 first derivative of -1/3*u**3 - 3 - 4*u - 2*u**2. Factor g(a).
-(a + 2)**2
Let q be -1 + 4 - 3*(-15 + -3). Suppose -7*w**2 - 61*w - 8 + 67*w**2 + q*w = 0. Calculate w.
-1/3, 2/5
Factor j**3 + 0 - 1/2*j**5 + 0*j**2 - 1/2*j + 0*j**4.
-j*(j - 1)**2*(j + 1)**2/2
Let v be -1 + 84/8 + 5. Let c = v - 14. Factor -1/2*a - 1/2*a**4 + 0 + c*a**3 + 1/2*a**2.
-a*(a - 1)**2*(a + 1)/2
Let z(u) be the third derivative of u**5/270 - u**4/18 + 8*u**3/27 + 7*u**2 - 5. Suppose z(g) = 0. Calculate g.
2, 4
Let q(f) = 81*f - 562. Let h be q(7). Let w(t) = t + 13. Let i be w(-9). Find j such that -2/5*j**3 + 6/5*j**2 - 6/5*j**i + 4/5*j + 0 - 2/5*j**h = 0.
-2, -1, 0, 1
Let y(u) be the third derivative of -u**8/420 + u**6/30 - u**5/15 + 7*u**3/6 - 3*u**2. Let l(a) be the first derivative of y(a). Find j such that l(j) = 0.
-2, 0, 1
Let m(o) be the third derivative of o**5/270 + o**4/54 - o**3/9 - 100*o**2 - 1. Factor m(w).
2*(w - 1)*(w + 3)/9
What is y in -114*y - 2*y**3 - 54*y**2 + 4*y**3 + 1014 - 1072 = 0?
-1, 29
Let b be (-16488)/(-96)*3/((-135)/(-6)). Let o = b - 102/5. Solve 25/4 + 1/4*f**2 + o*f = 0 for f.
-5
Let x(d) = -d**3 - 9*d**2 - 15*d - 56. Let u be x(-8). Factor u + 4/3*i**3 - 2/3*i**4 - 4/3*i + 2/3*i**2.
-2*i*(i - 2)*(i - 1)*(i + 1)/3
Let w = 1565 - 7822/5. Factor -w*l**2 + 6/5 + 3/5*l.
-3*(l - 2)*(l + 1)/5
Suppose 13*o - 240 = 7*o. Factor 76*m**5 - 27*m**3 - 33*m**5 - o*m**5.
3*m**3*(m - 3)*(m + 3)
Let b be (-8)/((-30 + -6)/18). Suppose 8/21 + 10/7*r**2 + 2/3*r**3 + 26/21*r + 2/21*r**b = 0. What is r?
-4, -1
Let w(i) be the third derivative of -i**5/330 + 4*i**4/3 - 704*i**3/3 + 70*i**2 - 1. Solve w(t) = 0 for t.
88
Factor -k**2 - 7*k + 0*k**2 - k + 745 - 760.
-(k + 3)*(k + 5)
Let s(p) be the third derivative of 0*p + 1/24*p**6 + 1/12*p**5 - 11*p**2 - 25/24*p**4 + 5/2*p**3 + 0. Factor s(w).
5*(w - 1)**2*(w + 3)
Let p(d) = d**2 + 3*d - 8. Let s be p(2). Factor -2*f**2 + 3*f**2 + 0*f**s - 4*f**2 + 18*f.
-3*f*(f - 6)
Let b(n) = 8*n + 105. Let t be b(-12). Let r be t/21*8/6. Let 0 - 2/7*k**2 + r*k = 0. What is k?
0, 2
Let p(m) = 10*m**2 + 16*m + 7. Let g(z) be the first derivative of -7*z**3/3 - 11*z**2/2 - 5*z - 2. Let b(c) = -7*g(c) - 5*p(c). Factor b(i).
-i*(i + 3)
Let q(o) be the third derivative of o**5/420 + o**4/4 - o**2 + 145. Factor q(m).
m*(m + 42)/7
Let r(b) = -85*b**2 + 170*b. Let k(h) = -15*h**2 + 15*h + 5. Let c(l) = 7*l**2 - 8*l - 2. Let v(u) = 5*c(u) + 2*k(u). Let m(y) = 2*r(y) + 35*v(y). Factor m(q).
5*q*(q - 2)
Let l(w) = 9*w**4 - 19*w**2 + 2*w - 4. Let v(p) = -140*p**3 - 20*p**2 + 10*p**4 + 140*p**3 - 5. Let i(d) = -5*l(d) + 4*v(d). Suppose i(x) = 0. Calculate x.
-2, 0, 1
Let d(q) be the second derivative of -q**6/15 + q**5/14 + 3*q**4/14 - 5*q**3/21 - 2*q**2/7 - q - 27. Solve d(z) = 0 for z.
