, 2
Let p(a) = 2*a**3 - 13*a**2 - 10*a + 24. Let w = 270 + -263. Let u be p(w). Suppose -3/2*f**3 - 3/4*f**4 + 6*f + 0 + u*f**2 = 0. Calculate f.
-2, 0, 2
Let r(a) be the first derivative of a**4/10 - 3*a**2/5 + 4*a/5 - 41. Solve r(d) = 0.
-2, 1
Suppose -10*f + 16*f + 360 = 0. Let a be 108/f - (-3 - -1). Factor 2/5*l - a*l**4 - l**2 + 4/5*l**3 + 0.
-l*(l - 2)*(l - 1)**2/5
Let v(s) = 1. Let d(h) = h. Let b(k) = d(k) - v(k). Let f(n) = -15*n**2 + 22*n - 7. Let q(r) = 2*b(r) - f(r). Factor q(l).
5*(l - 1)*(3*l - 1)
Suppose -4*r = -4*v - 20 + 16, -3*r = 4*v - 24. What is n in 42/17*n - 6*n**2 - 30/17*n**4 + 94/17*n**v - 4/17 = 0?
2/15, 1
Let d(r) = 6*r**3 + r**2 + 1. Let b be d(2). Factor b - 3 - 5*n**2 - 20*n + 7*n**2.
2*(n - 5)**2
Let f(t) be the second derivative of t**4/4 + t**3 - 12*t**2 + 443*t. Find i, given that f(i) = 0.
-4, 2
Factor 2/5 - 4/5*j + 2/5*j**2.
2*(j - 1)**2/5
Factor 3/4 - d + 1/4*d**2.
(d - 3)*(d - 1)/4
Let u(d) be the third derivative of -d**8/672 - 8*d**7/525 - 37*d**6/1200 - d**5/60 + 3*d**2 + 23. What is q in u(q) = 0?
-5, -1, -2/5, 0
Suppose 4*j = 5*j + 4*n - 2, 5*j + 2*n = 10. Let k be (-32)/(-12) - j/(-6). Find i, given that 4*i**4 - 2*i**5 - 4*i**2 + 0*i**5 + 4*i**5 - 2*i**k = 0.
-2, -1, 0, 1
Let c(j) be the third derivative of -1/3*j**4 + 8*j - 2*j**2 + 1/20*j**6 + 0 + 1/210*j**7 - 1/15*j**5 + 0*j**3 - 1/336*j**8. Factor c(m).
-m*(m - 2)**2*(m + 1)*(m + 2)
Let q be 1/(2/4 + 170/(-300)). Let v be 20/q*(-1)/7. Find a, given that 2/7*a - v + 2/21*a**5 + 0*a**4 + 4/21*a**2 - 8/21*a**3 = 0.
-2, -1, 1
Let y(t) be the third derivative of 3/40*t**4 + 1/600*t**6 - 6*t**2 + 0*t + 0 + 0*t**3 - 1/50*t**5. Factor y(a).
a*(a - 3)**2/5
Let x(g) = -g**3 - 57*g**2 - 111*g - 53. Let w be x(-55). Factor 0 + 1/2*m**w - m.
m*(m - 2)/2
Let a be (4/3 + (-150)/153)*2/6. Determine r, given that -6/17*r - a*r**3 + 8/17*r**2 + 0 = 0.
0, 1, 3
Let v(m) = 2*m**4 + 2*m**3 - 17*m**2 - 17*m + 3. Let k(t) = 3*t**4 + 3*t**3 - 18*t**2 - 18*t + 2. Let x(d) = 3*k(d) - 2*v(d). Suppose x(f) = 0. What is f?
-2, -1, 0, 2
Let r(l) be the second derivative of -l**5/60 + 23*l**4/12 - 385*l**3/6 - 1225*l**2/6 + 678*l. Factor r(v).
-(v - 35)**2*(v + 1)/3
Let p(h) be the second derivative of 1/3*h**4 - 3*h - 6*h**2 + 4/3*h**3 + 0. Factor p(a).
4*(a - 1)*(a + 3)
Let x be -2 - (4/(-2) - 2). Let y(b) = -2*b**2 - 20*b + 2. Let j be y(-10). Factor -x*w - 3*w**2 - 3*w**2 + 3*w**j + 5*w**2.
2*w*(w - 1)
Let h be ((-4)/(-14) - (-7665)/(-8820)) + (-5)/(-4). Let g be (-1)/6*(-4 + 0). Factor -g*l**3 + 2/3 - 2/3*l**2 + h*l.
-2*(l - 1)*(l + 1)**2/3
Let a(t) be the third derivative of -t**10/226800 - t**9/22680 + 7*t**5/20 - 10*t**2. Let p(x) be the third derivative of a(x). Factor p(s).
