 1/3 + u - 2/3*u**f - 1/3*u**5 - u**4.
-(u - 1)*(u + 1)**4/3
Let z(i) be the second derivative of -i**5/130 - 5*i**4/39 - 3*i**3/13 + 9*i + 2. Solve z(x) = 0 for x.
-9, -1, 0
Let f = -41 - -23. Let t be 2/(-3)*f/4. Factor -10*h**2 - 3*h - 2*h - 8*h**3 + t*h.
-2*h*(h + 1)*(4*h + 1)
What is j in 26*j**2 - 8 - 12*j + 20*j**2 + 8*j**3 - 34*j**2 = 0?
-2, -1/2, 1
Let h(o) = -147*o**3 + 65*o**2 + 72*o + 10. Let w be 4/(-6) + 33/9. Let a(r) = 147*r**3 - 66*r**2 - 72*r - 9. Let y(x) = w*h(x) + 2*a(x). Factor y(f).
-3*(f - 1)*(7*f + 2)**2
Let q be 6/4 + 7/14. Suppose 4 - 2*t**2 - 2*t - 6*t + 3*t**q + 4*t = 0. Calculate t.
2
Let b = 57 - 54. Let y(p) be the third derivative of 1/120*p**5 + 0 + 0*p + p**2 - 1/24*p**4 + 1/12*p**b. Determine o so that y(o) = 0.
1
Let r(o) be the second derivative of -o**6/120 - 3*o**5/80 - o**4/16 - o**3/24 + 4*o. Suppose r(f) = 0. What is f?
-1, 0
Solve -4*v**4 + 4*v**2 + 3*v**3 + 0*v**2 + 5*v**2 - 6*v**3 - 2*v = 0.
-2, 0, 1/4, 1
Let b be (-1)/(-2)*(1 - 1). Let p = b - -2. Factor -p*j**3 + j**2 - j + j**4 + j.
j**2*(j - 1)**2
Let s(w) be the second derivative of 0*w**2 + 0*w**6 + 2*w + 1/12*w**4 - 3/40*w**5 + 0*w**3 + 1/84*w**7 + 0. Suppose s(a) = 0. What is a?
-2, 0, 1
Let n = 13 + -7. Let x(j) = j**3 - 6*j**2 + 5. Let z be x(n). Suppose -3*c**3 + z*c**2 - 2*c**4 + 2*c - 3*c**2 + c**3 = 0. What is c?
-1, 0, 1
Let d(w) be the third derivative of -w**7/30 + w**6/24 + 3*w**5/20 - 5*w**4/24 - w**3/3 - 5*w**2. Solve d(t) = 0 for t.
-1, -2/7, 1
Suppose -26 = -n + 5*x, x + 5 = 1. Suppose 4*c + n = 6*c. Factor -7/2*b + 7/2*b**c + b**2 - 1.
(b - 1)*(b + 1)*(7*b + 2)/2
Let a(i) be the third derivative of i**7/280 + i**6/80 - i**4/16 - i**3/8 + 16*i**2. Suppose a(y) = 0. Calculate y.
-1, 1
Let r(n) be the first derivative of 2*n**5/5 - 5*n**4 + 74*n**3/3 - 60*n**2 + 72*n + 5. Factor r(y).
2*(y - 3)**2*(y - 2)**2
Let u = 921/10 - 92. Let p(z) be the second derivative of -u*z**5 - 2*z - 4/15*z**6 + 0*z**4 + 0*z**2 + 0*z**3 + 0. Let p(f) = 0. What is f?
-1/4, 0
Let u = -458/3 + 153. Determine j, given that u*j**4 + 2/3*j - 2/3*j**3 - 1/3 + 0*j**2 = 0.
-1, 1
Find z such that -5*z**2 + 5*z + z**2 - 5*z = 0.
0
Let k(p) = 3*p**5 + 8*p**4 - 3*p**3 - 3*p**2 + 5*p + 5. Suppose 5 = 2*n + 3*n. Let a(i) = i**4 + i + 1. Let f(c) = n*k(c) - 5*a(c). Find j, given that f(j) = 0.
-1, 0, 1
Let a be -2 - 8/(-36)*11. Factor a + 8/3*k**2 - 2*k - 10/9*k**3.
-2*(k - 1)**2*(5*k - 2)/9
Suppose 4*y - 14 = -k - 0*y, -5 = -4*k + y. Suppose k*n + 1 = 7. Factor n*l**3 - 2*l**3 + 0*l**3.
l**3
Let z(j) be the third derivative of j**7/315 - j**6/60 + j**5/90 + j**4/12 - 2*j**3/9 + 5*j**2. Factor z(y).
2*(y - 2)*(y - 1)**2*(y + 1)/3
Let i(r) = -r**3 + 6*r**2 + r - 2. Let x be i(6). Suppose -4*g + 6 = 5*n, n - 3 = 5*g + x. Solve 0*o - 1/2 + 1/2*o**n = 0.
-1, 1
Let p be (-9 - -1)*(-2)/4. Suppose -2 + p*t + t**2 + 0 + 6 = 0. What is t?