-1, -2/7, 1
Let r(u) = -u + 19. Let j be r(9). Suppose -5*y + 10 = -3*f, -5*f + j = 5*y - 0*f. Suppose 6*p - 2*p - 6*p - 1 - p**y = 0. What is p?
-1
Let o(p) be the third derivative of p**7/315 + 13*p**6/180 + 11*p**5/90 - 13*p**4/36 - 4*p**3/3 - 164*p**2. Suppose o(i) = 0. Calculate i.
-12, -1, 1
Let c = 479 + -476. Let u(d) = d**2 - d + 18. Let h be u(0). Factor 10*w + 21*w + w**3 - 14*w**2 + w**c - h - w.
2*(w - 3)**2*(w - 1)
Let q(i) = -26*i**3 - 168*i**2 - 125*i + 312. Let f(z) = 8*z**3 + 56*z**2 + 42*z - 104. Let g(w) = 7*f(w) + 2*q(w). Factor g(p).
4*(p - 1)*(p + 2)*(p + 13)
Let -3946 - 4333 + 796*o**2 - 22515*o - 7*o**3 + 1781 = 0. What is o?
-2/7, 57
Let u(f) be the first derivative of -3/20*f**5 + 4 - 5/2*f**2 + 1/10*f**6 - 9/8*f**4 + 0*f - f**3. Let o(k) be the second derivative of u(k). Factor o(p).
3*(p - 2)*(p + 1)*(4*p + 1)
Let i be 2/2*(-161)/(-2). Let g = -79 + i. Factor -9/4 - g*p - 1/4*p**2.
-(p + 3)**2/4
Let n(g) be the first derivative of -11*g**3/3 + g**2 - 3*g - 1. Let d(m) = -4*m**2 + m - 1. Let s(a) = -8*d(a) + 3*n(a). Factor s(f).
-(f + 1)**2
Let r(u) be the third derivative of -10*u**2 + 0 + 1/40*u**6 + 1/10*u**5 + 0*u**3 + 0*u - 3/8*u**4. Determine d so that r(d) = 0.
-3, 0, 1
Let i = 158 + -228. Let r = i - -70. Factor -3*f + r - 1/3*f**3 - 2*f**2.
-f*(f + 3)**2/3
Factor -64*d**2 + 862*d**4 - 866*d**4 - 48*d + 9*d**3 - 37*d**3.
-4*d*(d + 2)**2*(d + 3)
Let b be ((-3)/((-30)/(-4)))/(185/(-925)). Let t(h) be the first derivative of -h**4 - 8/5*h**5 + 0*h**3 + 0*h**b - 2/3*h**6 + 0*h + 9. Factor t(p).
-4*p**3*(p + 1)**2
Let 5/2*a**2 - 12 - a + 1/2*a**3 = 0. What is a?
-4, -3, 2
Solve 1/3*k - 5/6*k**2 - 1/6*k**3 + 4 = 0.
-4, -3, 2
Factor -2621*a**2 - a**3 + 2504*a**2 + 4*a**3 + 3969 + 945*a.
3*(a - 21)**2*(a + 3)
Let a(b) be the second derivative of b**6/165 + b**5/55 - 5*b**4/66 - 2*b**3/11 - 212*b - 2. Factor a(i).
2*i*(i - 2)*(i + 1)*(i + 3)/11
Let d(b) be the first derivative of 3*b**5/80 - b**4/4 - b**3/8 + 3*b**2/2 - 15*b + 6. Let q(t) be the first derivative of d(t). Suppose q(u) = 0. What is u?
-1, 1, 4
Let 2/9*s**2 + 0 + 38/9*s = 0. What is s?
-19, 0
Suppose 3*f - 2*c - 1 = -2, -10 = -2*c. Solve 10*r - 60*r**4 - 41*r**2 + 115*r**f - 11*r**2 - 13*r**2 = 0 for r.
0, 1/4, 2/3, 1
What is d in -100*d**3 - 230*d**2 - 114*d**5 - 122*d**5 - 155*d + 251*d**5 + 2*d**4 - 30 + 18*d**4 = 0?
-2, -1, -1/3, 3
Let y be (-28)/(-8) + (-6)/(-4). Factor -3 - 55*b**2 - 2 - 50*b + y + 5.
-5*(b + 1)*(11*b - 1)
Let z(q) = -34 + 30 + 3*q + 2*q. Let w be z(2). Factor -128*a**2 + 124*a**2 + 26*a - w*a - 16.
-4*(a - 4)*(a - 1)
Let m(f) be the first derivative of 11 - 35/26*f**4 - 16/13*f - 28/13*f**3 + 44/13*f**2 - 4/13*f**6 + 94/65*f**5. Let m(a) = 0. What is a?
