e the first derivative of d(u). Factor n(f).
-3*(f + 2)*(f + 3)
Suppose -4484 + 4484 = -39*g. Factor g + 3/8*d**4 + 0*d + 0*d**3 - 3/8*d**2.
3*d**2*(d - 1)*(d + 1)/8
Let p(b) be the third derivative of -b**6/360 + 7*b**5/180 + 17*b**4/72 + b**3/2 - 116*b**2. Factor p(w).
-(w - 9)*(w + 1)**2/3
Determine i so that 2/17*i**2 - 280/17 + 62/17*i = 0.
-35, 4
Find q such that -140/11 + 108/11*q**2 - 538/11*q + 82/11*q**3 + 8/11*q**4 = 0.
-7, -5, -1/4, 2
Suppose -933*l**2 + 3*l**5 - 374*l + 18*l**4 + 3*l**4 + 4800 + 4454*l - 195*l**3 = 0. Calculate l.
-8, -1, 5
Suppose 49 = 3*l + 4*l. Let c be ((-36)/l)/(6 - (-3904)/(-648)). Suppose 2187/7*a**3 - c*a**2 + 324/7*a - 24/7 = 0. What is a?
2/9
Let t(d) = -d**3 + 2*d**2 + 6*d - 4. Let g be t(3). Suppose 88 - 476 - 112 - g*i**2 + 100*i = 0. What is i?
10
Let z be 64/(-24) + 308/99. Factor -z*q - 2/3 + 2/9*q**2.
2*(q - 3)*(q + 1)/9
Let x(u) = -17*u + 34. Let t(c) = -18*c + 33. Let b(j) = -5*t(j) + 6*x(j). Let y be b(3). Solve 14/5*o + 2/5*o**y - 6/5 - 2*o**2 = 0 for o.
1, 3
Let m(p) be the first derivative of -4*p**5/5 - 30*p**4/7 - 48*p**3/7 - 16*p**2/7 + 20. Factor m(u).
-4*u*(u + 2)**2*(7*u + 2)/7
Let c(a) be the first derivative of -a**3/3 + 102*a**2 - 10404*a - 201. Find q, given that c(q) = 0.
102
Let g(v) = -245*v**3 + 160*v**2 + 55*v - 15. Let p = -33 - -18. Let l(q) = -35*q**3 + 23*q**2 + 8*q - 2. Let n(h) = p*l(h) + 2*g(h). Let n(i) = 0. What is i?
-2/7, 0, 1
Let j = -2522/3 + 841. Factor -4/3 + 4/3*i - j*i**2.
-(i - 2)**2/3
Let i be (-1 + 0 - -3)*1. Let q = i + -11. Let o(w) = 5*w**2 + 10*w + 9. Let p(x) = -11*x**2 - 21*x - 18. Let c(d) = q*o(d) - 4*p(d). Factor c(y).
-(y + 3)**2
Let j(b) = -11*b + 5*b - 16*b**2 + 15*b**2 - 10*b - 9. Suppose 4*p - 37 = 51. Let n(d) = 2*d. Let k(v) = p*n(v) + 2*j(v). Find s such that k(s) = 0.
3
Let i be ((-36)/(-64))/(51/136). Let i*c**5 + 0*c**4 + 0*c**2 - 3/2*c**3 + 0*c + 0 = 0. Calculate c.
-1, 0, 1
Let j(d) be the second derivative of d**7/8 + 3*d**6/40 - 21*d**5/40 - 3*d**4/8 + 7*d**3/8 + 9*d**2/8 + 118*d. Determine x so that j(x) = 0.
-1, -3/7, 1
Factor 6*j**3 + 8*j**2 + 20*j**4 - 3*j - 2*j**2 + 8*j**5 - 23*j**4 - 3 - 11*j**5.
-3*(j - 1)**2*(j + 1)**3
Let o(g) = 21*g + 569. Let d be o(-27). Let 45*z**d + 4/5 + 12*z = 0. Calculate z.
-2/15
Let d(n) be the first derivative of 2/45*n**3 + 9 + 1/5*n**2 + 4/15*n. Factor d(g).
2*(g + 1)*(g + 2)/15
Let j be (-87)/(-18)*2 + (-7)/(-21). Suppose 23*v**3 + 25*v**2 - j*v - 26*v**4 + v**4 - 13*v**3 = 0. What is v?
-1, 0, 2/5, 1
Factor 4*q**2 + 4*q**4 + 6036*q - 16*q**2 - 6052*q + 16 + 8*q**3.
4*(q - 1)**2*(q + 2)**2
Let u(r) = r**2 - r + 3. Let x(n) = 226*n - 220. Let g(t) = 2*u(t) - x(t). Find h such that g(h) = 0.
1, 113
Solve 18/7*y**3 + 3/7*y**5 + 12/7*y**4 + 3/7*y + 12/7*y**2 + 0 = 0 for y.