-2*s**3*(s + 4)/3
Let 59*v - 49059*v**2 + 49057*v**2 + 5*v = 0. What is v?
0, 32
Let y(m) be the third derivative of -m**7/735 + 31*m**6/105 - 961*m**5/35 + 29791*m**4/21 - 923521*m**3/21 - 4*m**2 - 10. Factor y(k).
-2*(k - 31)**4/7
Let d(x) = 2*x + 10. Let v be d(8). Let k = v + -24. Suppose -3*c + 2 - 4*c**2 + c + 0 + k*c**2 + 2*c**3 = 0. Calculate c.
-1, 1
Let k(h) be the first derivative of -2*h**4/51 + 13*h**3/51 - 3*h**2/17 - 2*h - 9. Let r(d) be the first derivative of k(d). Suppose r(o) = 0. Calculate o.
1/4, 3
Let g(m) = -2*m**4 - 13*m**3 - 9*m**2 + 2*m. Suppose -9 - 21 = -5*k. Suppose 0 = -n - 18 - k. Let y(b) = b**3 + b**2. Let x(s) = n*y(s) - 3*g(s). Factor x(u).
3*u*(u + 1)*(u + 2)*(2*u - 1)
Factor -25*d - 13*d**2 - 70 - d**2 + 19*d**2.
5*(d - 7)*(d + 2)
Let c(z) be the third derivative of -z**6/540 + z**5/45 - z**4/9 + 8*z**3/27 + 612*z**2. What is q in c(q) = 0?
2
Suppose 2*u - 2*h = 3*u - 217, 0 = 3*u - 4*h - 661. Solve 8*c**2 + 0 + 2 - u*c + 209*c = 0 for c.
1/4, 1
Factor -7/9*x**3 - 2/9 + 4/3*x**2 - 1/3*x.
-(x - 1)**2*(7*x + 2)/9
Let u = 21896 - 109456/5. Factor 16/5*s + u*s**2 + 4/5*s**4 + 4/5 + 16/5*s**3.
4*(s + 1)**4/5
Let n = -82 + 84. Let m(d) be the third derivative of -9/10*d**3 + 0 + 0*d - 1/100*d**5 + 4*d**n - 3/20*d**4. Factor m(r).
-3*(r + 3)**2/5
Determine p so that 105*p - 11*p**3 + 14*p**3 - 103 - 32*p**2 + 129 - 7*p**2 + 121 = 0.
-1, 7
Suppose 6*s - 10 = -82. Let q be (s/8)/(-1)*2/6. Solve -1/4 + 0*b**2 - q*b + 1/4*b**4 + 1/2*b**3 = 0.
-1, 1
Let a(o) be the first derivative of 2*o**3/9 + 181*o**2/12 + 15*o/2 + 682. Factor a(j).
(j + 45)*(4*j + 1)/6
Let i be 268/201 - ((-3)/12 + 15/(-36)). Let 12*j - 2/3*j**i - 54 = 0. What is j?
9
Let p(x) be the first derivative of -8*x**3/21 - 41*x**2 + 144*x/7 - 41. Suppose p(c) = 0. Calculate c.
-72, 1/4
Let q(j) = 3*j + 2. Let l be q(-6). Let b = -14 - l. What is p in 10*p + 22*p**2 - 2*p**3 - 4*p + 4 - 22*p**b = 0?
-1, 2
Suppose 96*t + 30 - 510 = 0. Factor -6/5*k**3 + 2/5*k**t + 0*k + 0*k**4 + 0 - 4/5*k**2.
2*k**2*(k - 2)*(k + 1)**2/5
Let h(f) be the second derivative of -f**7/945 + f**6/135 - f**5/45 + f**4/27 - f**3/27 - 6*f**2 + 7*f. Let k(c) be the first derivative of h(c). Factor k(s).
-2*(s - 1)**4/9
Let j(b) be the third derivative of 0*b**3 + 1/30*b**6 - 2/105*b**7 + 0 + 0*b**4 + 0*b**5 - 44*b**2 + 0*b. Factor j(n).
-4*n**3*(n - 1)
Let x(s) be the second derivative of s**4/126 - 2*s**3 + 189*s**2 - s + 13. Let x(m) = 0. Calculate m.
63
Let h(u) be the third derivative of u**8/70560 - u**7/2940 - 9*u**5/20 - 2*u**2. Let b(k) be the third derivative of h(k). Factor b(z).
2*z*(z - 6)/7
Let m = -66 + 68. Factor -11*b - 32*b - 25*b**m + 63*b - 8*b**3 + 6 + 7*b**2.