-1, 1/4, 2/3, 2
Determine x, given that -47*x + 3*x**2 + 100*x - 54*x - 6 - 2*x**2 = 0.
-2, 3
Let t(z) = 2*z**2 - 150*z + 150. Let u be t(74). Factor -2/3*v**3 - 42*v + 54 - 34/3*v**u.
-2*(v - 1)*(v + 9)**2/3
Suppose 26 = -118*i + 131*i. Factor 1/2*x + 0 + 1/2*x**i.
x*(x + 1)/2
Factor -65/4*k - 225/4 + 5/2*k**2.
5*(k - 9)*(2*k + 5)/4
Let p(h) = 3*h**2 - h + 1. Let s(o) = -2*o**3 - 6*o**2 - 16*o + 6. Let x(j) = -6*p(j) - s(j). Factor x(y).
2*(y - 3)*(y - 2)*(y - 1)
Let b(x) = 212064*x**2 - 2334*x - 7. Let i(a) = -35344*a**2 + 388*a + 1. Let q(s) = -4*b(s) - 26*i(s). What is y in q(y) = 0?
1/188
Let b be 5 + (2/(-1) - -1). Suppose -b = -3*y + y. Factor -3*m**3 + 3 - 4*m**2 - 3 - y*m**2.
-3*m**2*(m + 2)
Let y = -261294/13 + 20112. Factor 0 - 8/13*m - 64/13*m**2 - 90/13*m**3 + y*m**4.
2*m*(m - 1)*(9*m + 2)**2/13
Let n(m) be the second derivative of m**5/80 - 43*m**4/48 + 55*m**3/3 + 121*m**2/2 - 245*m. Factor n(x).
(x - 22)**2*(x + 1)/4
Let g be ((-4)/10)/((-4)/20). Let q = -459/2 + 234. Factor -q*k**3 + 10*k**g - 13/2*k + 1.
-(k - 1)**2*(9*k - 2)/2
Let i(x) be the first derivative of x**5 + 5*x**4 + 10*x**3/3 - 10*x**2 - 15*x + 25. Factor i(v).
5*(v - 1)*(v + 1)**2*(v + 3)
Let h(r) be the second derivative of -r**5/5 + 108*r**4 - 23328*r**3 + 2519424*r**2 + 413*r. Suppose h(u) = 0. What is u?
108
Let o(b) be the first derivative of b**4/4 + 3*b**3 + b**2/2 + 11*b + 16. Let r be o(-9). Factor 2/5*i**5 - 2*i**3 - 2/5*i**r + 16/5*i + 2/5*i**4 - 8/5.
2*(i - 1)**3*(i + 2)**2/5
Suppose 4*o + o + 3*j = -11, -5*o + 2*j = -24. Factor -392/11 - 2/11*x**o + 56/11*x.
-2*(x - 14)**2/11
Let u be (12/((-468)/65))/((-10)/52). Factor 2*o**2 - 20/3 - u*o.
2*(o - 5)*(3*o + 2)/3
Suppose -4*l + c = 3*c - 4, -10 = 5*c. Let i(f) be the second derivative of 2/9*f**l - 1/54*f**4 + 1/27*f**3 - 10*f + 0. Factor i(x).
-2*(x - 2)*(x + 1)/9
Let j = -1/13781 - -55127/41343. Find l, given that -2/9*l**2 + j*l - 10/9 = 0.
1, 5
Let r(n) = -30*n**2 + 115*n - 60. Let q(y) = 15*y**2 - 58*y + 30. Let i(l) = -5*q(l) - 3*r(l). Suppose i(p) = 0. What is p?
2/3, 3
Factor -16/7*v**2 + 40/7*v + 2/7*v**3 - 32/7.
2*(v - 4)*(v - 2)**2/7
Let g(h) = 12*h**2 + 559*h - 557. Let s(d) = 4*d**2 + 186*d - 186. Let r(p) = 2*g(p) - 7*s(p). Suppose r(w) = 0. Calculate w.
-47, 1
Let j(y) be the second derivative of -y**4/48 - y**3/8 + 9*y**2/4 - y. Let j(k) = 0. Calculate k.
-6, 3
Let o = 19536 + -19536. Suppose 5/4*l**3 + 0 + o*l - l**2 - 1/4*l**4 = 0. Calculate l.
0, 1, 4
Let w(l) be the third derivative of -l**5/100 + l**4/2 - 32*l**3/5 + 2*l**2 - 133. Factor w(c).
-3*(c - 16)*(c - 4)/5
Suppose 5*f - 24 = -2*w + 2*f, w = 4*f - 32. Factor w*i**2 - 6/13*i - 4/13 + 2/13*i**3.
2*(i - 2)*(i + 1)**2/13
Let k = 30 + -24. Find u such that -k*u - 1