-1, 0
Let u(w) be the second derivative of w**2 - 5/6*w**3 + 0 + 1/4*w**4 + 1/20*w**5 - 1/30*w**6 + 3*w. Factor u(r).
-(r - 1)**3*(r + 2)
Let h(p) be the second derivative of -p**5/20 + 7*p**4/4 - 20*p**3 + 50*p**2 - 339*p. Let h(l) = 0. What is l?
1, 10
Let y(c) = 24*c - 94. Let a be y(4). Suppose 4/7*w**a + 12/7 - 16/7*w = 0. Calculate w.
1, 3
Factor 2*m**2 - 27555 + 16981 - 536*m - 792*m - 99650 - 6*m**2.
-4*(m + 166)**2
Let a be ((-2304)/(-60))/(-16)*1/(-2). Determine m so that 0*m**2 + 0*m + 3/5*m**3 + a*m**4 + 0 + 3/5*m**5 = 0.
-1, 0
Factor -5*m**2 + 14*m - 16 - 74*m + 116 + 220.
-5*(m - 4)*(m + 16)
Let l(f) = 3*f - 11. Let o(q) = -5*q + 16. Let u(v) = 8*l(v) + 5*o(v). Let p be u(-10). Determine d, given that 2*d - 9 + 7*d - d**p + 2*d - 5*d = 0.
3
Let b(s) be the third derivative of 5/24*s**4 - 25*s**2 - 1/24*s**6 + 0 - 5/6*s**3 + 1/12*s**5 + 0*s. What is i in b(i) = 0?
-1, 1
Let u(a) = -a**5 + 144*a**4 - 6734*a**3 + 96339*a**2 + 338536*a + 235293. Let q(p) = -6*p**3 - p**2 + p + 1. Let w(v) = 5*q(v) + u(v). Factor w(r).
-(r - 49)**3*(r + 1)*(r + 2)
Suppose 27*i - 51 = 24*i. Suppose -s + i = 4*v, 5*s - 7 - 18 = 0. Determine d so that -4/5*d**2 + 2/5*d**v + 2/5*d + 0 = 0.
0, 1
Factor -5/2*d**2 + 5/2 + 0*d.
-5*(d - 1)*(d + 1)/2
Suppose -5*n + 4*a = -0*n + 137, a - 78 = 3*n. Let b = n + 27. Factor -8 + 2 - 5*i + i + b*i**2.
2*(i - 3)*(i + 1)
Let r be 1/(3/(-24)*-4). Let u be 91/(-52) + (-4)/(-3 - -2). Determine c so that -2 + u*c**3 - 3/2*c**r - 5*c = 0.
-2/3, 2
Factor 2/5 + 4/5*i + 2/5*i**2.
2*(i + 1)**2/5
Let g(c) = 90*c - 447. Let h be g(5). Let p(o) be the first derivative of 0*o + 4/5*o**h - 1/10*o**4 - 11 - 9/5*o**2. Factor p(s).
-2*s*(s - 3)**2/5
Let s = -14 + 22. Suppose 44 = s*a + 3*a. Determine c so that -2/7*c**a + 0 - 2/7*c + 2/7*c**3 + 2/7*c**2 = 0.
-1, 0, 1
Let r(i) be the first derivative of -1/78*i**4 - 1 + 1/130*i**5 + 0*i**2 + 0*i**3 - 4*i. Let z(l) be the first derivative of r(l). Factor z(d).
2*d**2*(d - 1)/13
Let z be (-38)/228*(-5 - -2 - 0). Let l(y) be the first derivative of 5 + z*y**4 + 6/7*y**3 + 0*y + 2/7*y**2. Factor l(j).
2*j*(j + 1)*(7*j + 2)/7
Let t(i) be the third derivative of -i**6/480 + i**5/20 - i**4/2 + 8*i**3/3 - 66*i**2 - 3*i. Factor t(f).
-(f - 4)**3/4
Let g = 184 - 182. Let i be -2*7/((-224)/12). Factor 3/4*t**g + i*t**3 + 0 + 0*t.
3*t**2*(t + 1)/4
Let p(u) = -5 - 2*u + 4 - 2. Let x be p(-6). Factor 0*g**4 - g**3 - 2*g**4 - 5*g + 6*g**3 - 5*g**4 + x*g**2 - 2.
-(g - 1)**2*(g + 1)*(7*g + 2)
Let k(o) = o**2 + 10*o + 2. Let w be k(-10). Solve 13*s**2 - 5*s**4 + s**3 - 18*s**w + 0*s**3 - 11*s**3 = 0 for s.
-1, 0
Let k = -109/31 + 5369/1333. Let j = -1/86 + k. Factor 0*c - j*c**3 - 1/2*c**4 + 1/2*c**2 + 0 + 1/2*c**5.
c**2*(c - 1)**2*(c + 1)/2
What is f in 960 + 48*f + 3/5*f**2 = 0?