-2
Suppose -2*h + z + 9 = -h, 3*z = h - 15. Let m = 2 + h. Factor -34/5*i**2 + 8/5*i**3 - 8/5 + m*i.
2*(i - 2)**2*(4*i - 1)/5
Determine d, given that 12*d**4 + 3 + 8*d**3 - 3 + 8*d**4 - 28*d**5 = 0.
-2/7, 0, 1
Suppose 3*k - 1 = 8. Find j, given that 4*j - j**k + 2*j - 3*j - 2 = 0.
-2, 1
Factor 5*n - 127*n**3 + 5*n**5 + 254*n**3 - 137*n**3.
5*n*(n - 1)**2*(n + 1)**2
Let t be ((-2)/6)/(50/(-24870)). Let g = -165 + t. Factor -2/5 + 2/5*i**4 + g*i + 0*i**2 - 4/5*i**3.
2*(i - 1)**3*(i + 1)/5
Let i = 42211/5505 + -2/1835. Let p = i - 149/21. Solve 4/7*j**5 + 2/7 + 4/7*j + 2/7*j**4 - 8/7*j**3 - p*j**2 = 0.
-1, -1/2, 1
Let w(q) be the third derivative of -q**7/5880 - q**6/1680 - q**4/12 - 6*q**2. Let h(c) be the second derivative of w(c). Solve h(x) = 0 for x.
-1, 0
Suppose 0 = m + 5*d + 7, -d = -m - 4*d + 3. Let b = -35/2 + m. Let 0*k + b*k**5 + 1/2*k**2 + 0 - 1/2*k**4 - 1/2*k**3 = 0. What is k?
-1, 0, 1
Factor -13*z + 10*z - 3 - 56*z**2 - 27*z - 16*z**3 + 5*z.
-(z + 3)*(4*z + 1)**2
Suppose 8 = 2*t - 2*m, 4*m + 8 - 37 = -5*t. Factor 4*v**4 + 4*v**t - 2*v**5 + 5*v**3 - 3*v**3.
2*v**3*(v + 1)**2
Let n(x) be the first derivative of x**3/2 - 9*x**2 + 54*x - 24. Suppose n(w) = 0. What is w?
6
Let k(i) be the second derivative of i**5/40 - i**4/6 + 5*i**3/12 - i**2/2 - 23*i. Factor k(o).
(o - 2)*(o - 1)**2/2
Let k(x) = -x**3 - 38*x**2 - 2*x - 72. Let j be k(-38). Factor -1/3*m**5 - 1/3*m - 1/3*m**j + 2/3*m**2 - 1/3 + 2/3*m**3.
-(m - 1)**2*(m + 1)**3/3
Let q(k) be the second derivative of -k**5/12 + 5*k**3/6 + 5*k**2/3 + 2*k - 1. Factor q(s).
-5*(s - 2)*(s + 1)**2/3
Factor 0*i**2 - 1/3 - 2/3*i + 2/3*i**3 + 1/3*i**4.
(i - 1)*(i + 1)**3/3
Let g(q) be the third derivative of -2*q**7/35 + 11*q**6/30 - 2*q**5/5 - 15*q**2. Suppose g(s) = 0. What is s?
0, 2/3, 3
Let s(t) be the second derivative of t**4/6 + t**3 + 2*t**2 - 24*t. Suppose s(o) = 0. Calculate o.
-2, -1
Suppose 14*o = 20*o. Find j such that o*j + 2/7*j**2 - 8/7 = 0.
-2, 2
Let q(x) be the first derivative of x**5/300 + x**4/40 + x**3/15 - 5*x**2/2 + 4. Let w(b) be the second derivative of q(b). Solve w(h) = 0 for h.
-2, -1
Let w = 373/3 - 124. Let l(o) be the first derivative of 0*o**3 - 1 + o**4 + 0*o**5 - o**2 - w*o**6 + 0*o. Factor l(f).
-2*f*(f - 1)**2*(f + 1)**2
Let m(v) be the third derivative of v**7/210 - v**6/30 + v**5/10 - v**4/6 + v**3/6 - 29*v**2. Determine j so that m(j) = 0.
1
Let a = -47 + 51. What is l in 2/9*l**2 + 0*l + 2/9*l**a - 4/9*l**3 + 0 = 0?
0, 1
Solve 5*r**3 - 5*r**4 - 23 + 9 + 14 = 0 for r.
0, 1
Let t(v) be the first derivative of -21*v**4 + 104*v**3/3 - 136*v**2/7 + 32*v/7 - 9. Factor t(r).
-4*(3*r - 2)*(7*r - 2)**2/7
Let z(p) be the first derivative of -2*p**5/5 - p**4 + 2*p**3 + 4*p**2 - 8*p + 1. Factor z(v).
-2*(v - 1)**2*(v + 2)**2
Suppose -3*w**2 + 118*w - 2*w**2 - 128*w = 0. What is w?
-2, 0
Let h = 3/52 + 75/52. Determine b so that -7/2*