-2*(b - 1)*(b + 3)*(4*b + 1)
Let v be 7 + 2*4/(-2). Let b(r) = -8*r**2 - 27*r - 45. Let p(d) = 15*d**2 + 55*d + 90. Let c(o) = v*p(o) + 5*b(o). Factor c(x).
5*(x + 3)**2
Suppose 18*l - 6 = 84. Factor -1/4*i**2 + 0*i - 1/4*i**l + 1/4*i**4 + 0 + 1/4*i**3.
-i**2*(i - 1)**2*(i + 1)/4
Suppose -3*v - 48*v = -77 - 76. Determine m, given that -3/2*m**2 + 1/2*m**4 + 0*m + 0 - m**v = 0.
-1, 0, 3
Let x be 1/4 + -1133*2/40. Let v = x - -57. Factor -v*j**3 + 0 - 12/5*j + 12/5*j**2.
-3*j*(j - 2)**2/5
Let r(o) be the third derivative of 0*o + 3/10*o**6 + 0 - 3/2*o**3 - 10*o**2 + 1/4*o**4 + 37/20*o**5. Suppose r(q) = 0. Calculate q.
-3, -1/3, 1/4
Let g be 51/34*(-28)/6 - (-2 - 5). Suppose g + 8/7*u**2 + 8/7*u**4 - 12/7*u**3 - 2/7*u - 2/7*u**5 = 0. What is u?
0, 1
Let t(h) be the third derivative of h**6/200 - 13*h**5/100 + 3*h**4/10 + 2*h**2 + 8. Factor t(o).
3*o*(o - 12)*(o - 1)/5
Let d(z) be the third derivative of 5*z**8/336 + z**7/21 - z**5/6 - 5*z**4/24 + 72*z**2. Factor d(j).
5*j*(j - 1)*(j + 1)**3
Let f(j) = -12*j**2 - 148*j - 4. Let p(a) = 14*a**2 + 147*a + 5. Let n(g) = 5*f(g) + 4*p(g). Factor n(r).
-4*r*(r + 38)
Let i(j) be the second derivative of 0*j**3 - 1/12*j**4 + 0 + 0*j**5 + 1/30*j**6 + 5*j + 0*j**2. Determine t so that i(t) = 0.
-1, 0, 1
Let i(a) be the first derivative of -a**5 - 7*a**4 + 29*a**3 - 35*a**2 + 16*a - 156. Factor i(j).
-(j - 1)**2*(j + 8)*(5*j - 2)
Let j(r) be the second derivative of -r**7/10 + 3*r**6/5 + 51*r**5/50 - 2*r**4 - 27*r**3/10 + 3*r**2 - 3*r + 2. Determine q, given that j(q) = 0.
-1, 2/7, 1, 5
Let b be 6 + (8 + -5 - 9). Let m(r) be the second derivative of b - 1/3*r**4 - 2/3*r**3 - 7*r + 0*r**2. Factor m(a).
-4*a*(a + 1)
Factor -28*x**2 + 52423 - 53623 + 360*x + x**2.
-3*(3*x - 20)**2
Let q(o) = -o**4 + o**2 - o - 1. Let h be 3 - 1/3*-3. Let j(p) = 7*p**4 - 15*p**3 + 17*p**2 - 5*p + 4. Let g(b) = h*q(b) + j(b). Find l, given that g(l) = 0.
0, 1, 3
Let g(y) be the second derivative of 6*y**6/5 - 7*y**5/5 - 47*y**4/3 - 74*y**3/3 - 12*y**2 + 36*y. Suppose g(l) = 0. What is l?
-1, -2/9, 3
Let f(u) be the first derivative of -1/18*u**4 - 2 + 7*u + u**2 - 2/9*u**3. Let o(j) be the first derivative of f(j). Suppose o(h) = 0. What is h?
-3, 1
Let u(k) be the third derivative of 0 + 0*k - 4/9*k**3 - 1/180*k**6 + 1/36*k**4 + 35*k**2 + 2/45*k**5. Factor u(m).
-2*(m - 4)*(m - 1)*(m + 1)/3
Let t(m) be the first derivative of -2 + 0*m + 1/12*m**3 - 1/4*m**2. Find f, given that t(f) = 0.
0, 2
Let o(j) be the first derivative of 2*j**3/5 + 18*j**2 + 336*j/5 + 179. Factor o(q).
6*(q + 2)*(q + 28)/5
Let x(l) be the second derivative of 10/3*l**3 + 10*l**2 + 0 - 5*l + 5/12*l**4. What is c in x(c) = 0?
-2
Suppose -12*r + 21*r = 54. Let t be (2 + (-6)/r)/((-2)/(-6)). Factor 0 + 16/7*c - 2*c**4 + 60/7*c**t - 72/7*c**2.
-2*c*(c - 2)**2*(7*c - 2)/7
Le