-40
Let y be ((-336)/(-46) - 5) + -2. Let u = y + -5/92. Solve -1/2*a**3 + 0*a + 0 + 0*a**2 + u*a**4 = 0 for a.
0, 2
Determine w, given that 3/2*w**2 - 63/8*w + 15/8 = 0.
1/4, 5
Let h(b) be the first derivative of 3*b**2/2 + 30*b - 31. Let f be h(-9). Factor 0*y + 0 + 0*y**2 + 4/7*y**5 - 8/7*y**4 + 4/7*y**f.
4*y**3*(y - 1)**2/7
Let s = -67 - -69. Determine y, given that 14*y**s - 5*y**3 + 10*y**2 - 19*y**2 = 0.
0, 1
Let p(v) be the third derivative of v**6/450 + v**5/450 - v**4/90 - v**3/45 - v**2 - 172. Solve p(x) = 0.
-1, -1/2, 1
Suppose -5*v - 2 = -92. Let q be (v/(-144))/(1/(-30)). Factor 27/4*h**2 + 3/4*h**4 - 21/4*h - q*h**3 + 3/2.
3*(h - 2)*(h - 1)**3/4
Factor 0 - 3/4*x + 1/2*x**2 + 1/4*x**3.
x*(x - 1)*(x + 3)/4
Let z(k) be the third derivative of -k**7/2520 - k**6/360 + k**5/90 + k**3/3 - 31*k**2. Let n(m) be the first derivative of z(m). Factor n(u).
-u*(u - 1)*(u + 4)/3
Let x(t) = -t**5 - t**4 + 2*t**3 + 2*t - 1. Let j(r) = -15*r**5 - 15*r**4 + 42*r**3 + 24*r - 12. Let k(d) = j(d) - 12*x(d). Factor k(m).
-3*m**3*(m - 2)*(m + 3)
Factor -10*g**2 + 2*g**4 - 7*g**4 - 15 - 32*g - 30*g**3 - 18*g - 50*g**2.
-5*(g + 1)**3*(g + 3)
Let c = 1/5 - 39/20. Let i = 33/4 + c. Determine u so that -9/2*u**2 - i*u**3 - 9/4*u**4 - 1/4*u**5 + 27/4*u + 27/4 = 0.
-3, -1, 1
Let -3/8*z**4 + 3/8*z**2 + 3/8*z + 0 - 3/8*z**3 = 0. What is z?
-1, 0, 1
Let v be ((-318)/14)/(-5 - 1006/4). Let j = v - -3/133. Factor 1/9*h**4 + j*h**3 + 0 + 0*h + 0*h**2.
h**3*(h + 1)/9
Suppose 7*r + 385 - 399 = 0. Solve 3*b + 9/2*b**r + 3/2*b**3 + 0 = 0 for b.
-2, -1, 0
Let z(a) be the first derivative of 0*a + 0*a**4 + 0*a**3 + 3/2*a**6 + 2/5*a**5 + 0*a**2 + 38. Factor z(r).
r**4*(9*r + 2)
Let c(h) be the first derivative of -h**6/450 + h**5/50 + 2*h**4/15 - 11*h**3/3 + 10. Let r(k) be the third derivative of c(k). Factor r(x).
-4*(x - 4)*(x + 1)/5
Let p(a) be the second derivative of -1/4*a**4 + 16*a + 5/2*a**3 + 0 + 0*a**2. Determine f, given that p(f) = 0.
0, 5
Let q(v) be the third derivative of 1/18*v**4 + 0*v**3 + 1/180*v**6 + 0 + 13*v**2 + 0*v + 1/30*v**5. Factor q(a).
2*a*(a + 1)*(a + 2)/3
Factor -10/11*n**2 + 0 - 2/11*n**4 + 4/11*n + 8/11*n**3.
-2*n*(n - 2)*(n - 1)**2/11
Suppose 35*r + 28*r = 54*r + 45. Solve r - 25/6*q**2 - 65/6*q = 0 for q.
-3, 2/5
Let j = 691/21522 - -3/422. Let o(z) be the first derivative of -2/17*z**5 - j*z**3 - 9 + 2/17*z**2 + 0*z - 4/17*z**4. What is q in o(q) = 0?
-1, 0, 2/5
Let d(b) = -b**3 - 8*b**2 - 7*b + 5. Let i be d(-7). Suppose -y + 5*y + 6 = 3*p, 10 = 5*p + i*y. What is o in -12*o**2 - o + o**5 - p*o**4 + 14*o**2 + 0*o = 0?
-1, 0, 1
Suppose -5*k + 10 = 2*b - 8*k, b - 4 = k. Factor -2/5*v**b - 6/5*v - 4/5.
